Package ‘manymome’

October 7, 2023
Title Mediation, Moderation and Moderated-Mediation After Model
Fitting
Version 0.1.13
Description Computes indirect effects, conditional effects, and conditional
indirect effects in a structural equation model or path model after model
fitting, with no need to define any user parameters or label any paths in
the model syntax, using the approach presented in Cheung and Cheung
(2023) <doi:10.3758/s13428-023-02224-z>. Can also form bootstrap
confidence intervals by doing bootstrapping only once and reusing the
bootstrap estimates in all subsequent computations. Supports bootstrap
confidence intervals for standardized (partially or completely) indirect
effects, conditional effects, and conditional indirect effects as described
in Cheung (2009) <doi:10.3758/BRM.41.2.425> and Cheung, Cheung, Lau, Hui,
and Vong (2022) <doi:10.1037/hea0001188>. Model fitting can be done by
structural equation modeling using lavaan() or regression using lm().

URL https://sfcheung.github.io/manymome/

BugReports https://github.com/sfcheung/manymome/issues
License GPL (>= 3)
Encoding UTF-8
RoxygenNote 7.2.3
Suggests knitr, rmarkdown, semPlot, semptools, semTools, Amelia, mice,
testthat (>= 3.0.0)
Config/testthat/edition 3
Config/testthat/parallel true
Config/testthat/start-first cond_indirect_*
Imports lavaan, boot, parallel, pbapply, stats, ggplot2, igraph, MASS,
methods
Depends R (>= 3.5.0)
LazyData true
VignetteBuilder knitr

1
2 R topics documented:

NeedsCompilation no
Author Shu Fai Cheung [aut, cre] (<https://orcid.org/0000-0002-9871-9448>),
Sing-Hang Cheung [aut] (<https://orcid.org/0000-0001-5182-0752>)
Maintainer Shu Fai Cheung <shufai.cheung@gmail.com>
Repository CRAN
Date/Publication 2023-10-06 22:40:02 UTC

R topics documented:
all_indirect_paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
check_path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
coef.cond_indirect_diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
coef.cond_indirect_effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
coef.delta_med . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
coef.indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
coef.indirect_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
coef.indirect_proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
coef.lm_from_lavaan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
cond_indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
cond_indirect_diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
confint.cond_indirect_diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
confint.cond_indirect_effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
confint.delta_med . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
confint.indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
confint.indirect_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
data_med . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
data_med_complicated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
data_med_mod_a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
data_med_mod_ab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
data_med_mod_ab1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
data_med_mod_b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
data_med_mod_b_mod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
data_med_mod_parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
data_med_mod_parallel_cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
data_med_mod_serial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
data_med_mod_serial_cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
data_med_mod_serial_parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
data_med_mod_serial_parallel_cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
data_mod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
data_mod2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
data_mod_cat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
data_mome_demo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
data_mome_demo_missing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
data_parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
data_sem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
data_serial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
R topics documented: 3

data_serial_parallel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
data_serial_parallel_latent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
delta_med . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
do_boot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
do_mc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
factor2var . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
fit2boot_out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
fit2mc_out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
get_one_cond_indirect_effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
get_prod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
index_of_mome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
indirect_effects_from_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
indirect_i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
indirect_proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
lm2boot_out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
lm2list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
lm_from_lavaan_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
math_indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
merge_mod_levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
modmed_x1m3w4y1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
mod_levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
plot.cond_indirect_effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
predict.lm_from_lavaan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
predict.lm_from_lavaan_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
predict.lm_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
print.all_paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
print.boot_out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
print.cond_indirect_diff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
print.cond_indirect_effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
print.delta_med . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
print.indirect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
print.indirect_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
print.indirect_proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
print.lm_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
print.mc_out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
simple_mediation_latent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
subsetting_cond_indirect_effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
subsetting_wlevels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
summary.lm_list . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
terms.lm_from_lavaan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
total_indirect_effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Index 116
4 all_indirect_paths

all_indirect_paths Enumerate All Indirect Effects in a Model

Description

Check all indirect paths in a model and return them as a list of arguments of x, y, and m, to be used
by indirect_effect().

Usage

all_indirect_paths(fit = NULL, exclude = NULL, x = NULL, y = NULL)

all_paths_to_df(all_paths)

Arguments

fit A fit object. Either the output of lavaan::lavaan() or its wrapper such as
lavaan::sem(), or a list of the output of lm() or the output of lm2list().
exclude A character vector of variables to be excluded in the search, such as control
variables.
x A character vector of variables that will be included as the x variables. If sup-
plied, only paths that start from these variables will be included in the search. If
NULL, the default, then all variables that are one of the predictors in at least one
regression equation will be included in the search.
y A character vector of variables that will be included as the y variables. If sup-
plied, only paths that start from these variables will be included in the search. If
NULL, the default, then all variables that are the outcome variables in at least one
regression equation will be included in the search.
all_paths An all_paths-class object. For example, the output of all_indirect_paths().

Details

It makes use of igraph::all_simple_paths() to identify paths in a model.

Value

all_indirect_paths() returns a list of the class all_paths. Each argument is a list of three
character vectors, x, the name of the predictor that starts a path, y, the name of the outcome that
ends a path, and m, a character vector of one or more names of the mediators, from x to y. This class
has a print method.
all_paths_to_df() returns a data frame with three columns, x, y, and m, which can be used by
functions such as indirect_effect().
all_indirect_paths 5

Functions

• all_indirect_paths(): Enumerate all indirect paths.

• all_paths_to_df(): Convert the output of all_indirect_paths() to a data frame with
three columns: x, y, and m.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also

indirect_effect(), lm2list(). many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)
# All indirect paths
out1 <- all_indirect_paths(fit)
out1
names(out1)

# Exclude c1 and c2 in the search

out2 <- all_indirect_paths(fit, exclude = c("c1", "c2"))
out2
names(out2)

# Exclude c1 and c2, and only consider paths start

# from x and end at y
out3 <- all_indirect_paths(fit, exclude = c("c1", "c2"),
x = "x",
y = "y")
out3
names(out3)
6 check_path

check_path Check a Path Exists in a Model

Description
It checks whether a path, usually an indirect path, exists in a model.

Usage
check_path(x, y, m = NULL, fit = NULL, est = NULL)

Arguments
x Character. The name of predictor at the start of the path.
y Character. The name of the outcome variable at the end of the path.
m A vector of the variable names of the mediators. The path goes from the first
mediator successively to the last mediator. If NULL, the default, the path goes
from x to y.
fit The fit object. Currently only supports a lavaan::lavaan object or a list of outputs
of lm(). It can also be a lavaan.mi object returned by semTools::runMI() or
its wrapper, such as semTools::sem.mi().
est The output of lavaan::parameterEstimates(). If NULL, the default, it will be
generated from fit. If supplied, fit will ge ignored.

Details
It checks whether the path defined by a predictor (x), an outcome (y), and optionally a sequence of
mediators (m), exists in a model. It can check models in a lavaan::lavaan object or a list of outputs
of lm(). It also support lavaan.mi objects returned by semTools::runMI() or its wrapper, such
as semTools::sem.mi().
For example, in the ql in lavaan syntax

m1 ~ x
m2 ~ m1
m3 ~ x
y ~ m2 + m3

This path is valid: x = "x", y = "y", m = c("m1", "m2")

This path is invalid: x = "x", y = "y", m = c("m2")
This path is also invalid: x = "x", y = "y", m = c("m1", "m2")

Value
A logical vector of length one. TRUE if the path is valid, FALSE if the path is invalid.
coef.cond_indirect_diff 7

Examples

library(lavaan)
data(data_serial_parallel)
dat <- data_serial_parallel
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE)

# The following paths are valid

check_path(x = "x", y = "y", m = c("m11", "m12"), fit = fit)
check_path(x = "x", y = "y", m = "m2", fit = fit)
# The following paths are invalid
check_path(x = "x", y = "y", m = c("m11", "m2"), fit = fit)
check_path(x = "x", y = "y", m = c("m12", "m11"), fit = fit)

coef.cond_indirect_diff
Print the Output of ’cond_indirect_diff()’

Description
Extract the change in conditional indirect effect.

Usage
## S3 method for class 'cond_indirect_diff'
coef(object, ...)

Arguments
object The output of cond_indirect_diff().
... Optional arguments. Ignored.

Details
The coef method of the cond_indirect_diff-class object.

Value
Scalar: The change of conditional indirect effect in object.
8 coef.cond_indirect_effects

See Also
cond_indirect_diff()

coef.cond_indirect_effects
Estimates of Conditional Indirect Effects or Conditional Effects

Description
Return the estimates of the conditional indirect effects or conditional effects for all levels in the
output of cond_indirect_effects().

Usage
## S3 method for class 'cond_indirect_effects'
coef(object, ...)

Arguments
object The output of cond_indirect_effects().
... Optional arguments. Ignored by the function.

Details
It extracts and returns the column ind or std in the output of cond_indirect_effects().

Value
A numeric vector: The estimates of the conditional effects or conditional indirect effects.

See Also
cond_indirect_effects()

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ m1
y ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
coef.delta_med 9

est <- parameterEstimates(fit)

# Conditional effects from x to m1 when w1 is equal to each of the levels

out1 <- cond_indirect_effects(x = "x", y = "m1",
wlevels = c("w1"), fit = fit)
out1
coef(out1)

# Conditional indirect effects from x1 through m1 and m2 to y,

out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
wlevels = c("w1", "w4"), fit = fit)
out2
coef(out2)

# Standardized conditional indirect effects from x1 through m1 and m2 to y,

out2std <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
wlevels = c("w1", "w4"), fit = fit,
standardized_x = TRUE, standardized_y = TRUE)
out2std
coef(out2std)

coef.delta_med Delta_Med in a ’delta_med’-Class Object

Description
Return the estimate of Delta_Med in a ’delta_med’-class object.

Usage
## S3 method for class 'delta_med'
coef(object, ...)

Arguments
object The output of delta_med().
... Optional arguments. Ignored.

Details
It just extracts and returns the element delta_med in the output of delta_med(), the estimate of
the Delta_Med proposed by Liu, Yuan, and Li (2023), an R2 -like measure of indirect effect.

Value
A scalar: The estimate of Delta_Med.
10 coef.indirect

Author(s)
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

References
Liu, H., Yuan, K.-H., & Li, H. (2023). A systematic framework for defining R-squared measures in
mediation analysis. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000571

See Also
delta_med()

Examples

library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit)
dm
print(dm, full = TRUE)
coef(dm)

coef.indirect Extract the Indirect Effect or Conditional Indirect Effect

Description
Return the estimate of the indirect effect in the output of indirect_effect() or or the conditional
indirect in the output of cond_indirect().

Usage
## S3 method for class 'indirect'
coef(object, ...)

Arguments
object The output of indirect_effect() or cond_indirect().
... Optional arguments. Ignored by the function.
coef.indirect 11

Details

It extracts and returns the element indirect. in an object.

If standardized effect is requested when calling indirect_effect() or cond_indirect(), the
effect returned is also standardized.

Value

A scalar: The estimate of the indirect effect or conditional indirect effect.

See Also

indirect_effect() and cond_indirect().

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ x
y ~ m1 + m2 + x
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for indirect_effect():

# Inidrect effect from x through m2 to y

out1 <- indirect_effect(x = "x", y = "y", m = "m2", fit = fit)
out1
coef(out1)

# Conditional Indirect effect from x1 through m1 to y,

# when w1 is 1 SD above mean
hi_w1 <- mean(dat$w1) + sd(dat$w1)
out2 <- cond_indirect(x = "x", y = "y", m = "m1",
wvalues = c(w1 = hi_w1), fit = fit)
out2
coef(out2)
12 coef.indirect_list

coef.indirect_list Extract the Indirect Effects from a ’indirect_list’ Object

Description
Return the estimates of the indirect effects in the output of many_indirect_effects().

Usage
## S3 method for class 'indirect_list'
coef(object, ...)

Arguments
object The output of many_indirect_effects().
... Optional arguments. Ignored by the function.

Details
It extracts the estimates in each ’indirect’-class object in the list.
If standardized effect is requested when calling many_indirect_effects(), the effects returned
are also standardized.

Value
A numeric vector of the indirect effects.

See Also
many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
x = "x",
coef.indirect_proportion 13

y = "y")
paths
# Indirect effect estimates
out <- many_indirect_effects(paths,
fit = fit)
out
coef(out)

coef.indirect_proportion
Extract the Proportion of Effect Mediated

Description
Return the proportion of effect mediated in the output of indirect_proportion().

Usage
## S3 method for class 'indirect_proportion'
coef(object, ...)

Arguments
object The output of indirect_proportion()
... Not used.

Details
It extracts and returns the element proportion in the input object.

Value
A scalar: The proportion of effect mediated.

See Also
indirect_proportion()

Examples

library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
14 coef.lm_from_lavaan

y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
out <- indirect_proportion(x = "x",
y = "y",
m = "m",
fit = fit)
out
coef(out)

coef.lm_from_lavaan Coefficients of an ’lm_from_lavaan’-Class Object

Description

Returns the path coefficients of the terms in an lm_from_lavaan-class object.

Usage

## S3 method for class 'lm_from_lavaan'

coef(object, ...)

Arguments

object A ’lm_from_lavaan’-class object.

... Additional arguments. Ignored.

Details

An lm_from_lavaan-class object converts a regression model for a variable in a lavaan-class ob-

ject to a formula-class object. This function simply extracts the path coefficients estimates. Inter-
cept is always included, and set to zero if mean structure is not in the source lavaan-class object.
This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced
users and developers.

Value

A numeric vector of the path coefficients.

See Also

lm_from_lavaan_list()
cond_indirect 15

Examples
library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
coef(fit_list$m)
coef(fit_list$y)

cond_indirect Conditional, Indirect, and Conditional Indirect Effects

Description
Compute the conditional effects, indirect effects, or conditional indirect effects in a structural model
fitted by lm(), lavaan::sem(), or semTools::sem.mi().

Usage
cond_indirect(
x,
y,
m = NULL,
fit = NULL,
est = NULL,
implied_stats = NULL,
wvalues = NULL,
standardized_x = FALSE,
standardized_y = FALSE,
boot_ci = FALSE,
level = 0.95,
boot_out = NULL,
R = 100,
seed = NULL,
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE,
save_boot_full = FALSE,
prods = NULL,
get_prods_only = FALSE,
save_boot_out = TRUE,
16 cond_indirect

mc_ci = FALSE,
mc_out = NULL,
save_mc_full = FALSE,
save_mc_out = TRUE,
ci_out = NULL,
save_ci_full = FALSE,
save_ci_out = TRUE,
ci_type = NULL
)

cond_indirect_effects(
wlevels,
x,
y,
m = NULL,
fit = NULL,
w_type = "auto",
w_method = "sd",
sd_from_mean = NULL,
percentiles = NULL,
est = NULL,
implied_stats = NULL,
boot_ci = FALSE,
R = 100,
seed = NULL,
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE,
boot_out = NULL,
output_type = "data.frame",
mod_levels_list_args = list(),
mc_ci = FALSE,
mc_out = NULL,
ci_out = NULL,
ci_type = NULL,
...
)

indirect_effect(
x,
y,
m = NULL,
fit = NULL,
est = NULL,
implied_stats = NULL,
standardized_x = FALSE,
standardized_y = FALSE,
cond_indirect 17

boot_ci = FALSE,
level = 0.95,
boot_out = NULL,
R = 100,
seed = NULL,
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE,
save_boot_full = FALSE,
mc_ci = FALSE,
mc_out = NULL,
save_mc_full = FALSE,
save_mc_out = TRUE,
ci_out = NULL,
save_ci_full = FALSE,
save_ci_out = TRUE,
ci_type = NULL
)

many_indirect_effects(paths, ...)

Arguments
x Character. The name of the predictor at the start of the path.
y Character. The name of the outcome variable at the end of the path.
m A vector of the variable names of the mediator(s). The path goes from the first
mediator successively to the last mediator. If NULL, the default, the path goes
from x to y.
fit The fit object. Can be a lavaan::lavaan object or a list of lm() outputs. It can also
be a lavaan.mi object returned by semTools::runMI() or its wrapper, such as
semTools::sem.mi().
est The output of lavaan::parameterEstimates(). If NULL, the default, it will be
generated from fit. If supplied, fit will be ignored.
implied_stats Implied means, variances, and covariances of observed variables, of the form of
the output of lavaan::lavInspect() with what set to "implied". The stan-
dard deviations are extracted from this object for standardization. Default is
NULL, and implied statistics will be computed from fit if required.
wvalues A numeric vector of named elements. The names are the variable names of the
moderators, and the values are the values to which the moderators will be set to.
Default is NULL.
standardized_x Logical. Whether x will be standardized. Default is FALSE.
standardized_y Logical. Whether y will be standardized. Default is FALSE.
boot_ci Logical. Whether bootstrap confidence interval will be formed. Default is
FALSE.
level The level of confidence for the bootstrap confidence interval. Default is .95.
18 cond_indirect

boot_out If boot_ci is TRUE, users can supply pregenerated bootstrap estimates. This can
be the output of do_boot(). For indirect_effect() and cond_indirect_effects(),
this can be the output of a previous call to cond_indirect_effects(), indirect_effect(),
or cond_indirect() with bootstrap confidence intervals requested. These stored
estimates will be reused such that there is no need to do bootstrapping again. If
not supplied, the function will try to generate them from fit.
R Integer. If boot_ci is TRUE, boot_out is NULL, and bootstrap standard errors
not requested if fit is a lavaan object, this function will do bootstrapping on
fit. R is the number of bootstrap samples. Default is 100. For Monte Carlo
simulation, this is the number of replications.
seed If bootstrapping or Monte Carlo simulation is conducted, this is the seed for the
bootstrapping or simulation. Default is NULL and seed is not set.
parallel Logical. If bootstrapping is conducted, whether parallel processing will be used.
Default is TRUE. If fit is a list of lm() outputs, parallel processing will not be
used.
ncores Integer. The number of CPU cores to use when parallel is TRUE. Default is
the number of non-logical cores minus one (one minimum). Will raise an error
if greater than the number of cores detected by parallel::detectCores(). If
ncores is set, it will override make_cluster_args in do_boot().
make_cluster_args
A named list of additional arguments to be passed to parallel::makeCluster().
For advanced users. See parallel::makeCluster() for details. Default is
list().
progress Logical. Display bootstrapping progress or not. Default is TRUE.
save_boot_full If TRUE, full bootstrapping results will be stored. Default is FALSE.
prods The product terms found. For internal use.
get_prods_only IF TRUE, will quit early and return the product terms found. The results can be
passed to the prod argument when calling this function. Default is FALSE. This
function is for internal use.
save_boot_out If boot_out is supplied, whether it will be saved in the output. Default is TRUE.
mc_ci Logical. Whether Monte Carlo confidence interval will be formed. Default is
FALSE.
mc_out If mc_ci is TRUE, users can supply pregenerated Monte Carlo estimates. This can
be the output of do_mc(). For indirect_effect() and cond_indirect_effects(),
this can be the output of a previous call to cond_indirect_effects(), indirect_effect(),
or cond_indirect() with Monte Carlo confidence intervals requested. These
stored estimates will be reused such that there is no need to do Monte Carlo
simulation again. If not supplied, the function will try to generate them from
fit.
save_mc_full If TRUE, full Monte Carlo results will be stored. Default is FALSE.
save_mc_out If mc_out is supplied, whether it will be saved in the output. Default is TRUE.
ci_out If ci_type is supplied, this is the corresponding argument. If ci_type is "boot",
this argument will be used as boot_out. If ci_type is "mc", this argument will
be used as mc_out.
cond_indirect 19

save_ci_full If TRUE, full bootstrapping or Monte Carlo results will be stored. Default is
FALSE.
save_ci_out If either mc_out or boot_out is supplied, whether it will be saved in the output.
Default is TRUE.
ci_type The type of confidence intervals to be formed. Can be either "boot" (boot-
strapping) or "mc" (Monte Carlo). If not supplied or is NULL, will check other
arguments (e.g, boot_ci and mc_ci). If supplied, will override boot_ci and
mc_ci.
wlevels The output of merge_mod_levels(), or the moderator(s) to be passed to mod_levels_list().
If all the moderators can be represented by one variable, that is, each moderator
is (a) a numeric variable, (b) a dichotomous categorical variable, or (c) a factor
or string variable used in lm() in fit, then it is a vector of the names of the
moderators as appeared in the data frame. If at least one of the moderators is a
categorical variable represented by more than one variable, such as user-created
dummy variables used in lavaan::sem(), then it must be a list of the names
of the moderators, with such moderators represented by a vector of names. For
example: list("w1", c("gpgp2", "gpgp3"), the first moderator w1 and the
second moderator a three-categorical variable represented by gpgp2 and gpgp3.
w_type Character. Whether the moderator is a "numeric" variable or a "categorical"
variable. If "auto", the function will try to determine the type automatically.
See mod_levels_list() for further information.
w_method Character, either "sd" or "percentile". If "sd", the levels are defined by the
distance from the mean in terms of standard deviation. if "percentile", the
levels are defined in percentiles. See mod_levels_list() for further informa-
tion.
sd_from_mean A numeric vector. Specify the distance in standard deviation from the mean for
each level. Default is c(-1, 0, 1) when there is only one moderator, and c(-1,
1) when there are more than one moderator. Ignored if w_method is not equal
to "sd". See mod_levels_list() for further information.
percentiles A numeric vector. Specify the percentile (in proportion) for each level. Default
is c(.16, .50, .84) if there is one moderator, and c(.16, .84) when there are
more than one moderator. Ignored if w_method is not equal to "percentile".
See mod_levels_list() for further information.
output_type The type of output of cond_indirect_effects(). If "data.frame", the de-
fault, the output will be converted to a data frame. If any other values, the output
is a list of the outputs from cond_indirect().
mod_levels_list_args
Additional arguments to be passed to mod_levels_list() if it is called for
creating the levels of moderators. Default is list().
... For many_indirect_effects(), these are arguments to be passed to indirect_effect().
paths The output of all_indirect_paths()

Details
For a model with a mediation path moderated by one or more moderators, cond_indirect_effects()
can be used to compute the conditional indirect effect from one variable to another variable, at one
or more set of selected value(s) of the moderator(s).
20 cond_indirect

If only the effect for one set of value(s) of the moderator(s) is needed, cond_indirect() can be
used.
If only the mediator(s) is/are specified (m) and no values of moderator(s) are specified, then the
indirect effect from one variable (x) to another variable (y) is computed. A convenient wrapper
indirect_effect() can be used to compute the indirect effect.
If only the value(s) of moderator(s) is/are specified (wvalues or wlevels) and no mediators (m)
are specified when calling cond_indirect_effects() or cond_indirect(), then the conditional
direct effects from one variable to another are computed.
All three functions support using nonparametric bootstrapping (for lavaan or lm outputs) or Monte
Carlo simulation (for lavaan outputs only) to form confidence intervals. Bootstrapping or Monte
Carlo simulation only needs to be done once. These are the possible ways to form bootstrapping:

1. Do bootstrapping or Monte Carlo simulation in the first call to one of these functions, by set-
ting boot_ci or mc_ci to TRUE and R to the number of bootstrap samples or replications, level
to the level of confidence (default .95 or 95%), and seed to reproduce the results (parallel
and ncores are optional for bootstrapping). This will take some time to run for bootstrapping.
The output will have all bootstrap or Monte Carlo estimates stored. This output, whether
it is from indirect_effect(), cond_indirect_effects(), or cond_indirect(), can be
reused by any of these three functions by setting boot_out (for bootstrapping) or mc_out (for
Monte Carlo simulation) to this output. They will form the confidence intervals using the
stored bootstrap or Monte Carlo estimates.
2. Do bootstrapping using do_boot() or Monte Carlo simulation us8ing do_mc(). The output
can be used in the boot_out (for bootstrapping) or mc_out (for Monte Carlo simulation)
argument of indirect_effect(), cond_indirect_effects() and cond_indirect().
3. For bootstrapping, if lavaan::sem() is used to fit a model and se = "boot" is used, do_boot()
can extract them to generate a boot_out-class object that again can be used in the boot_out
argument.

If boot_out or mc_out is set, arguments such as R, seed, and parallel will be ignored.

Value
indirect_effect() and cond_indirect() return an indirect-class object.
cond_indirect_effects() returns a cond_indirect_effects-class object.
These two classes of objects have their own print methods for printing the results (see print.indirect()
and print.cond_indirect_effects()). They also have a coef method for extracting the esti-
mates (coef.indirect() and coef.cond_indirect_effects()) and a confint method for ex-
tracting the confidence intervals (confint.indirect() and confint.cond_indirect_effects()).
Addition and subtraction can also be conducted on indirect-class object to estimate and test a
function of effects (see math_indirect)

Functions
• cond_indirect(): Compute conditional, indirect, or conditional indirect effects for one set
of levels.
• cond_indirect_effects(): Compute the conditional effects or conditional indirect effects
for several sets of levels of the moderator(s).
cond_indirect 21

• indirect_effect(): Compute the indirect effect. A wrapper of cond_indirect(). Can be

used when there is no moderator.
• many_indirect_effects(): Compute the indirect effects along more than one paths. It call
indirect_effect() once for each of the path.

See Also
mod_levels() and merge_mod_levels() for generating levels of moderators. do_boot for doing
bootstrapping before calling these functions.

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x + d1 * w1 + e1 * x:w1
m2 ~ a2 * x
y ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)
hi_w1 <- mean(dat$w1) + sd(dat$w1)

# Examples for cond_indirect():

# Conditional effect from x to m1 when w1 is 1 SD above mean

cond_indirect(x = "x", y = "m1",
wvalues = c(w1 = hi_w1), fit = fit)

# Indirect effect from x1 through m2 to y

indirect_effect(x = "x", y = "y", fit = fit)

# Conditional Indirect effect from x1 through m1 to y, when w1 is 1 SD above mean

cond_indirect(x = "x", y = "y", m = "m1",
wvalues = c(w1 = hi_w1), fit = fit)

# Examples for cond_indirect_effects():

# Create levels of w1, the moderators

w1levels <- mod_levels("w1", fit = fit)
w1levels

# Conditional effects from x to m1 when w1 is equal to each of the levels

cond_indirect_effects(x = "x", y = "m1",
wlevels = w1levels, fit = fit)

# Conditional Indirect effect from x1 through m1 to y,

# when w1 is equal to each of the levels
22 cond_indirect_diff

cond_indirect_effects(x = "x", y = "y", m = "m1",

wlevels = w1levels, fit = fit)

# Examples for many_indirect_effects():

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)

# All indirect paths from x to y

paths <- all_indirect_paths(fit,
x = "x",
y = "y")
paths

# Indirect effect estimates

out <- many_indirect_effects(paths,
fit = fit)
out

cond_indirect_diff Differences In Conditional Indirect Effects

Description
Compute the difference in conditional indirect effects between two sets of levels of the moderators.

Usage
cond_indirect_diff(output, from = NULL, to = NULL, level = 0.95)

Arguments
output A cond_indirect_effects-class object: The output of cond_indirect_effects().
from A row number of output.
to A row number of output. The change in indirect effects is computed by the
change in the level(s) of the moderator(s) from Row from to Row to.
level The level of confidence for the confidence interval. Default is .95.
cond_indirect_diff 23

Details

Ths function takes the output of cond_indirect_effects() and computes the difference in con-
ditional indirect effects between any two rows, that is, between levels of the moderator, or two sets
of levels of the moderators when the path has more than one moderator.
The difference is meaningful when the difference between the two levels or sets of levels are mean-
ingful. For example, if the two levels are the mean of the moderator and one standard deviation
above mean of the moderator, then this difference is the change in indirect effect when the modera-
tor increases by one standard deviation.
If the two levels are 0 and 1, then this difference is the index of moderated mediation as proposed by
Hayes (2015). (This index can also be computed directly by index_of_mome(), designed specifi-
cally for this purpose.)
The function can also compute the change in the standardized indirect effect between two levels of
a moderator or two sets of levels of the moderators.
This function is intended to be a general purpose function that allows users to compute the difference
between any two levels or sets of levels that are meaningful in a context.
This function itself does not set the levels of comparison. The levels to be compared need to be
set when calling cond_indirect_effects(). This function extracts required information from the
output of cond_indirect_effects().
If bootstrap or Monte Carlo estimates are available in the input or bootstrap or Monte Carlo confi-
dence intervals are requested in calling cond_indirect_effects(), cond_indirect_diff() will
also form the percentile confidence interval for the difference in conditional indirect effects using
the stored estimates.

Value

A cond_indirect_diff-class object. This class has a print method (print.cond_indirect_diff()),

a coef method (coef.cond_indirect_diff()), and a confint method (confint.cond_indirect_diff()).

Functions

• cond_indirect_diff(): Compute the difference in in conditional indirect effect between

two rows in the output of cond_indirect_effects().

References

Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral
Research, 50(1), 1-22. doi:10.1080/00273171.2014.962683

See Also

index_of_mome() for computing the index of moderated mediation, index_of_momome() for com-
puting the index of moderated moderated mediation, cond_indirect_effects(), mod_levels(),
and merge_mod_levels() for preparing the levels to be compared.
24 confint.cond_indirect_diff

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
mod <-
"
m1 ~ a * x + f * w1 + d * xw1
y ~ b * m1 + cp * x
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Create levels of w1, the moderators

w1levels <- mod_levels("w1", fit = fit)
w1levels

# Conditional effects from x to y when w1 is equal to each of the levels

boot_out <- fit2boot_out_do_boot(fit, R = 40, seed = 4314, progress = FALSE)
out <- cond_indirect_effects(x = "x", y = "y", m = "m1",
wlevels = w1levels, fit = fit,
boot_ci = TRUE, boot_out = boot_out)
out
out_ind <- cond_indirect_diff(out, from = 2, to = 1)
out_ind
coef(out_ind)
confint(out_ind)

confint.cond_indirect_diff
Confidence Interval of the Output of ’cond_indirect_diff()’

Description

Extract the confidence interval the output of cond_indirect_diff().

Usage

## S3 method for class 'cond_indirect_diff'

confint(object, parm, level = 0.95, ...)
confint.cond_indirect_effects 25

Arguments
object The output of cond_indirect_diff().
parm Ignored.
level The level of confidence for the confidence interval. Default is .95. Must match
the level of the stored confidence interval.
... Optional arguments. Ignored.

Details
The confint method of the cond_indirect_diff-class object.
The type of confidence intervals depends on the call used to create the object. This function merely
extracts the stored confidence intervals.

Value
A one-row-two-column data frame of the confidence limits. If confidence interval is not available,
the limits are NAs.

confint.cond_indirect_effects
Confidence Intervals of Indirect Effects or Conditional Indirect Effects

Description
Return the confidence intervals of the conditional indirect effects or conditional effects in the output
of cond_indirect_effects().

Usage
## S3 method for class 'cond_indirect_effects'
confint(object, parm, level = 0.95, ...)

Arguments
object The output of cond_indirect_effects().
parm Ignored. Always returns the confidence intervals of the effects for all levels
stored.
level The level of confidence, default is .95, returning the 95% confidence interval.
Ignored for now and will use the level of the stored intervals.
... Additional arguments. Ignored by the function.

Details
It extracts and returns the columns for confidence intervals, if available.
The type of confidence intervals depends on the call used to compute the effects. This function
merely retrieves the confidence intervals stored, if any, which could be formed by nonparametric
bootstrapping, Monte Carlo simulation, or other methods to be supported in the future.
26 confint.delta_med

Value
A data frame with two columns, one for each confidence limit of the confidence intervals. The
number of rows is equal to the number of rows of object.

See Also
cond_indirect_effects()

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ m1
y ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

# Create levels of w1 and w4

w1levels <- mod_levels("w1", fit = fit)
w1levels
w4levels <- mod_levels("w4", fit = fit)
w4levels
w1w4levels <- merge_mod_levels(w1levels, w4levels)

# Conditional effects from x to m1 when w1 is equal to each of the levels

# R should be at least 2000 or 5000 in real research.
out1 <- suppressWarnings(cond_indirect_effects(x = "x", y = "m1",
wlevels = w1levels, fit = fit,
boot_ci = TRUE, R = 20, seed = 54151,
parallel = FALSE,
progress = FALSE))
confint(out1)

confint.delta_med Confidence Interval for Delta_Med in a ’xxx’-Class Object

Description
Return the confidence interval of the Delta_Med in the output of delta_med().
confint.delta_med 27

Usage
## S3 method for class 'delta_med'
confint(object, parm, level = NULL, ...)

Arguments
object The output of delta_med().
parm Not used because only one parameter, the Delta_Med, is allowed.
level The level of confidence, default is NULL and the level used when the object was
created will be used.
... Optional arguments. Ignored.

Details
It returns the nonparametric bootstrap percentile confidence interval of Delta_Med, proposed byLiu,
Yuan, and Li (2023). The object must be the output of delta_med(), with bootstrap confidence
interval requested when calling delta_med(). However, the level of confidence can be different
from that used when call delta_med().

Value
A one-row matrix of the confidence interval. All values are NA if bootstrap confidence interval was
not requested when calling delta_med().

Author(s)
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also
delta_med()

Examples

library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)

# Call do_boot() to generate

# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
R = 45,
28 confint.indirect

seed = 879,
parallel = FALSE,
progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit,
boot_out = boot_out,
progress = FALSE)
dm_boot
confint(dm_boot)

confint.indirect Confidence Interval of Indirect Effect or Conditional Indirect Effect

Description
Return the confidence interval of the indirect effect or conditional indirect effect stored in the output
of indirect_effect() or cond_indirect().

Usage
## S3 method for class 'indirect'
confint(object, parm, level = 0.95, ...)

Arguments
object The output of indirect_effect() or cond_indirect().
parm Ignored because the stored object always has only one parameter.
level The level of confidence, default is .95, returning the 95% confidence interval.
... Additional arguments. Ignored by the function.

Details
It extracts and returns the stored confidence interval if available.
The type of confidence interval depends on the call used to compute the effect. This function
merely retrieves the stored estimates, which could be generated by nonparametric bootstrapping,
Monte Carlo simulation, or other methods to be supported in the future, and uses them to form the
percentile confidence interval.

Value
A numeric vector of two elements, the limits of the confidence interval.
confint.indirect_list 29

See Also
indirect_effect() and cond_indirect()

Examples

dat <- modmed_x1m3w4y1

# Indirect Effect

library(lavaan)
mod1 <-
"
m1 ~ x
m2 ~ m1
y ~ m2 + x
"
fit <- sem(mod1, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
# R should be at least 2000 or 5000 in real research.
out1 <- indirect_effect(x = "x", y = "y",
m = c("m1", "m2"),
fit = fit,
boot_ci = TRUE, R = 45, seed = 54151,
parallel = FALSE,
progress = FALSE)
out1
confint(out1)

confint.indirect_list Confidence Intervals of Indirect Effects in an ’indirect_list’ Object

Description
Return the confidence intervals of the indirect effects stored in the output of many_indirect_effects().

Usage
## S3 method for class 'indirect_list'
confint(object, parm = NULL, level = 0.95, ...)

Arguments
object The output of many_indirect_effects().
parm Ignored for now.
level The level of confidence, default is .95, returning the 95% confidence interval.
... Additional arguments. Ignored by the function.
30 confint.indirect_list

Details
It extracts and returns the stored confidence interval if available.
The type of confidence intervals depends on the call used to compute the effects. This function
merely retrieves the stored estimates, which could be generated by nonparametric bootstrapping,
Monte Carlo simulation, or other methods to be supported in the future, and uses them to form the
percentile confidence interval.

Value
A two-column data frame. The columns are the limits of the confidence intervals.

See Also
many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
x = "x",
y = "y")
paths
# Indirect effect estimates
# R should be 2000 or even 5000 in real research
# parallel should be used in real research.
fit_boot <- do_boot(fit, R = 45, seed = 8974,
parallel = FALSE,
progress = FALSE)
out <- many_indirect_effects(paths,
fit = fit,
boot_ci = TRUE,
boot_out = fit_boot)
out
confint(out)
data_med 31

data_med Sample Dataset: Simple Mediation

Description
A simple mediation model.

Usage
data_med

Format
A data frame with 100 rows and 5 variables:

x Predictor. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
ab := a * b
"
fit <- sem(mod, data_med, fixed.x = FALSE)
parameterEstimates(fit)

data_med_complicated Sample Dataset: A Complicated Mediation Model

Description
A mediation model with two predictors, two pathways,

Usage
data_med_complicated
32 data_med_mod_a

Format
A data frame with 300 rows and 5 variables:
x1 Predictor 1. Numeric.
x2 Predictor 2. Numeric.
m11 Mediator 1 in Path 1. Numeric.
m12 Mediator 2 in Path 1. Numeric.
m2 Mediator in Path 2. Numeric.
y1 Outcome variable 1. Numeric.
y2 Outcome variable 2. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
data(data_med_complicated)
dat <- data_med_complicated
summary(lm_m11 <- lm(m11 ~ x1 + x1 + x2 + c1 + c2, dat))
summary(lm_m12 <- lm(m12 ~ m11 + x1 + x2 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x1 + x2 + c1 + c2, dat))
summary(lm_y1 <- lm(y1 ~ m11 + m12 + m2 + x1 + x2 + c1 + c2, dat))
summary(lm_y2 <- lm(y2 ~ m11 + m12 + m2 + x1 + x2 + c1 + c2, dat))

data_med_mod_a Sample Dataset: Simple Mediation with a-Path Moderated

Description
A simple mediation model with a-path moderated.

Usage
data_med_mod_a

Format
A data frame with 100 rows and 6 variables:
x Predictor. Numeric.
w Moderator. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.
data_med_mod_ab 33

Examples
library(lavaan)
data(data_med_mod_a)
data_med_mod_a$xw <-
data_med_mod_a$x *
data_med_mod_a$w
mod <-
"
m ~ a * x + w + d * xw + c1 + c2
y ~ b * m + x + w + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := (a + d * (m_w - sqrt(v_w))) * b
ab_hi := (a + d * (m_w + sqrt(v_w))) * b
"
fit <- sem(mod, data_med_mod_a,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 11, 12, 31:33), ]

data_med_mod_ab Sample Dataset: Simple Mediation with Both Paths Moderated (Two
Moderators)

Description

A simple mediation model with a-path and b-path each moderated by a moderator.

Usage

data_med_mod_ab

Format

A data frame with 100 rows and 7 variables:

x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.
34 data_med_mod_ab1

Examples
library(lavaan)
data(data_med_mod_ab)
data_med_mod_ab$xw1 <-
data_med_mod_ab$x *
data_med_mod_ab$w1
data_med_mod_ab$mw2 <-
data_med_mod_ab$m *
data_med_mod_ab$w2
mod <-
"
m ~ a * x + w1 + d1 * xw1 + c1 + c2
y ~ b * m + x + w1 + w2 + d2 * mw2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
ab := a * b
ab_lolo := (a + d1 * (m_w1 - sqrt(v_w1))) * (b + d2 * (m_w2 - sqrt(v_w2)))
ab_lohi := (a + d1 * (m_w1 - sqrt(v_w1))) * (b + d2 * (m_w2 + sqrt(v_w2)))
ab_hilo := (a + d1 * (m_w1 + sqrt(v_w1))) * (b + d2 * (m_w2 - sqrt(v_w2)))
ab_hihi := (a + d1 * (m_w1 + sqrt(v_w1))) * (b + d2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_ab,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 10, 41:45), ]

data_med_mod_ab1 Sample Dataset: Simple Mediation with Both Paths Moderated By a

Moderator

Description
A simple mediation model with a-path and b-path moderated by one moderator.

Usage
data_med_mod_ab1

Format
A data frame with 100 rows and 6 variables:
x Predictor. Numeric.
w Moderator. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.
data_med_mod_b 35

Examples
library(lavaan)
data(data_med_mod_ab1)
data_med_mod_ab1$xw <-
data_med_mod_ab1$x *
data_med_mod_ab1$w
data_med_mod_ab1$mw <-
data_med_mod_ab1$m *
data_med_mod_ab1$w
mod <-
"
m ~ a * x + w + da * xw + c1 + c2
y ~ b * m + x + w + db * mw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := (a + da * (m_w - sqrt(v_w))) * (b + db * (m_w - sqrt(v_w)))
ab_hi := (a + da * (m_w + sqrt(v_w))) * (b + db * (m_w + sqrt(v_w)))
"
fit <- sem(mod, data_med_mod_ab1,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 9, 38:40), ]

data_med_mod_b Sample Dataset: Simple Mediation with b-Path Moderated

Description
A simple mediation model with b-path moderated.

Usage
data_med_mod_b

Format
A data frame with 100 rows and 6 variables:

x Predictor. Numeric.
w Moderator. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.
36 data_med_mod_b_mod

Examples
library(lavaan)
data(data_med_mod_b)
data_med_mod_b$mw <-
data_med_mod_b$m *
data_med_mod_b$w
mod <-
"
m ~ a * x + w + c1 + c2
y ~ b * m + x + d * mw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
ab := a * b
ab_lo := a * (b + d * (m_w - sqrt(v_w)))
ab_hi := a * (b + d * (m_w + sqrt(v_w)))
"
fit <- sem(mod, data_med_mod_b,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 5, 7, 10, 11, 30:32), ]

data_med_mod_b_mod Sample Dataset: A Simple Mediation Model with b-Path Moderated-

Moderation

Description

A simple mediation model with moderated-mediation on the b-path.

Usage

data_med_mod_b_mod

Format

A data frame with 100 rows and 5 variables:

x Predictor. Numeric.
w1 Moderator on b-path. Numeric.
w2 Moderator on the moderating effect of w1. Numeric.
m Mediator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.
data_med_mod_parallel 37

Examples
data(data_med_mod_b_mod)
dat <- data_med_mod_b_mod
summary(lm_m <- lm(m ~ x + c1 + c2, dat))
summary(lm_y <- lm(y ~ m*w1*w2 + x + c1 + c2, dat))

data_med_mod_parallel Sample Dataset: Parallel Mediation with Two Moderators

Description
A parallel mediation model with a1-path and b2-path moderated.

Usage
data_med_mod_parallel

Format
A data frame with 100 rows and 8 variables:
x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_med_mod_parallel)
data_med_mod_parallel$xw1 <-
data_med_mod_parallel$x *
data_med_mod_parallel$w1
data_med_mod_parallel$m2w2 <-
data_med_mod_parallel$m2 *
data_med_mod_parallel$w2
mod <-
"
m1 ~ a1 * x + w1 + da1 * xw1 + c1 + c2
m2 ~ a2 * x + w1 + c1 + c2
y ~ b1 * m1 + b2 * m2 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
38 data_med_mod_parallel_cat

w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
a1b1 := a1 * b1
a2b2 := a2 * b2
a1b1_w1lo := (a1 + da1 * (m_w1 - sqrt(v_w1))) * b1
a1b1_w1hi := (a1 + da1 * (m_w1 + sqrt(v_w1))) * b2
a2b2_w2lo := a2 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
a2b2_w2hi := a2 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_parallel,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 10, 11, 15, 48:53), ]

data_med_mod_parallel_cat
Sample Dataset: Parallel Moderated Mediation with Two Categorical
Moderators

Description
A parallel mediation model with two categorical moderators.

Usage
data_med_mod_parallel_cat

Format
A data frame with 300 rows and 8 variables:
x Predictor. Numeric.
w1 Moderator. String. Values: "group1", "group2", "group3"
w2 Moderator. String. Values: "team1", "team2"
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
data(data_med_mod_parallel_cat)
dat <- data_med_mod_parallel_cat
summary(lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x*w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m1*w2 + m2*w2 + m1 + x + w1 + c1 + c2, dat))
data_med_mod_serial 39

data_med_mod_serial Sample Dataset: Serial Mediation with Two Moderators

Description
A simple mediation model with a-path and b2-path moderated.

Usage
data_med_mod_serial

Format
A data frame with 100 rows and 8 variables:

x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_med_mod_serial)
data_med_mod_serial$xw1 <-
data_med_mod_serial$x *
data_med_mod_serial$w1
data_med_mod_serial$m2w2 <-
data_med_mod_serial$m2 *
data_med_mod_serial$w2
mod <-
"
m1 ~ a * x + w1 + da1 * xw1 + c1 + c2
m2 ~ b1 * m1 + x + w1 + c1 + c2
y ~ b2 * m2 + m1 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
ab1b2 := a * b1 * b2
ab1b2_lolo := (a + da1 * (m_w1 - sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
ab1b2_lohi := (a + da1 * (m_w1 - sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
ab1b2_hilo := (a + da1 * (m_w1 + sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
40 data_med_mod_serial_cat

ab1b2_hihi := (a + da1 * (m_w1 + sqrt(v_w1))) * b1 * (b2 + db2 * (m_w2 + sqrt(v_w2)))

"
fit <- sem(mod, data_med_mod_serial,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 11, 16, 49:53), ]

data_med_mod_serial_cat
Sample Dataset: Serial Moderated Mediation with Two Categorical
Moderators

Description

A serial mediation model with two categorical moderators.

Usage

data_med_mod_serial_cat

Format

A data frame with 300 rows and 8 variables:

x Predictor. Numeric.
w1 Moderator. String. Values: "group1", "group2", "group3"
w2 Moderator. String. Values: "team1", "team2"
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
data(data_med_mod_serial_cat)
dat <- data_med_mod_serial_cat
summary(lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ m1 + x + w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m2*w2 + m1 + x + w1 + c1 + c2, dat))
data_med_mod_serial_parallel 41

data_med_mod_serial_parallel
Sample Dataset: Serial-Parallel Mediation with Two Moderators

Description
A serial-parallel mediation model with some paths moderated.

Usage
data_med_mod_serial_parallel

Format
A data frame with 100 rows and 9 variables:

x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
m11 Mediator 1 in Path 1. Numeric.
m12 Mediator 2 in Path 2. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_med_mod_serial_parallel)
data_med_mod_serial_parallel$xw1 <-
data_med_mod_serial_parallel$x *
data_med_mod_serial_parallel$w1
data_med_mod_serial_parallel$m2w2 <-
data_med_mod_serial_parallel$m2 *
data_med_mod_serial_parallel$w2
mod <-
"
m11 ~ a1 * x + w1 + da11 * xw1 + c1 + c2
m12 ~ b11 * m11 + x + w1 + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b12 * m12 + b2 * m2 + m11 + x + w1 + w2 + db2 * m2w2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
42 data_med_mod_serial_parallel_cat

a1b11b22 := a1 * b11 * b12

a2b2 := a2 * b2
ab := a1b11b22 + a2b2
a1b11b12_w1lo := (a1 + da11 * (m_w1 - sqrt(v_w1))) * b11 * b12
a1b11b12_w1hi := (a1 + da11 * (m_w1 + sqrt(v_w1))) * b11 * b12
a2b2_w2lo := a2 * (b2 + db2 * (m_w2 - sqrt(v_w2)))
a2b2_w2hi := a2 * (b2 + db2 * (m_w2 + sqrt(v_w2)))
"
fit <- sem(mod, data_med_mod_serial_parallel,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[parameterEstimates(fit)$label != "", ]

data_med_mod_serial_parallel_cat
Sample Dataset: Serial-Parallel Moderated Mediation with Two Cat-
egorical Moderators

Description
A serial-parallel mediation model with two categorical moderators.

Usage
data_med_mod_serial_parallel_cat

Format
A data frame with 300 rows and 8 variables:
x Predictor. Numeric.
w1 Moderator. String. Values: "group1", "group2", "group3"
w2 Moderator. String. Values: "team1", "team2"
m11 Mediator 1 in Path 1. Numeric.
m12 Mediator 2 in Path 1. Numeric.
m2 Mediator in Path 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
data(data_med_mod_serial_parallel_cat)
dat <- data_med_mod_serial_parallel_cat
summary(lm_m11 <- lm(m11 ~ x*w1 + c1 + c2, dat))
summary(lm_m12 <- lm(m12 ~ m11 + x + w1 + c1 + c2, dat))
summary(lm_m2 <- lm(m2 ~ x + w1 + c1 + c2, dat))
summary(lm_y <- lm(y ~ m12 + m2*w2 + m12 + x + c1 + c2, dat))
data_mod 43

data_mod Sample Dataset: One Moderator

Description
A one-moderator model.

Usage
data_mod

Format
A data frame with 100 rows and 5 variables:
x Predictor. Numeric.
w Moderator. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_mod)
data_mod$xw <- data_mod$x * data_mod$w
mod <-
"
y ~ a * x + w + d * xw + c1 + c2
w ~~ v_w * w
w ~ m_w * 1
a_lo := a + d * (m_w - sqrt(v_w))
a_hi := a + d * (m_w + sqrt(v_w))
"
fit <- sem(mod, data_mod, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 3, 6, 7, 24, 25), ]

data_mod2 Sample Dataset: Two Moderators

Description
A two-moderator model.

Usage
data_mod2
44 data_mod_cat

Format

A data frame with 100 rows and 6 variables:

x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples

library(lavaan)
data(data_mod2)
data_mod2$xw1 <- data_mod2$x * data_mod2$w1
data_mod2$xw2 <- data_mod2$x * data_mod2$w2
mod <-
"
y ~ a * x + w1 + w2 + d1 * xw1 + d2 * xw2 + c1 + c2
w1 ~~ v_w1 * w1
w1 ~ m_w1 * 1
w2 ~~ v_w2 * w2
w2 ~ m_w2 * 1
a_lolo := a + d1 * (m_w1 - sqrt(v_w1)) + d2 * (m_w2 - sqrt(v_w2))
a_lohi := a + d1 * (m_w1 - sqrt(v_w1)) + d2 * (m_w2 + sqrt(v_w2))
a_hilo := a + d1 * (m_w1 + sqrt(v_w1)) + d2 * (m_w2 - sqrt(v_w2))
a_hihi := a + d1 * (m_w1 + sqrt(v_w1)) + d2 * (m_w2 + sqrt(v_w2))
"
fit <- sem(mod, data_mod2, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 5, 8:11, 34:37), ]

data_mod_cat Sample Dataset: Moderation with One Categorical Moderator

Description

A moderation model with a categorical moderator.

Usage

data_mod_cat
data_mome_demo 45

Format
A data frame with 300 rows and 5 variables:

x Predictor. Numeric.
w Moderator. String. Values: "group1", "group2", "group3"
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
data(data_mod_cat)
dat <- data_mod_cat
summary(lm_y <- lm(y ~ x*w + c1 + c2, dat))

data_mome_demo Sample Dataset: A Complicated Moderated-Mediation Model

Description
Generated from a complicated moderated-mediation model for demonstration.

Usage
data_mome_demo

Format
A data frame with 200 rows and 11 variables:

x1 Predictor 1. Numeric.
x2 Predictor 2. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
m3 Mediator 3. Numeric.
y1 Outcome Variable 1. Numeric.
y2 Outcome Variable 2. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 21. Numeric.
c1 Control Variable 1. Numeric.
c2 Control Variable 2. Numeric.
46 data_mome_demo_missing

Details
The model:

# w1x1 <- x1 * w1
# w2m2 <- w2 * m2
m1 ~ x1 + w1 + w1x1 + x2 + c1 + c2
m2 ~ m1 + c1 + c2
m3 ~ x2 + x1 + c1 + c2
y1 ~ m2 + w2 + w2m2 + x1 + x2 + m3 + c1 + c2
y2 ~ m3 + x2 + x1 + m2 + c1 + c2
# Covariances excluded for brevity

data_mome_demo_missing
Sample Dataset: A Complicated Moderated-Mediation Model With
Missing Data

Description
Generated from a complicated moderated-mediation model for demonstration, with missing data

Usage
data_mome_demo_missing

Format
A data frame with 200 rows and 11 variables:

x1 Predictor 1. Numeric.
x2 Predictor 2. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
m3 Mediator 3. Numeric.
y1 Outcome Variable 1. Numeric.
y2 Outcome Variable 2. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 21. Numeric.
c1 Control Variable 1. Numeric.
c2 Control Variable 2. Numeric.
data_parallel 47

Details
A copy of data_mome_demo with some randomly selected cells changed to NA. The number of
cases with no missing data is 169.
The model:

# w1x1 <- x1 * w1
# w2m2 <- w2 * m2
m1 ~ x1 + w1 + w1x1 + x2 + c1 + c2
m2 ~ m1 + c1 + c2
m3 ~ x2 + x1 + c1 + c2
y1 ~ m2 + w2 + w2m2 + x1 + x2 + m3 + c1 + c2
y2 ~ m3 + x2 + x1 + m2 + c1 + c2
# Covariances excluded for brevity

data_parallel Sample Dataset: Parallel Mediation

Description
A parallel mediation model.

Usage
data_parallel

Format
A data frame with 100 rows and 6 variables:
x Predictor. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_parallel)
mod <-
"
m1 ~ a1 * x + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b2 * m2 + b1 * m1 + x + c1 + c2
indirect1 := a1 * b1
48 data_sem

indirect2 := a2 * b2
indirect := a1 * b1 + a2 * b2
"
fit <- sem(mod, data_parallel,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 7, 8, 27:29), ]

data_sem Sample Dataset: A Latent Variable Mediation Model With 4 Factors

Description

This data set is for testing functions in a four-factor structural model.

Usage

data_sem

Format

A data frame with 200 rows and 14 variables:

x01 Indicator. Numeric.

x02 Indicator. Numeric.
x03 Indicator. Numeric.
x04 Indicator. Numeric.
x05 Indicator. Numeric.
x06 Indicator. Numeric.
x07 Indicator. Numeric.
x08 Indicator. Numeric.
x09 Indicator. Numeric.
x10 Indicator. Numeric.
x11 Indicator. Numeric.
x12 Indicator. Numeric.
x13 Indicator. Numeric.
x14 Indicator. Numeric.
data_serial 49

Examples
data(data_sem)
dat <- data_med_mod_b_mod
mod <-
'f1 =~ x01 + x02 + x03
f2 =~ x04 + x05 + x06 + x07
f3 =~ x08 + x09 + x10
f4 =~ x11 + x12 + x13 + x14
f3 ~ a1*f1 + a2*f2
f4 ~ b1*f1 + b3*f3
a1b3 := a1 * b3
a2b3 := a2 * b3
'
fit <- lavaan::sem(model = mod, data = data_sem)
summary(fit)

data_serial Sample Dataset: Serial Mediation

Description
A serial mediation model.

Usage
data_serial

Format
A data frame with 100 rows and 6 variables:

x Predictor. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_serial)
mod <-
"
m1 ~ a * x + c1 + c2
m2 ~ b1 * m1 + x + c1 + c2
50 data_serial_parallel

y ~ b2 * m2 + m1 + x + c1 + c2
indirect := a * b1 * b2
"
fit <- sem(mod, data_serial,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 8, 28), ]

data_serial_parallel Sample Dataset: Serial-Parallel Mediation

Description
A mediation model with both serial and parallel components.

Usage
data_serial_parallel

Format
A data frame with 100 rows and 7 variables:
x Predictor. Numeric.
m11 Mediator 1 in Path 1. Numeric.
m12 Mediator 2 in Path 1. Numeric.
m2 Mediator in Path 2. Numeric.
y Outcome variable. Numeric.
c1 Control variable. Numeric.
c2 Control variable. Numeric.

Examples
library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ a11 * x + c1 + c2
m12 ~ b11 * m11 + x + c1 + c2
m2 ~ a2 * x + c1 + c2
y ~ b12 * m12 + b2 * m2 + m11 + x + c1 + c2
indirect1 := a11 * b11 * b12
indirect2 := a2 * b2
indirect := a11 * b11 * b12 + a2 * b2
"
fit <- sem(mod, data_serial_parallel,
meanstructure = TRUE, fixed.x = FALSE)
parameterEstimates(fit)[c(1, 4, 8, 11, 12, 34:36), ]
data_serial_parallel_latent 51

data_serial_parallel_latent
Sample Dataset: A Latent Mediation Model With Three Mediators

Description
Generated from a 3-mediator mediation model among eight latent factors, fx1, fx2, fm11, fm12,
fy1, and fy2, each has three indicators.

Usage
data_serial_parallel_latent

Format
A data frame with 500 rows and 21 variables:

x1 Indicator of fx1. Numeric.

x2 Indicator of fx1. Numeric.
x3 Indicator of fx1. Numeric.
x4 Indicator of fx2. Numeric.
x5 Indicator of fx2. Numeric.
x6 Indicator of fx2. Numeric.
m11a Indicator of fm11. Numeric.
m11b Indicator of fm11. Numeric.
m11c Indicator of fm11. Numeric.
m12a Indicator of fm12. Numeric.
m12b Indicator of fm12. Numeric.
m12c Indicator of fm12. Numeric.
m2a Indicator of fm2. Numeric.
m2b Indicator of fm2. Numeric.
m2c Indicator of fm2. Numeric.
y1 Indicator of fy1. Numeric.
y2 Indicator of fy1. Numeric.
y3 Indicator of fy1. Numeric.
y4 Indicator of fy2. Numeric.
y5 Indicator of fy2. Numeric.
y6 Indicator of fy2. Numeric.
52 delta_med

Details
The model:

fx1 =~ x1 + x2 + x3
fx2 =~ x4 + x5 + x6
fm11 =~ m11a + m11b + m11c
fm12 =~ m12a + m12b + m12c
fm2 =~ m2a + m2b + m2c
fy1 =~ y1 + y2 + y3
fy2 =~ y3 + y4 + y5
fm11 ~ a1 * fx1
fm12 ~ b11 * fm11 + a2m * fx2
fm2 ~ a2 * fx2
fy1 ~ b12 * fm12 + b11y1 * fm11 + cp1 * fx1
fy2 ~ b2 * fm2 + cp2 * fx2
a1b11b12 := a1 * b11 * b12
a1b11y1 := a1 * b11y1
a2b2 := a2 * b2
a2mb12 := a2m * b12

delta_med Delta_Med by Liu, Yuan, and Li (2023)

Description
It computes the Delta_Med proposed by Liu, Yuan, and Li (2023), an R2 -like measure of indirect
effect.

Usage
delta_med(
x,
y,
m,
fit,
paths_to_remove = NULL,
boot_out = NULL,
level = 0.95,
progress = TRUE,
skip_check_single_x = FALSE,
skip_check_m_between_x_y = FALSE,
skip_check_x_to_y = FALSE,
skip_check_latent_variables = FALSE
)
delta_med 53

Arguments

x The name of the x variable. Must be supplied as a quoted string.

y The name of the y variable. Must be supplied as a quoted string.
m A vector of the variable names of the mediator(s). If more than one mediators,
they do not have to be on the same path from x to y. Cannot be NULL for this
function.
fit The fit object. Must be a lavaan::lavaan object.
paths_to_remove
A character vector of paths users want to manually remove, specified in lavaan
model syntax. For example, c("m2~x", "m3~m2") removes the path from x to
m2 and the path from m2 to m3. The default is NULL, and the paths to remove
will be determined using the method by Liu et al. (2023). If supplied, then only
paths specified explicitly will be removed.
boot_out The output of do_boot(). If supplied, the stored bootstrap estimates will be
used to form the nonparametric percentile bootstrap confidence interval of Delta_Med.
level The level of confidence of the bootstrap confidence interval. Default is .95.
progress Logical. Display bootstrapping progress or not. Default is TRUE.
skip_check_single_x
Logical Check whether the model has one and only one x-variable. Default is
TRUE.
skip_check_m_between_x_y
Logical. Check whether all m variables are along a path from x to y. Default is
TRUE.
skip_check_x_to_y
Logical. Check whether there is a direct path from x to y. Default is TRUE.
skip_check_latent_variables
Logical. Check whether the model has any latent variables. Default is TRUE.

Details

It computes Delta_Med, an R2 -like effect size measure for the indirect effect from one variable (the
y-variable) to another variable (the x-variable) through one or more mediators (m, or m1, m2, etc.
when there are more than one mediator).
The Delta_Med of one or more mediators was computed as the difference between two R2 s:

• R12 , the R2 when y is predicted by x and all mediators.

• R22 , the R2 when the mediator(s) of interest is/are removed from the models, while the error
term(s) of the mediator(s) is/are kept.

Delta_Med is given by R12 − R22 .

Please refer to Liu et al. (2023) for the technical details.
The function can also form a nonparametric percentile bootstrap confidence of Delta_Med.
54 delta_med

Value
A delta_med class object. It is a list-like object with these major elements:
• delta_med: The Delta_Med.
• x: The name of the x-variable.
• y: The name of the y-variable.
• m: A character vector of the mediator(s) along a path. The path runs from the first element to
the last element.
This class has a print method, a coef method, and a confint method. See print.delta_med(),
coef.delta_med(), and confint.delta_med().

Implementation
The function identifies all the path(s) pointing to the mediator(s) of concern and fixes the path(s) to
zero, effectively removing the mediator(s). However, the model is not refitted, hence keeping the
estimates of all other parameters unchanged. It then uses lavaan::lav_model_set_parameters()
to update the parameters, lavaan::lav_model_implied() to update the implied statistics, and
then calls lavaan::lavInspect() to retrieve the implied variance of the predicted values of y for
computing the R22 . Subtracting this R22 from R12 of y can then yield Delta_Med.

Model Requirements
For now, by defaul, it only computes Delta_Med for the types of models discussed in Liu et al.
(2023):
• Having one predictor (the x-variable).
• Having one or more mediators, the m-variables, with arbitrary way to mediate the effect of x
on the outcome variable (y-variable).
• Having one or more outcome variables. Although their models only have outcome variables,
the computation of the Delta_Med is not affected by the presence of other outcome variables.
• Having no control variables.
• The mediator(s), m, and the y-variable are continuous.
• x can be continuous or categorical. If categorical, it needs to be handle appropriately when
fitting the model.
• x has a direct path to y.
• All the mediators listed in the argument m is present in at least one path from x to y.
• None of the paths from x to y are moderated.
It can be used for other kinds of models but support for them is disabled by default. To use this
function for cases not discussed in Liu et al. (2023), please disable relevant requirements stated
above using the relevant skip_check_* arguments. An error will be raised if the models failed any
of the checks not skipped by users.

References
Liu, H., Yuan, K.-H., & Li, H. (2023). A systematic framework for defining R-squared measures in
mediation analysis. Psychological Methods. Advance online publication. https://doi.org/10.1037/met0000571
do_boot 55

See Also
print.delta_med(), coef.delta_med(), and confint.delta_med().

Examples

library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit)
dm
print(dm, full = TRUE)

# Call do_boot() to generate

# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
R = 45,
seed = 879,
parallel = FALSE,
progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit,
boot_out = boot_out,
progress = FALSE)
dm_boot
confint(dm_boot)

do_boot Bootstrap Estimates for ’indirect_effects’ and ’cond_indirect_effects’

Description
Generate bootstrap estimates to be used by cond_indirect_effects(), indirect_effect(), and
cond_indirect(),
56 do_boot

Usage
do_boot(
fit,
R = 100,
seed = NULL,
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE
)

Arguments
fit Either (a) a list of lm class objects, or the output of lm2list() (i.e., an lm_list-
class object), or (b) the output of lavaan::sem().
R The number of bootstrap samples. Default is 100.
seed The seed for the bootstrapping. Default is NULL and seed is not set.
parallel Logical. Whether parallel processing will be used. Default is TRUE.
ncores Integer. The number of CPU cores to use when parallel is TRUE. Default is
the number of non-logical cores minus one (one minimum). Will raise an error
if greater than the number of cores detected by parallel::detectCores(). If
ncores is set, it will override make_cluster_args.
make_cluster_args
A named list of additional arguments to be passed to parallel::makeCluster().
For advanced users. See parallel::makeCluster() for details. Default is
list(), no additional arguments.
progress Logical. Display progress or not. Default is TRUE.

Details
It does nonparametric bootstrapping to generate bootstrap estimates of the parameter estimates in
a model fitted either by lavaan::sem() or by a sequence of calls to lm(). The stored estimates
can then be used by cond_indirect_effects(), indirect_effect(), and cond_indirect() to
form bootstrapping confidence intervals.
This approach removes the need to repeat bootstrapping in each call to cond_indirect_effects(),
indirect_effect(), and cond_indirect(). It also ensures that the same set of bootstrap samples
is used in all subsequent analysis.
It determines the type of the fit object automatically and then calls lm2boot_out(), fit2boot_out(),
or fit2boot_out_do_boot().

Value
A boot_out-class object that can be used for the boot_out argument of cond_indirect_effects(),
indirect_effect(), and cond_indirect() for forming bootstrap confidence intervals. The ob-
ject is a list with the number of elements equal to the number of bootstrap samples. Each element
is a list of the parameter estimates and sample variances and covariances of the variables in each
bootstrap sample.
do_mc 57

See Also
lm2boot_out(), fit2boot_out(), and fit2boot_out_do_boot(), which implements the boot-
strapping.

Examples
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set parallel and progress to FALSE
# Parallel processing is enabled by default and
# progress is displayed by default.
lm_boot_out <- do_boot(lm_out, R = 50, seed = 1234,
parallel = FALSE,
progress = FALSE)
wlevels <- mod_levels(w = "w", fit = lm_out)
wlevels
out <- cond_indirect_effects(wlevels = wlevels,
x = "x",
y = "y",
m = "m",
fit = lm_out,
boot_ci = TRUE,
boot_out = lm_boot_out)
out

do_mc Monte Carlo Estimates for ’indirect_effects’ and

’cond_indirect_effects’

Description
Generate Monte Carlo estimates to be used by cond_indirect_effects(), indirect_effect(),
and cond_indirect(),

Usage
do_mc(
fit,
R = 100,
seed = NULL,
parallel = TRUE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE
58 do_mc

gen_mc_est(fit, R = 100, seed = NULL)

Arguments
fit The output of lavaan::sem(). It can also be a lavaan.mi object returned by
semTools::runMI() or its wrapper, such as semTools::sem.mi(). The output
of stats::lm() is not supported.
R The number of replications. Default is 100.
seed The seed for the generating Monte Carlo estimates. Default is NULL and seed is
not set.
parallel Not used. Kept for compatibility with do_boot().
ncores Not used. Kept for compatibility with do_boot().
make_cluster_args
Not used. Kept for compatibility with do_boot().
progress Logical. Display progress or not. Default is TRUE.

Details
It uses the parameter estimates and their variance-covariance matrix to generate Monte Carlo es-
timates of the parameter estimates in a model fitted by lavaan::sem(). The stored estimates can
then be used by cond_indirect_effects(), indirect_effect(), and cond_indirect() to form
Monte Carlo confidence intervals.
It also supports a model estimated by multiple imputation using semTools::runMI() or its wrapper,
such as semTools::sem.mi(). The pooled estimates and their variance-covariance matrix will be
used to generate the Monte Carlo estimates.
This approach removes the need to repeat Monte Carlo simulation in each call to cond_indirect_effects(),
indirect_effect(), and cond_indirect(). It also ensures that the same set of Monte Carlo es-
timates is used in all subsequent analysis.

Value
A mc_out-class object that can be used for the mc_out argument of cond_indirect_effects(),
indirect_effect(), and cond_indirect() for forming Monte Carlo confidence intervals. The
object is a list with the number of elements equal to the number of Monte Carlo replications. Each
element is a list of the parameter estimates and sample variances and covariances of the variables
in each Monte Carlo replication.

Functions
• do_mc(): A general purpose function for creating Monte Carlo estimates to be reused by other
functions. It returns a mc_out-class object.
• gen_mc_est(): Generate Monte Carlo estimates and store them in the external slot: external$manymome$mc.
For advanced users.
factor2var 59

See Also

fit2mc_out(), which implements the Monte Carlo simulation.

Examples

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(mod, dat)
# In real research, R should be 5000 or even 10000
mc_out <- do_mc(fit, R = 100, seed = 1234)
wlevels <- mod_levels(w = "w", fit = fit)
wlevels
out <- cond_indirect_effects(wlevels = wlevels,
x = "x",
y = "y",
m = "m",
fit = fit,
mc_ci = TRUE,
mc_out = mc_out)
out

factor2var Create Dummy Variables

Description

Create dummy variables from a categorical variable.

Usage

factor2var(
x_value,
x_contrasts = "contr.treatment",
prefix = "",
add_rownames = TRUE
)
60 fit2boot_out

Arguments
x_value The vector of categorical variable.
x_contrasts The contrast to be used. Default is "constr.treatment".
prefix The prefix to be added to the variables to be created. Default is "".
add_rownames Whether row names will be added to the output. Default is TRUE.

Details
Its main use is for creating dummy variables (indicator variables) from a categorical variable, to be
used in lavaan::sem().
Optionally, the other contrasts can be used through the argument x_contrasts.

Value
It always returns a matrix with the number of rows equal to the length of the vector (x_value). If
the categorical has only two categories and so only one dummy variable is needed, the output is still
a one-column "matrix" in R.

Examples
dat <- data_mod_cat
dat <- data.frame(dat,
factor2var(dat$w, prefix = "gp", add_rownames = FALSE))
head(dat[, c("w", "gpgroup2", "gpgroup3")], 15)

fit2boot_out Bootstrap Estimates for a lavaan Output

Description
Generate bootstrap estimates from the output of lavaan::sem().

Usage
fit2boot_out(fit)

fit2boot_out_do_boot(
fit,
R = 100,
seed = NULL,
parallel = FALSE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE,
internal = list()
)
fit2boot_out 61

Arguments
fit The fit object. This function only supports a lavaan::lavaan object.
R The number of bootstrap samples. Default is 100.
seed The seed for the random resampling. Default is NULL.
parallel Logical. Whether parallel processing will be used. Default is NULL.
ncores Integer. The number of CPU cores to use when parallel is TRUE. Default is
the number of non-logical cores minus one (one minimum). Will raise an error
if greater than the number of cores detected by parallel::detectCores(). If
ncores is set, it will override make_cluster_args.
make_cluster_args
A named list of additional arguments to be passed to parallel::makeCluster().
For advanced users. See parallel::makeCluster() for details. Default is
list().
progress Logical. Display progress or not. Default is TRUE.
internal A list of arguments to be used internally for debugging. Default is list().

Details
This function is for advanced users. do_boot() is a function users should try first because do_boot()
has a general interface for input-specific functions like this one.
If bootstrapping confidence intervals was requested when calling lavaan::sem() by setting se =
"boot", fit2boot_out() can be used to extract the stored bootstrap estimates so that they can be
reused by indirect_effect(), cond_indirect_effects() and related functions to form boot-
strapping confidence intervals for effects such as indirect effects and conditional indirect effects.
If bootstrapping confidence was not requested when fitting the model by lavaan::sem(), fit2boot_out_do_boot()
can be used to generate nonparametric bootstrap estimates from the output of lavaan::sem() and
store them for use by indirect_effect(), cond_indirect_effects(), and related functions.
This approach removes the need to repeat bootstrapping in each call to indirect_effect(), cond_indirect_effects(),
and related functions. It also ensures that the same set of bootstrap samples is used in all subsequent
analyses.

Value
A boot_out-class object that can be used for the boot_out argument of indirect_effect(),
cond_indirect_effects(), and related functions for forming bootstrapping confidence intervals.
The object is a list with the number of elements equal to the number of bootstrap samples. Each
element is a list of the parameter estimates and sample variances and covariances of the variables
in each bootstrap sample.

Functions
• fit2boot_out(): Process stored bootstrap estimates for functions such as cond_indirect_effects().
• fit2boot_out_do_boot(): Do bootstrapping and store information to be used by cond_indirect_effects()
and related functions. Support parallel processing.
62 fit2mc_out

See Also
do_boot(), the general purpose function that users should try first before using this function.

Examples

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"

# Bootstrapping not requested in calling lavaan::sem()

fit <- sem(model = mod, data = dat, fixed.x = FALSE,
se = "none", baseline = FALSE)
fit_boot_out <- fit2boot_out_do_boot(fit = fit,
R = 40,
seed = 1234,
progress = FALSE)
out <- cond_indirect_effects(wlevels = "w",
x = "x",
y = "y",
m = "m",
fit = fit,
boot_ci = TRUE,
boot_out = fit_boot_out)
out

fit2mc_out Monte Carlo Estimates for a lavaan Output

Description
Generate Monte Carlo estimates from the output of lavaan::sem().

Usage
fit2mc_out(fit, progress = TRUE)

Arguments
fit The fit object. This function only supports a lavaan::lavaan object. It can also
be a lavaan.mi object returned by semTools::runMI() or its wrapper, such as
semTools::sem.mi().
fit2mc_out 63

progress Logical. Display progress or not. Default is TRUE.

Details
This function is for advanced users. do_mc() is a function users should try first because do_mc()
has a general interface for input-specific functions like this one.
fit2mc_out() can be used to extract the stored Monte Carlo estimates so that they can be reused
by indirect_effect(), cond_indirect_effects() and related functions to form Monte Carlo
confidence intervals for effects such as indirect effects and conditional indirect effects.
This approach removes the need to repeat Monte Carlo simulation in each call to indirect_effect(),
cond_indirect_effects(), and related functions. It also ensures that the same set of Monte Carlo
estimates is used in all subsequent analyses.

Value
A mc_out-class object that can be used for the mc_out argument of indirect_effect(), cond_indirect_effects(),
and related functions for forming Monte Carlo confidence intervals.
The object is a list with the number of elements equal to the number of Monte Carlo replications.
Each element is a list of the parameter estimates and sample variances and covariances of the vari-
ables in each Monte Carlo replication.

See Also
do_mc(), the general purpose function that users should try first before using this function.

Examples

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"

fit <- sem(model = mod, data = dat, fixed.x = FALSE,

baseline = FALSE)
# In real research, R should be 5000 or even 10000.
fit <- gen_mc_est(fit, R = 100, seed = 453253)
fit_mc_out <- fit2mc_out(fit)
out <- cond_indirect_effects(wlevels = "w",
x = "x",
y = "y",
m = "m",
fit = fit,
mc_ci = TRUE,
64 get_one_cond_indirect_effect

mc_out = fit_mc_out)
out

get_one_cond_indirect_effect
Get The Conditional Indirect Effect for One Row of
’cond_indirect_effects’ Output

Description

Return the conditional indirect effect of one row of the output of cond_indirect_effects().

Usage

get_one_cond_indirect_effect(object, row)

get_one_cond_effect(object, row)

Arguments

object The output of cond_indirect_effects().

row The row number of the row to be retrieved.

Details

It just extracts the corresponding output of cond_indirect() from the requested row.

Value

An indirect-class object, similar to the output of indirect_effect() and cond_indirect().

See [indirect_effect)] and cond_indirect() for details on these classes.
[indirect_effect)]: R:indirect_effect) cond_indirect(): R:cond_indirect()

Functions

• get_one_cond_effect(): An alias to get_one_cond_indirect_effect()

See Also

cond_indirect_effects
get_prod 65

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ m1
y ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

# Conditional effects from x to m1

# when w1 is equal to each of the default levels
out1 <- cond_indirect_effects(x = "x", y = "m1",
wlevels = c("w1", "w4"), fit = fit)
get_one_cond_indirect_effect(out1, 3)

# Conditional Indirect effect from x1 through m1 to y,

# when w1 is equal to each of the levels
out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
wlevels = c("w1", "w4"), fit = fit)
get_one_cond_indirect_effect(out2, 4)

get_prod Product Terms (if Any) Along a Path

Description
Identify the product term(s), if any, along a path in a model and return the term(s), with the variables
involved and the coefficient(s) of the term(s).

Usage
get_prod(
x,
y,
operator = ":",
fit = NULL,
est = NULL,
data = NULL,
expand = FALSE
)
66 get_prod

Arguments
x Character. Variable name.
y Character. Variable name.
operator Character. The string used to indicate a product term. Default is ":", used in
both lm() and lavaan::sem() for observed variables.
fit The fit object. Currently only supports a lavaan::lavaan object. It can also be
a lavaan.mi object returned by semTools::runMI() or its wrapper, such as
semTools::sem.mi().
est The output of lavaan::parameterEstimates(). If NULL, the default, it will be
generated from fit. If supplied, fit will ge ignored.
data Data frame (optional). If supplied, it will be used to identify the product terms.
expand Whether products of more than two terms will be searched. FALSE by default.

Details
This function is used by several functions in manymome to identify product terms along a path. If
possible, this is done by numerically checking whether a column in a dataset is the product of two
other columns. If not possible (e.g., the "product term" is the "product" of two latent variables,
formed by the products of indicators), then it requires the user to specify an operator.
The detailed workflow of this function can be found in the article https://sfcheung.github.io/
manymome/articles/get_prod.html
This function is not intended to be used by users. It is exported such that advanced users or devel-
opers can use it.

Value
If at least one product term is found, it returns a list with these elements:

• prod: The names of the product terms found.

• b: The coefficients of these product terms.
• w: The variable, other than x, in each product term.
• x: The x-variable, that is, where the path starts.
• y: The y-variable, that is, where the path ends.

It returns NA if no product term is found along the path.

Examples

dat <- modmed_x1m3w4y1

library(lavaan)
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ m1 + w2 + m1:w2
m3 ~ m2
index_of_mome 67

y ~ m3 + w4 + m3:w4 + x + w3 + x:w3 + x:w4

"
fit <- sem(model = mod,
data = dat,
meanstructure = TRUE,
fixed.x = FALSE)

# One product term

get_prod(x = "x", y = "m1", fit = fit)
# Two product terms
get_prod(x = "x", y = "y", fit = fit)
# No product term
get_prod(x = "m2", y = "m3", fit = fit)

index_of_mome Index of Moderated Mediation and Index of Moderated Moderated

Mediation

Description
It computes the index of moderated mediation and the index of moderated moderated mediation
proposed by Hayes (2015, 2018).

Usage
index_of_mome(
x,
y,
m = NULL,
w = NULL,
fit = NULL,
boot_ci = FALSE,
level = 0.95,
boot_out = NULL,
R = 100,
seed = NULL,
progress = TRUE,
mc_ci = FALSE,
mc_out = NULL,
ci_type = NULL,
ci_out = NULL,
...
)

index_of_momome(
x,
y,
68 index_of_mome

m = NULL,
w = NULL,
z = NULL,
fit = NULL,
boot_ci = FALSE,
level = 0.95,
boot_out = NULL,
R = 100,
seed = NULL,
progress = TRUE,
mc_ci = FALSE,
mc_out = NULL,
ci_type = NULL,
ci_out = NULL,
...
)

Arguments
x Character. The name of the predictor at the start of the path.
y Character. The name of the outcome variable at the end of the path.
m A vector of the variable names of the mediator(s). The path goes from the first
mediator successively to the last mediator. If NULL, the default, the path goes
from x to y.
w Character. The name of the moderator.
fit The fit object. Can be a lavaan::lavaan object, a list of lm() outputs, or an
object created by lm2list(). It can also be a lavaan.mi object returned by
semTools::runMI() or its wrapper, such as semTools::sem.mi().
boot_ci Logical. Whether bootstrap confidence interval will be formed. Default is
FALSE.
level The level of confidence for the bootstrap confidence interval. Default is .95.
boot_out If boot_ci is TRUE, users can supply pregenerated bootstrap estimates. This can
be the output of do_boot(). For indirect_effect() and cond_indirect_effects(),
this can be the output of a previous call to cond_indirect_effects(), indirect_effect(),
or cond_indirect() with bootstrap confidence intervals requested. These stored
estimates will be reused such that there is no need to do bootstrapping again. If
not supplied, the function will try to generate them from fit.
R Integer. If boot_ci is TRUE, boot_out is NULL, and bootstrap standard errors
not requested if fit is a lavaan object, this function will do bootstrapping on
fit. R is the number of bootstrap samples. Default is 100. For Monte Carlo
simulation, this is the number of replications.
seed If bootstrapping or Monte Carlo simulation is conducted, this is the seed for the
bootstrapping or simulation. Default is NULL and seed is not set.
progress Logical. Display bootstrapping progress or not. Default is TRUE.
mc_ci Logical. Whether Monte Carlo confidence interval will be formed. Default is
FALSE.
index_of_mome 69

mc_out If mc_ci is TRUE, users can supply pregenerated Monte Carlo estimates. This can
be the output of do_mc(). For indirect_effect() and cond_indirect_effects(),
this can be the output of a previous call to cond_indirect_effects(), indirect_effect(),
or cond_indirect() with Monte Carlo confidence intervals requested. These
stored estimates will be reused such that there is no need to do Monte Carlo
simulation again. If not supplied, the function will try to generate them from
fit.
ci_type The type of confidence intervals to be formed. Can be either "boot" (boot-
strapping) or "mc" (Monte Carlo). If not supplied or is NULL, will check other
arguments (e.g, boot_ci and mc_ci). If supplied, will override boot_ci and
mc_ci.
ci_out If ci_type is supplied, this is the corresponding argument. If ci_type is "boot",
this argument will be used as boot_out. If ci_type is "mc", this argument will
be used as mc_out.
... Arguments to be passed to cond_indirect_effects()
z Character. The name of the second moderator, for computing the index of mod-
erated moderated mediation.

Details
The function index_of_mome() computes the index of moderated mediation proposed by Hayes
(2015). It supports any path in a model with one (and only one) component path moderated. For
example, x->m1->m2->y with x->m1 moderated by w. It measures the change in indirect effect when
the moderator increases by one unit.
The function index_of_momome() computes the index of moderated moderated mediation proposed
by Hayes (2018). It supports any path in a model, with two component paths moderated, each by
one moderator. For example, x->m1->m2->y with x->m1 moderated by w and m2->y moderated by
z. It measures the change in the index of moderated mediation of one moderator when the other
moderator increases by one unit.

Value
It returns a cond_indirect_diff-class object. This class has a print method (print.cond_indirect_diff()),
a coef method for extracting the index (coef.cond_indirect_diff()), and a confint method for
extracting the confidence interval if available (confint.cond_indirect_diff()).

Functions
• index_of_mome(): Compute the index of moderated mediation.
• index_of_momome(): Compute the index of moderated moderated mediation.

References
Hayes, A. F. (2015). An index and test of linear moderated mediation. Multivariate Behavioral
Research, 50(1), 1-22. doi:10.1080/00273171.2014.962683
Hayes, A. F. (2018). Partial, conditional, and moderated moderated mediation: Quantification, in-
ference, and interpretation. Communication Monographs, 85(1), 4-40. doi:10.1080/03637751.2017.1352100
70 index_of_mome

See Also
cond_indirect_effects()

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
mod <-
"
m1 ~ a * x + f * w1 + d * xw1
y ~ b * m1 + cp * x
ind_mome := d * b
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# R should be at least 2000 or even 5000 in real research.

# parallel is set to TRUE by default.
# Therefore, in research, the argument parallel can be omitted.
out_mome <- index_of_mome(x = "x", y = "y", m = "m1", w = "w1",
fit = fit,
boot_ci = TRUE,
R = 42,
seed = 4314,
parallel = FALSE,
progress = FALSE)
out_mome
coef(out_mome)
# From lavaan
print(est[19, ], nd = 8)
confint(out_mome)

library(lavaan)
dat <- modmed_x1m3w4y1
dat$xw1 <- dat$x * dat$w1
dat$m1w4 <- dat$m1 * dat$w4
mod <-
"
m1 ~ a * x + f1 * w1 + d1 * xw1
y ~ b * m1 + f4 * w4 + d4 * m1w4 + cp * x
ind_momome := d1 * d4
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)
indirect_effects_from_list 71

# See the example of index_of_mome on how to request

# bootstrap confidence interval.
out_momome <- index_of_momome(x = "x", y = "y", m = "m1",
w = "w1", z = "w4",
fit = fit)
out_momome
coef(out_momome)
print(est[32, ], nd = 8)

indirect_effects_from_list
Coefficient Table of an ’indirect_list’ Class Object

Description
Create a coefficient table for the point estimates and confidence intervals (if available) in the output
of many_indirect_effects().

Usage
indirect_effects_from_list(object, add_sig = TRUE, pvalue = FALSE, se = FALSE)

Arguments
object The output of indirect_effect() or cond_indirect().
add_sig Whether a column of significance test results will be added. Default is TRUE.
pvalue Logical. If TRUE, asymmetric p-values based on bootstrapping will be added
available. Default is FALSE.
se Logical. If TRUE and confidence intervals are available, the standard errors of
the estimates are also added. They are simply the standard deviations of the
bootstrap estimates or Monte Carlo simulated values, depending on the method
used to form the confidence intervals.

Details
If bootstrapping confidence interval was requested, this method has the option to add p-values
computed by the method presented in Asparouhov and Muthén (2021). Note that these p-values is
asymmetric bootstrap p-values based on the distribution of the bootstrap estimates. They are not
computed based on the distribution under the null hypothesis.
For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of
its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a
confidence interval with a lower confidence level will exclude zero.
72 indirect_effects_from_list

Value

A data frame with the indirect effect estimates and confidence intervals (if available). It also has A
string column, "Sig", for #’ significant test results if add_sig is TRUE and confidence intervals are
available.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download
Bootstrap%20-%20Pvalue.pdf

See Also

many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)

# All indirect paths from x to y

paths <- all_indirect_paths(fit,
x = "x",
y = "y")
paths

# Indirect effect estimates

out <- many_indirect_effects(paths,
fit = fit)
out

# Create a data frame of the indirect effect estimates

out_df <- indirect_effects_from_list(out)

out_df
indirect_i 73

indirect_i Indirect Effect (No Bootstrapping)

Description
It computes an indirect effect, optionally conditional on the value(s) of moderator(s) if present.

Usage
indirect_i(
x,
y,
m = NULL,
fit = NULL,
est = NULL,
implied_stats = NULL,
wvalues = NULL,
standardized_x = FALSE,
standardized_y = FALSE,
computation_digits = 5,
prods = NULL,
get_prods_only = FALSE,
data = NULL,
expand = TRUE,
warn = TRUE,
allow_mixing_lav_and_obs = TRUE
)

Arguments
x Character. The name of the predictor at the start of the path.
y Character. The name of the outcome variable at the end of the path.
m A vector of the variable names of the mediator(s). The path goes from the first
mediator successively to the last mediator. If NULL, the default, the path goes
from x to y.
fit The fit object. Currently only supports lavaan::lavaan objects. Support for lists
of lm() output is implemented by high level functions such as indirect_effect()
and cond_indirect_effects(). It can also be a lavaan.mi object returned by
semTools::runMI() or its wrapper, such as semTools::sem.mi().
est The output of lavaan::parameterEstimates(). If NULL, the default, it will be
generated from fit. If supplied, fit will be ignored.
implied_stats Implied means, variances, and covariances of observed variables and latent vari-
ables (if any), of the form of the output of lavaan::lavInspect() with what
set to "implied", but with means extracted with what set to "mean.ov" and
74 indirect_i

"mean.lv". The standard deviations are extracted from this object for standard-
ization. Default is NULL, and implied statistics will be computed from fit if
required.
wvalues A numeric vector of named elements. The names are the variable names of the
moderators, and the values are the values to which the moderators will be set to.
Default is NULL.
standardized_x Logical. Whether x will be standardized. Default is FALSE.
standardized_y Logical. Whether y will be standardized. Default is FALSE.
computation_digits
The number of digits in storing the computation in text. Default is 3.
prods The product terms found. For internal use.
get_prods_only IF TRUE, will quit early and return the product terms found. The results can be
passed to the prod argument when calling this function. Default is FALSE. For
internal use.
data Data frame (optional). If supplied, it will be used to identify the product terms.
For internal use.
expand Whether products of more than two terms will be searched. TRUE by default. For
internal use.
warn If TRUE, the default, the function will warn against possible misspecification,
such as not setting the value of a moderator which moderate one of the compo-
nent path. Set this to FALSE will suppress these warnings. Suppress them only
when the moderators are omitted intentionally.
allow_mixing_lav_and_obs
If TRUE, it accepts a path with both latent variables and observed variables. De-
fault is TRUE.

Details

This function is a low-level function called by indirect_effect(), cond_indirect_effects(),

and cond_indirect(), which call this function multiple times if bootstrap confidence interval is
requested.
This function usually should not be used directly. It is exported for advanced users and developers

Value

It returns an indirect-class object. This class has the following methods: coef.indirect(),
print.indirect(). The confint.indirect() method is used only when called by cond_indirect()
or cond_indirect_effects().

See Also

indirect_effect(), cond_indirect_effects(), and cond_indirect(), the high level func-

tions that should usually be used.
indirect_proportion 75

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x + b1 * w1 + d1 * x:w1
m2 ~ a2 * m1 + b2 * w2 + d2 * m1:w2
m3 ~ a3 * m2 + b3 * w3 + d3 * m2:w3
y ~ a4 * m3 + b4 * w4 + d4 * m3:w4
"
fit <- sem(mod, dat, meanstructure = TRUE,
fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

wvalues <- c(w1 = 5, w2 = 4, w3 = 2, w4 = 3)

# Compute the conditional indirect effect by indirect_i()

indirect_1 <- indirect_i(x = "x", y = "y", m = c("m1", "m2", "m3"), fit = fit,
wvalues = wvalues)

# Manually compute the conditional indirect effect

indirect_2 <- (est[est$label == "a1", "est"] +
wvalues["w1"] * est[est$label == "d1", "est"]) *
(est[est$label == "a2", "est"] +
wvalues["w2"] * est[est$label == "d2", "est"]) *
(est[est$label == "a3", "est"] +
wvalues["w3"] * est[est$label == "d3", "est"]) *
(est[est$label == "a4", "est"] +
wvalues["w4"] * est[est$label == "d4", "est"])
# They should be the same
coef(indirect_1)
indirect_2

indirect_proportion Proportion of Effect Mediated

Description
It computes the proportion of effect mediated along a pathway.

Usage
indirect_proportion(x, y, m = NULL, fit = NULL)

Arguments
x The name of the x variable. Must be supplied as a quoted string.
76 indirect_proportion

y The name of the y variable. Must be supplied as a quoted string.

m A vector of the variable names of the mediator(s). The path goes from the first
mediator successively to the last mediator. Cannot be NULL for this function.
fit The fit object. Can be a lavaan::lavaan object or a list of lm() outputs. It can also
be a lavaan.mi object returned by semTools::runMI() or its wrapper, such as
semTools::sem.mi().

Details
The proportion of effect mediated along a path from x to y is the indirect effect along this path
divided by the total effect from x to y (Alwin & Hauser, 1975). This total effect is equal to the sum
of all indirect effects from x to y and the direct effect from x to y.
To ensure that the proportion can indeed be interpreted as a proportion, this function computes the
the proportion only if the signs of all the indirect and direct effects from x to y are same (i.e., all
effects positive or all effects negative).

Value
An indirect_proportion class object. It is a list-like object with these major elements:

• proportion: The proportion of effect mediated.

• x: The name of the x-variable.
• y: The name of the y-variable.
• m: A character vector of the mediator(s) along a path. The path runs from the first element to
the last element.

This class has a print method and a coef method.

References
Alwin, D. F., & Hauser, R. M. (1975). The decomposition of effects in path analysis. American
Sociological Review, 40(1), 37. doi:10.2307/2094445

See Also
print.indirect_proportion() for the print method, and coef.indirect_proportion() for
the coef method.

Examples

library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
lm2boot_out 77

fit <- sem(mod, dat, fixed.x = FALSE)

out <- indirect_proportion(x = "x",
y = "y",
m = "m",
fit = fit)
out

lm2boot_out Bootstrap Estimates for lm Outputs

Description
Generate bootstrap estimates for models in a list of ’lm’ outputs.

Usage
lm2boot_out(outputs, R = 100, seed = NULL, progress = TRUE)

lm2boot_out_parallel(
outputs,
R = 100,
seed = NULL,
parallel = FALSE,
ncores = max(parallel::detectCores(logical = FALSE) - 1, 1),
make_cluster_args = list(),
progress = TRUE
)

Arguments
outputs A list of lm class objects, or the output of lm2list() (i.e., an lm_list-class
object).
R The number of bootstrap samples. Default is 100.
seed The seed for the random resampling. Default is NULL.
progress Logical. Display progress or not. Default is TRUE.
parallel Logical. Whether parallel processing will be used. Default is NULL.
ncores Integer. The number of CPU cores to use when parallel is TRUE. Default is
the number of non-logical cores minus one (one minimum). Will raise an error
if greater than the number of cores detected by parallel::detectCores(). If
ncores is set, it will override make_cluster_args.
make_cluster_args
A named list of additional arguments to be passed to parallel::makeCluster().
For advanced users. See parallel::makeCluster() for details. Default is
list().
78 lm2boot_out

Details
This function is for advanced users. do_boot() is a function users should try first because do_boot()
has a general interface for input-specific functions like this one.
It does nonparametric bootstrapping to generate bootstrap estimates of the regression coefficients in
the regression models of a list of lm() outputs, or an lm_list-class object created by lm2list().
The stored estimates can be used by indirect_effect(), cond_indirect_effects(), and re-
lated functions in forming bootstrapping confidence intervals for effects such as indirect effect and
conditional indirect effects.
This approach removes the need to repeat bootstrapping in each call to indirect_effect(), cond_indirect_effects(),
and related functions. It also ensures that the same set of bootstrap samples is used in all subsequent
analyses.

Value
A boot_out-class object that can be used for the boot_out argument of indirect_effect(),
cond_indirect_effects(), and related functions for forming bootstrapping confidence intervals.
The object is a list with the number of elements equal to the number of bootstrap samples. Each
element is a list of the parameter estimates and sample variances and covariances of the variables
in each bootstrap sample.

Functions
• lm2boot_out(): Generate bootstrap estimates using one process (serial, without paralleliza-
tion).
• lm2boot_out_parallel(): Generate bootstrap estimates using parallel processing.

See Also
do_boot(), the general purpose function that users should try first before using this function.

Examples

data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set progress to FALSE
# Progress is displayed by default.
lm_boot_out <- lm2boot_out(lm_out, R = 100, seed = 1234,
progress = FALSE)
out <- cond_indirect_effects(wlevels = "w",
x = "x",
y = "y",
m = "m",
fit = lm_out,
boot_ci = TRUE,
lm2list 79

boot_out = lm_boot_out)
out

lm2list Join ’lm()’ Output to Form an ’lm_list‘-Class Object

Description
The resulting model can be used by indirect_effect(), cond_indirect_effects(), or cond_indirect()
as a path method, as if fitted by lavaan::sem().

Usage
lm2list(...)

Arguments
... The lm() outputs to be grouped in a list.

Details
If a path model with mediation and/or moderation is fitted by a set of regression models using lm(),
this function can combine them to an object of the class lm_list that represents a path model,
as one fitted by structural equation model functions such as lavaan::sem(). This class of object
can be used by some functions, such as indirect_effect(), cond_indirect_effects(), and
cond_indirect() as if they were the output of fitting a path model, with the regression coefficients
treated as path coefficients.
The regression outputs to be combined need to meet the following requirements:

• All models must be connected to at least one another model. That is, a regression model must
either have (a) at least on predictor that is the outcome variable of another model, or (b) its
outcome variable the predictor of another model.
• All models must be fitted to the same sample. This implies that the sample size must be the
same in all analysis.

Value
It returns an lm_list-class object that forms a path model represented by a set of regression models.
This class has a summary method that shows the summary of each regression model stored (see
summary.lm_list()), and a print method that prints the models stored (see print.lm_list()).

See Also
summary.lm_list() and print.lm_list() for related methods, indirect_effect() and cond_indirect_effects()
which accept lm_list-class objects as input.
80 lm_from_lavaan_list

Examples

data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
summary(lm_serial_parallel)

# Compute indirect effect from x to y through m11 and m12

outm11m12 <- cond_indirect(x = "x", y = "y",
m = c("m11", "m12"),
fit = lm_serial_parallel)
outm11m12
# Compute indirect effect from x to y
# through m11 and m12 with bootstrapping CI
# R should be at least 2000 or even 5000 in read study.
# In real research, parallel and progress can be omitted.
# They are est to TRUE by default.
outm11m12 <- cond_indirect(x = "x", y = "y",
m = c("m11", "m12"),
fit = lm_serial_parallel,
boot_ci = TRUE,
R = 100,
seed = 1234,
parallel = FALSE,
progress = FALSE)
outm11m12

lm_from_lavaan_list ’lavaan’-class to ’lm_from_lavaan_list’-Class

Description
Converts the regression models in a lavaan-class model to an lm_from_lavaan_list-class object.

Usage
lm_from_lavaan_list(fit)

Arguments
fit A lavaan-class object, usually the output of lavaan::lavaan() or its wrap-
pers.
math_indirect 81

Details
It identifies all dependent variables in a lavaan model and creates an lm_from_lavaan-class object
for each of them.
This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced
users and developers.

Value
An lm_from_lavaan_list-class object, which is a list of lm_from_lavaan objects. It has a
predict-method (predict.lm_from_lavaan_list()) for computing the predicted values from
one variable to another.

See Also
predict.lm_from_lavaan_list

Examples
library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list, x = "x", y = "y", m = "m", newdata = tmp)

math_indirect Math Operators for ’indirect’-Class Objects

Description
Mathematic operators for ’indirect’-class object, the output of indirect_effect() and cond_indirect().

Usage
## S3 method for class 'indirect'
e1 + e2

## S3 method for class 'indirect'

e1 - e2
82 math_indirect

Arguments
e1 An ’indirect’-class object.
e2 An ’indirect’-class object.

Details
For now, only + operator and - operator are supported. These operators can be used to estimate and
test a function of effects between the same pair of variables but along different paths.
For example, they can be used to compute and test the total effects along different paths. They can
also be used to compute and test the difference between the effects along two paths.
The operators will check whether an operation is valid. An operation is not valid if
1. the two paths do not start from the same variable,
2. the two paths do not end at the same variable, (c) a path appears in both objects,
3. moderators are involved but they are not set to the same values in both objects, and
4. bootstrap estimates stored in boot_out, if any, are not identical.
5. Monte Carlo simulated estimates stored in mc_out, if any, are not identical.

Value
An ’indirect’-class object with a list of effects stored. See indirect_effect() on details for this
class.

See Also
indirect_effect() and cond_indirect()

Examples
library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x + d1 * w1 + e1 * x:w1
m2 ~ m1 + a2 * x
y ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)
hi_w1 <- mean(dat$w1) + sd(dat$w1)

# Examples for cond_indirect():

# Conditional effect from x to m1 when w1 is 1 SD above mean

out1 <- cond_indirect(x = "x", y = "y", m = c("m1", "m2"),
wvalues = c(w1 = hi_w1), fit = fit)
out2 <- cond_indirect(x = "x", y = "y", m = c("m2"),
merge_mod_levels 83

wvalues = c(w1 = hi_w1), fit = fit)

out3 <- cond_indirect(x = "x", y = "y",
wvalues = c(w1 = hi_w1), fit = fit)

out12 <- out1 + out2

out12
out123 <- out1 + out2 + out3
out123
coef(out1) + coef(out2) + coef(out3)

merge_mod_levels Merge the Generated Levels of Moderators

Description

Merge the levels of moderators generated by mod_levels() into a data frame.

Usage

merge_mod_levels(...)

Arguments

... The output from mod_levels(), or a list of levels generated by mod_levels_list().

Details

It merges the levels of moderators generated by mod_levels() into a data frame, with each row
represents a combination of the levels. The output is to be used by cond_indirect_effects().
Users usually do not need to use this function because cond_indirect_effects() will merge the
levels internally if necessary. This function is used when users need to customize the levels for each
moderator and so cannot use mod_levels_list() or the default levels in cond_indirect_effects().

Value

A wlevels-class object, which is a data frame of the combinations of levels, with additional at-
tributes about the levels.

See Also

mod_levels() on generating the levels of a moderator.

84 modmed_x1m3w4y1

Examples

data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w2_levels <- mod_levels(lm_out, w = "w2")
w2_levels
merge_mod_levels(w1_levels, w2_levels)

modmed_x1m3w4y1 Sample Dataset: Moderated Serial Mediation

Description
Generated from a serial mediation model with one predictor, three mediators, and one outcome
variable, with one moderator in each stage.

Usage
modmed_x1m3w4y1

Format
A data frame with 200 rows and 11 variables:

x Predictor. Numeric.
w1 Moderator 1. Numeric.
w2 Moderator 2. Numeric.
w3 Moderator 3. Numeric.
w4 Moderator 4. Numeric.
m1 Mediator 1. Numeric.
m2 Mediator 2. Numeric.
m3 Mediator 3. Numeric.
y Outcome variable. Numeric.
gp Three values: "earth", "mars", "venus". String.
city Four values: "alpha", "beta", "gamma", "sigma". String.
mod_levels 85

mod_levels Create Levels of Moderators

Description
Create levels of moderators to be used by indirect_effect(), cond_indirect_effects(), and
cond_indirect().

Usage
mod_levels(
w,
fit,
w_type = c("auto", "numeric", "categorical"),
w_method = c("sd", "percentile"),
sd_from_mean = c(-1, 0, 1),
percentiles = c(0.16, 0.5, 0.84),
extract_gp_names = TRUE,
prefix = NULL,
values = NULL,
reference_group_label = NULL,
descending = TRUE
)

mod_levels_list(
...,
fit,
w_type = "auto",
w_method = "sd",
sd_from_mean = NULL,
percentiles = NULL,
extract_gp_names = TRUE,
prefix = NULL,
descending = TRUE,
merge = FALSE
)

Arguments
w Character. The names of the moderator. If the moderator is categorical with 3
or more groups, this is the vector of the indicator variables.
fit The fit object. Can be a lavaan::lavaan object or a list of lm() outputs. It can also
be a lavaan.mi object returned by semTools::runMI() or its wrapper, such as
semTools::sem.mi().
w_type Character. Whether the moderator is a "numeric" variable or a "categorical"
variable. If "auto", the function will try to determine the type automatically.
86 mod_levels

w_method Character, either "sd" or "percentile". If "sd", the levels are defined by the
distance from the mean in terms of standard deviation. if "percentile", the
levels are defined in percentiles.
sd_from_mean A numeric vector. Specify the distance in standard deviation from the mean for
each level. Default is c(-1, 0, 1) for mod_levels(). For mod_levels_list(),
the default is c(-1, 0, 1) when there is only one moderator, and c(-1, 1) when
there are more than one moderator. Ignored if w_method is not equal to "sd".
percentiles A numeric vector. Specify the percentile (in proportion) for each level. Default
is c(.16, .50, .84) for mod_levels(), corresponding approximately to one
standard deviation below mean, mean, and one standard deviation above mean
in a normal distribution. For mod_levels_list(), default is c(.16, .50, .84)
if there is one moderator, and c(.16, .84) when there are more than one mod-
erator. Ignored if w_method is not equal to "percentile".
extract_gp_names
Logical. If TRUE, the default, the function will try to determine the name of each
group from the variable names.
prefix Character. If extract_gp_names is TRUE and prefix is supplied, it will be
removed from the variable names to create the group names. Default is NULL,
and the function will try to determine the prefix automatically.
values For numeric moderators, a numeric vector. These are the values to be used and
will override other options. For categorical moderators, a named list of numeric
vector, each vector has length equal to the number of indicator variables. If the
vector is named, the names will be used to label the values. For example, if set
to list(gp1 = c(0, 0), gp3 = c(0, 1), two levels will be returned, one
named gp1 with the indicator variables equal to 0 and 0, the other named gp3
with the indicator variables equal to 0 and 1. Default is NULL.
reference_group_label
For categorical moderator, if the label for the reference group (group with all in-
dicators equal to zero) cannot be determined, the default label is "Reference".
To change it, set reference_group_label to the desired label. Ignored if
values is set.
descending If TRUE (default), the rows are sorted in descending order for numerical moder-
ators: The highest value on the first row and the lowest values on the last row.
For user supplied values, the first value is on the last row and the last value is on
the first row. If FALSE, the rows are sorted in ascending order.
... The names of moderators variables. For a categorical variable, it should be a
vector of variable names.
merge If TRUE, mod_levels_list() will call merge_mod_levels() and return the
merged levels. Default is FALSE.

Details
It creates values of a moderator that can be used to compute conditional effect or conditional indirect
effect. By default, for a numeric moderator, it uses one standard deviation below mean, mean, and
one standard deviation above mean. The percentiles of these three levels in a normal distribution
(16th, 50th, and 84th) can also be used. For categorical variable, it will simply collect the unique
categories in the data.
mod_levels 87

The generated levels are then used by cond_indirect() and cond_indirect_effects().

If a model has more than one moderator, mod_levels_list() can be used to generate combinations
of levels. The output can then passed to cond_indirect_effects() to compute the conditional
effects or conditional indirect effects for all the combinations.

Value
mod_levels() returns a wlevels-class object which is a data frame with additional attributes about
the levels.
mod_levels_list() returns a list of wlevels-class objects, or a wlevels-class object which is a
data frame of the merged levels if merge = TRUE.

Functions
• mod_levels(): Generate levels for one moderator.
• mod_levels_list(): Generate levels for several moderators.

See Also
cond_indirect_effects() for computing conditional indiret effects; merge_mod_levels() for
merging levels of moderators.

Examples

library(lavaan)
data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w2_levels <- mod_levels(lm_out, w = "w2")
w2_levels
# Indirect effect from x to y through m, at the first levels of w1 and w2
cond_indirect(x = "x", y = "y", m = "m",
fit = lm_out,
wvalues = c(w1 = w1_levels$w1[1],
w2 = w2_levels$w2[1]))
# Can form the levels based on percentiles
w1_levels2 <- mod_levels(lm_out, w = "w1", w_method = "percentile")
w1_levels2
# Form the levels from a lavaan output
# Compute the product terms before fitting the model
dat$mw2 <- dat$m * dat$w2
mod <-
"
m ~ x + w1 + x:w1 + c1 + c2
y ~ m + x + w1 + w2 + mw2 + c1 + c2
88 plot.cond_indirect_effects

"
fit <- sem(mod, dat, fixed.x = FALSE)
cond_indirect(x = "x", y = "y", m = "m",
fit = fit,
wvalues = c(w1 = w1_levels$w1[1],
w2 = w2_levels$w2[1]))
# Can pass all levels to cond_indirect_effects()
# First merge the levels by merge_mod_levels()
w1w2_levels <- merge_mod_levels(w1_levels, w2_levels)
cond_indirect_effects(x = "x", y = "y", m = "m",
fit = fit,
wlevels = w1w2_levels)

# mod_levels_list() forms a combinations of levels in one call

# It returns a list, by default.
# Form the levels from a list of lm() outputs
# "merge = TRUE" is optional. cond_indirect_effects will merge the levels
# automatically.
w1w2_levels <- mod_levels_list("w1", "w2", fit = fit, merge = TRUE)
w1w2_levels
cond_indirect_effects(x = "x", y = "y", m = "m",
fit = fit, wlevels = w1w2_levels)
# Can work without merge = TRUE:
w1w2_levels <- mod_levels_list("w1", "w2", fit = fit)
w1w2_levels
cond_indirect_effects(x = "x", y = "y", m = "m",
fit = fit, wlevels = w1w2_levels)

plot.cond_indirect_effects
Plot Conditional Effects

Description
Plot the conditional effects for different levels of moderators.

Usage
## S3 method for class 'cond_indirect_effects'
plot(
x,
x_label,
w_label = "Moderator(s)",
y_label,
plot.cond_indirect_effects 89

title,
x_from_mean_in_sd = 1,
x_method = c("sd", "percentile"),
x_percentiles = c(0.16, 0.84),
x_sd_to_percentiles = NA,
note_standardized = TRUE,
no_title = FALSE,
line_width = 1,
point_size = 5,
graph_type = c("default", "tumble"),
...
)

Arguments
x The output of cond_indirect_effects(). (Named x because it is required in
the naming of arguments of the plot generic function.)
x_label The label for the X-axis. Default is the value of the predictor in the output of
cond_indirect_effects().
w_label The label for the legend for the lines. Default is "Moderator(s)".
y_label The label for the Y-axis. Default is the name of the response variable in the
model.
title The title of the graph. If not supplied, it will be generated from the variable
names or labels (in x_label, y_label, and w_label). If "", no title will be
printed. This can be used when the plot is for manuscript submission and figures
are required to have no titles.
x_from_mean_in_sd
How many SD from mean is used to define "low" and "high" for the focal vari-
able. Default is 1.
x_method How to define "high" and "low" for the focal variable levels. Default is in terms
of the standard deviation of the focal variable, "sd". If equal to "percentile",
then the percentiles of the focal variable in the dataset is used.
x_percentiles If x_method is "percentile", then this argument specifies the two percentiles
to be used, divided by 100. It must be a vector of two numbers. The default is
c(.16, .84), the 16th and 84th percentiles, which corresponds approximately
to one SD below and above mean for a normal distribution, respectively.
x_sd_to_percentiles
If x_method is "percentile" and this argument is set to a number, this number
will be used to determine the percentiles to be used. The lower percentile is
the percentile in a normal distribution that is x_sd_to_percentiles SD below
the mean. The upper percentile is the percentile in a normal distribution that is
x_sd_to_percentiles SD above the mean. Therefore, if x_sd_to_percentiles
is set to 1, then the lower and upper percentiles are 16th and 84th, respectively.
Default is NA.
note_standardized
If TRUE, will check whether a variable has SD nearly equal to one. If yes, will
report this in the plot. Default is TRUE.
90 plot.cond_indirect_effects

no_title If TRUE, title will be suppressed. Default is FALSE.

line_width The width of the lines as used in ggplot2::geom_segment(). Default is 1.
point_size The size of the points as used in ggplot2::geom_point(). Default is 5.
graph_type If "default", the typical line-graph with equal end-points will be plotted. If
"tubmle", then the tumble graph proposed by Bodner (2016) will be plotted.
Default is "default".
... Additional arguments. Ignored.

Details
This function is a plot method of the output of cond_indirect_effects(). It will use the levels
of moderators in the output.
It plots the conditional effect from x to y in a model for different levels of the moderators.
It does not support conditional indirect effects. If there is one or more mediators in x, it will raise
an error.

Value
A ggplot2 graph. Plotted if not assigned to a name. It can be further modified like a usual ggplot2
graph.

References
Bodner, T. E. (2016). Tumble graphs: Avoiding misleading end point extrapolation when graphing
interactions from a moderated multiple regression analysis. Journal of Educational and Behavioral
Statistics, 41(6), 593-604. doi:10.3102/1076998616657080

See Also
cond_indirect_effects()

Examples
library(lavaan)
dat <- modmed_x1m3w4y1
n <- nrow(dat)
set.seed(860314)
dat$gp <- sample(c("gp1", "gp2", "gp3"), n, replace = TRUE)
dat <- cbind(dat, factor2var(dat$gp, prefix = "gp", add_rownames = FALSE))

# Categorical moderator

mod <-
"
m3 ~ m1 + x + gpgp2 + gpgp3 + x:gpgp2 + x:gpgp3
y ~ m2 + m3 + x
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE)
out_mm_1 <- mod_levels(c("gpgp2", "gpgp3"),
predict.lm_from_lavaan 91

sd_from_mean = c(-1, 1),

fit = fit)
out_1 <- cond_indirect_effects(wlevels = out_mm_1, x = "x", y = "m3", fit = fit)
plot(out_1)
plot(out_1, graph_type = "tumble")

# Numeric moderator

dat <- modmed_x1m3w4y1

mod2 <-
"
m3 ~ m1 + x + w1 + x:w1
y ~ m3 + x
"
fit2 <- sem(mod2, dat, meanstructure = TRUE, fixed.x = FALSE)
out_mm_2 <- mod_levels("w1",
w_method = "percentile",
percentiles = c(.16, .84),
fit = fit2)
out_mm_2
out_2 <- cond_indirect_effects(wlevels = out_mm_2, x = "x", y = "m3", fit = fit2)
plot(out_2)
plot(out_2, graph_type = "tumble")

predict.lm_from_lavaan
Predicted Values of a ’lm_from_lavaan’-Class Object

Description

Compute the predicted values based on the model stored in a ’lm_from_lavaan‘-class object.

Usage

## S3 method for class 'lm_from_lavaan'

predict(object, newdata, ...)

Arguments

object A ’lm_from_lavaan’-class object.

newdata Required. A data frame of the new data. It must be a data frame.
... Additional arguments. Ignored.
92 predict.lm_from_lavaan_list

Details
An lm_from_lavaan-class method that converts a regression model for a variable in a lavaan
model to a formula object. This function uses the stored model to compute predicted values using
user-supplied data.
This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced
users and developers.

Value
A numeric vector of the predicted values, with length equal to the number of rows of user-supplied
data.

See Also
lm_from_lavaan_list()

Examples
library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list$m, newdata = tmp)
predict(fit_list$y, newdata = tmp)

predict.lm_from_lavaan_list
Predicted Values of an ’lm_from_lavaan_list’-Class Object

Description
It computes the predicted values based on the models stored in an ’lm_from_lavaan_list‘-class ob-
ject.

Usage
## S3 method for class 'lm_from_lavaan_list'
predict(object, x = NULL, y = NULL, m = NULL, newdata, ...)
predict.lm_from_lavaan_list 93

Arguments

object A ’lm_from_lavaan’-class object.

x The variable name at the start of a path.
y The variable name at the end of a path.
m Optional. The mediator(s) from x to y. A numeric vector of the names of the
mediators. The path goes from the first element to the last element. For example,
if m = c("m1", "m2"), then the path is x -> m1 -> m2 -> y.
newdata Required. A data frame of the new data. It must be a data frame.
... Additional arguments. Ignored.

Details

An lm_from_lavaan_list-class object is a list of lm_from_lavaan-class objects.

This is an advanced helper used by plot.cond_indirect_effects(). Exported for advanced
users and developers.

Value

A numeric vector of the predicted values, with length equal to the number of rows of user-supplied
data.

See Also

lm_from_lavaan_list()

Examples

library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
tmp <- data.frame(x = 1, c1 = 2, c2 = 3, m = 4)
predict(fit_list, x = "x", y = "y", m = "m", newdata = tmp)
94 predict.lm_list

predict.lm_list Predicted Values of an ’lm_list’-Class Object

Description
Compute the predicted values based on the models stored in an ’lm_list‘-class object.

Usage
## S3 method for class 'lm_list'
predict(object, x = NULL, y = NULL, m = NULL, newdata, ...)

Arguments
object An ’lm_list’-class object.
x The variable name at the start of a path.
y The variable name at the end of a path.
m Optional. The mediator(s) from x to y. A numeric vector of the names of the
mediators. The path goes from the first element to the last element. For example,
if m = c("m1", "m2"), then the path is x -> m1 -> m2 -> y.
newdata Required. A data frame of the new data. It must be a data frame.
... Additional arguments. Ignored.

Details
An lm_list-class object is a list of lm-class objects, this function is similar to the stats::predict()
method of lm() but it works on a system defined by a list of regression models.
This is an advanced helper used by some functions in this package. Exported for advanced users.

Value
A numeric vector of the predicted values, with length equal to the number of rows of user-supplied
data.

See Also
lm2list()

Examples
data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
print.all_paths 95

lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)

lm_serial_parallel
summary(lm_serial_parallel)
newdat <- data_serial_parallel[3:5, ]
predict(lm_serial_parallel,
x = "x",
y = "y",
m = "m2",
newdata = newdat)

print.all_paths Print ’all_paths’ Class Object

Description

Print the content of ’all_paths’-class object, which can be generated by all_indirect_paths().

Usage

## S3 method for class 'all_paths'

print(x, ...)

Arguments

x A ’all_paths’-class object.
... Optional arguments.

Details

This function is used to print the paths identified in a readable format.

Value

x is returned invisibly. Called for its side effect.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also

all_indirect_paths()
96 print.boot_out

Examples
library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)
# All indirect paths
out1 <- all_indirect_paths(fit)
out1

print.boot_out Print a boot_out-Class Object

Description
Print the content of the output of do_boot() or related functions.

Usage
## S3 method for class 'boot_out'
print(x, ...)

Arguments
x The output of do_boot(), or any boot_out-class object returned by similar
functions.
... Other arguments. Not used.

Value
x is returned invisibly. Called for its side effect.

Examples

data(data_med_mod_ab1)
dat <- data_med_mod_ab1
lm_m <- lm(m ~ x*w + c1 + c2, dat)
lm_y <- lm(y ~ m*w + x + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
# In real research, R should be 2000 or even 5000
# In real research, no need to set parallel to FALSE
print.cond_indirect_diff 97

# In real research, no need to set progress to FALSE

# Progress is displayed by default.
lm_boot_out <- do_boot(lm_out, R = 100,
seed = 1234,
progress = FALSE,
parallel = FALSE)
# Print the output of do_boot()
lm_boot_out

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
dat$"x:w" <- dat$x * dat$w
dat$"m:w" <- dat$m * dat$w
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(model = mod, data = dat, fixed.x = FALSE,
se = "none", baseline = FALSE)
# In real research, R should be 2000 or even 5000
# In real research, no need to set progress to FALSE
# In real research, no need to set parallel to FALSE
# Progress is displayed by default.
fit_boot_out <- do_boot(fit = fit,
R = 40,
seed = 1234,
parallel = FALSE,
progress = FALSE)
# Print the output of do_boot()
fit_boot_out

print.cond_indirect_diff
Print the Output of ’cond_indirect_diff’

Description

Print the output of cond_indirect_diff().

Usage

## S3 method for class 'cond_indirect_diff'

print(x, digits = 3, pvalue = FALSE, pvalue_digits = 3, se = FALSE, ...)
98 print.cond_indirect_effects

Arguments
x The output of cond_indirect_diff().
digits The number of decimal places in the printout.
pvalue Logical. If TRUE, asymmetric p-value based on bootstrapping will be printed if
available. Default is FALSE.
pvalue_digits Number of decimal places to display for the p-value. Default is 3.
se Logical. If TRUE and confidence intervals are available, the standard errors of
the estimates are also printed. They are simply the standard deviations of the
bootstrap estimates or Monte Carlo simulated values, depending on the method
used to form the confidence intervals.
... Optional arguments. Ignored.

Details
The print method of the cond_indirect_diff-class object.
If bootstrapping confidence interval was requested, this method has the option to print a p-value
computed by the method presented in Asparouhov and Muthén (2021). Note that this p-value is
asymmetric bootstrap p-value based on the distribution of the bootstrap estimates. It is not computed
based on the distribution under the null hypothesis.
For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of
its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a
confidence interval with a lower confidence level will exclude zero.

Value
It returns x invisibly. Called for its side effect.

References
Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download
Bootstrap%20-%20Pvalue.pdf

See Also
cond_indirect_diff()

print.cond_indirect_effects
Print a ’cond_indirect_effects’ Class Object

Description
Print the content of the output of cond_indirect_effects()
print.cond_indirect_effects 99

Usage
## S3 method for class 'cond_indirect_effects'
print(
x,
digits = 3,
annotation = TRUE,
pvalue = FALSE,
pvalue_digits = 3,
se = FALSE,
...
)

Arguments
x The output of cond_indirect_effects().
digits Number of digits to display. Default is 3.
annotation Logical. Whether the annotation after the table of effects is to be printed. Default
is TRUE.
pvalue Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if
available. Default is FALSE.
pvalue_digits Number of decimal places to display for the p-values. Default is 3.
se Logical. If TRUE and confidence intervals are available, the standard errors of
the estimates are also printed. They are simply the standard deviations of the
bootstrap estimates or Monte Carlo simulated values, depending on the method
used to form the confidence intervals.
... Other arguments. Not used.

Details
The print method of the cond_indirect_effects-class object.
If bootstrapping confidence intervals were requested, this method has the option to print p-values
computed by the method presented in Asparouhov and Muthén (2021). Note that these p-values
are asymmetric bootstrap p-values based on the distribution of the bootstrap estimates. They not
computed based on the distribution under the null hypothesis.
For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of
its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a
confidence interval with a lower confidence level will exclude zero.

Value
x is returned invisibly. Called for its side effect.

References
Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download
Bootstrap%20-%20Pvalue.pdf
100 print.delta_med

See Also

cond_indirect_effects()

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x + d1 * w1 + e1 * x:w1
m2 ~ a2 * x
y ~ b1 * m1 + b2 * m2 + cp * x
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)

# Conditional effects from x to m1 when w1 is equal to each of the default levels

cond_indirect_effects(x = "x", y = "m1",
wlevels = "w1", fit = fit)

# Conditional Indirect effect from x1 through m1 to y,

# when w1 is equal to each of the default levels
out <- cond_indirect_effects(x = "x", y = "y", m = "m1",
wlevels = "w1", fit = fit)
out

print(out, digits = 5)

print(out, annotation = FALSE)

print.delta_med Print a ’delta_med’ Class Object

Description

Print the content of a delta_med-class object.

Usage

## S3 method for class 'delta_med'

print(x, digits = 3, level = NULL, full = FALSE, ...)
print.delta_med 101

Arguments
x A delta_med-class object.
digits The number of digits after the decimal. Default is 3.
level The level of confidence of bootstrap confidence interval, if requested when cre-
ated. If NULL, the default, the level requested when calling delta_med() is used.
If not null, then this level will be used.
full Logical. Whether additional information will be printed. Default is FALSE.
... Optional arguments. Ignored.

Details
It prints the output of delta_med(), which is a delta_med-class object.

Value
x is returned invisibly. Called for its side effect.

Author(s)
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also
delta_med()

Examples

library(lavaan)
dat <- data_med
mod <-
"
m ~ x
y ~ m + x
"
fit <- sem(mod, dat)
dm <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit)
dm
print(dm, full = TRUE)

# Call do_boot() to generate

# bootstrap estimates
# Use 2000 or even 5000 for R in real studies
# Set parallel to TRUE in real studies for faster bootstrapping
boot_out <- do_boot(fit,
R = 45,
seed = 879,
102 print.indirect

parallel = FALSE,
progress = FALSE)
# Remove 'progress = FALSE' in practice
dm_boot <- delta_med(x = "x",
y = "y",
m = "m",
fit = fit,
boot_out = boot_out,
progress = FALSE)
dm_boot
confint(dm_boot)
confint(dm_boot,
level = .90)

print.indirect Print an ’indirect’ Class Object

Description
Print the content of the output of indirect_effect() or cond_indirect().

Usage
## S3 method for class 'indirect'
print(x, digits = 3, pvalue = FALSE, pvalue_digits = 3, se = FALSE, ...)

Arguments
x The output of indirect_effect() or cond_indirect().
digits Number of digits to display. Default is 3.
pvalue Logical. If TRUE, asymmetric p-value based on bootstrapping will be printed if
available.
pvalue_digits Number of decimal places to display for the p-value. Default is 3.
se Logical. If TRUE and confidence interval is available, the standard error of the
estimate is also printed. This is simply the standard deviation of the bootstrap
estimates or Monte Carlo simulated values, depending on the method used to
form the confidence interval.
... Other arguments. Not used.

Details
The print method of the indirect-class object.
If bootstrapping confidence interval was requested, this method has the option to print a p-value
computed by the method presented in Asparouhov and Muthén (2021). Note that this p-value is
asymmetric bootstrap p-value based on the distribution of the bootstrap estimates. It is not computed
based on the distribution under the null hypothesis.
print.indirect 103

For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of
its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a
confidence interval with a lower confidence level will exclude zero.
We recommend using confidence interval directly. Therefore, p-value is not printed by default.
Nevertheless, users who need it can request it by setting pvalue to TRUE.

Value
x is returned invisibly. Called for its side effect.

References
Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download
Bootstrap%20-%20Pvalue.pdf

See Also
indirect_effect() and cond_indirect()

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ a1 * x + b1 * w1 + d1 * x:w1
m2 ~ a2 * m1 + b2 * w2 + d2 * m1:w2
m3 ~ a3 * m2 + b3 * w3 + d3 * m2:w3
y ~ a4 * m3 + b4 * w4 + d4 * m3:w4
"
fit <- sem(mod, dat,
meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

wvalues <- c(w1 = 5, w2 = 4, w3 = 2, w4 = 3)

indirect_1 <- cond_indirect(x = "x", y = "y",

m = c("m1", "m2", "m3"),
fit = fit,
wvalues = wvalues)
indirect_1

dat <- modmed_x1m3w4y1

mod2 <-
"
m1 ~ a1 * x
m2 ~ a2 * m1
m3 ~ a3 * m2
y ~ a4 * m3 + x
"
104 print.indirect_list

fit2 <- sem(mod2, dat,

meanstructure = TRUE, fixed.x = FALSE,
se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

indirect_2 <- indirect_effect(x = "x", y = "y",

m = c("m1", "m2", "m3"),
fit = fit2)
indirect_2
print(indirect_2, digits = 5)

print.indirect_list Print an ’indirect_list’ Class Object

Description
Print the content of the output of many_indirect_effects().

Usage
## S3 method for class 'indirect_list'
print(
x,
digits = 3,
annotation = TRUE,
pvalue = FALSE,
pvalue_digits = 3,
se = FALSE,
...
)

Arguments
x The output of many_indirect_effects().
digits Number of digits to display. Default is 3.
annotation Logical. Whether the annotation after the table of effects is to be printed. Default
is TRUE.
pvalue Logical. If TRUE, asymmetric p-values based on bootstrapping will be printed if
available.
pvalue_digits Number of decimal places to display for the p-values. Default is 3.
se Logical. If TRUE and confidence intervals are available, the standard errors of
the estimates are also printed. They are simply the standard deviations of the
bootstrap estimates or Monte Carlo simulated values, depending on the method
used to form the confidence intervals.
... Other arguments. Not used.
print.indirect_list 105

Details
The print method of the indirect_list-class object.
If bootstrapping confidence interval was requested, this method has the option to print a p-value
computed by the method presented in Asparouhov and Muthén (2021). Note that this p-value is
asymmetric bootstrap p-value based on the distribution of the bootstrap estimates. It is not computed
based on the distribution under the null hypothesis.
For a p-value of a, it means that a 100(1 - a)% bootstrapping confidence interval will have one of
its limits equal to 0. A confidence interval with a higher confidence level will include zero, while a
confidence interval with a lower confidence level will exclude zero.

Value
x is returned invisibly. Called for its side effect.

References
Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download
Bootstrap%20-%20Pvalue.pdf

See Also
many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)
# All indirect paths from x to y
paths <- all_indirect_paths(fit,
x = "x",
y = "y")
paths
# Indirect effect estimates
out <- many_indirect_effects(paths,
fit = fit)
out
106 print.indirect_proportion

print.indirect_proportion
Print an ’indirect_proportion’-Class Object

Description
Print the content of an ’indirect_proportion’-class object, the output of indirect_proportion().

Usage
## S3 method for class 'indirect_proportion'
print(x, digits = 3, annotation = TRUE, ...)

Arguments
x An ’indirect_proportion’-class object.
digits Number of digits to display. Default is 3.
annotation Logical. Whether additional information should be printed. Default is TRUE.
... Optional arguments. Not used.

Details
The print method of the indirect_proportion-class object, which is produced by indirect_proportion().
In addition to the proportion of effect mediated, it also prints additional information such as the path
for which the proportion is computed, and all indirect path(s) from the x-variable to the y-variable.
To get the proportion as a scalar, use the coef method of indirect_proportion objects.

Value
x is returned invisibly. Called for its side effect.

See Also
indirect_proportion()

Examples

library(lavaan)
dat <- data_med
head(dat)
mod <-
"
m ~ x + c1 + c2
y ~ m + x + c1 + c2
"
fit <- sem(mod, dat, fixed.x = FALSE)
print.lm_list 107

out <- indirect_proportion(x = "x",

y = "y",
m = "m",
fit = fit)
out
print(out, digits = 5)

print.lm_list Print an lm_list-Class Object

Description

Print the content of the output of lm2list().

Usage

## S3 method for class 'lm_list'

print(x, ...)

Arguments

x The output of lm2list().

... Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Examples

data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
108 print.mc_out

print.mc_out Print a mc_out-Class Object

Description

Print the content of the output of do_mc() or related functions.

Usage

## S3 method for class 'mc_out'

print(x, ...)

Arguments

x The output of do_mc(), or any mc_out-class object returned by similar func-

tions.
... Other arguments. Not used.

Value

x is returned invisibly. Called for its side effect.

Examples

library(lavaan)
data(data_med_mod_ab1)
dat <- data_med_mod_ab1
mod <-
"
m ~ x + w + x:w + c1 + c2
y ~ m + w + m:w + x + c1 + c2
"
fit <- sem(mod, dat)
# In real research, R should be 5000 or even 10000
mc_out <- do_mc(fit, R = 100, seed = 1234)

# Print the output of do_boot()

mc_out
simple_mediation_latent 109

simple_mediation_latent
Sample Dataset: A Simple Latent Mediation Model

Description

Generated from a simple mediation model among xthree latent factors, fx, fm, and fy, xeach has
three indicators.

Usage

simple_mediation_latent

Format

A data frame with 200 rows and 11 variables:

x1 Indicator of fx. Numeric.

x2 Indicator of fx. Numeric.
x3 Indicator of fx. Numeric.
m1 Indicator of fm. Numeric.
m2 Indicator of fm. Numeric.
m3 Indicator of fm. Numeric.
y1 Indicator of fy. Numeric.
y2 Indicator of fy. Numeric.
y3 Indicator of fy. Numeric.

Details

The model:

fx =~ x1 + x2 + x3
fm =~ m1 + m2 + m3
fy =~ y1 + y2 + y3
fm ~ a * fx
fy ~ b * fm + cp * fx
indirect := a * b
110 subsetting_cond_indirect_effects

subsetting_cond_indirect_effects
Extraction Methods for ’cond_indirect_effects’ Outputs

Description
For subsetting a ’cond_indirect_effects’-class object.

Usage
## S3 method for class 'cond_indirect_effects'
x[i, j, drop = if (missing(i)) TRUE else length(j) == 1]

Arguments
x A ’cond_indirect_effects’-class object.
i A numeric vector of row number(s), a character vector of row name(s), or a
logical vector of row(s) to be selected.
j A numeric vector of column number(s), a character vector of column name(s),
or a logical vector of column(s) to be selected.
drop Whether dropping a dimension if it only have one row/column.

Details
Customized [ for ’cond_indirect_effects’-class objects, to ensure that these operations work as
they would be on a data frame object, while information specific to conditional effects is modified
correctly.

Value
A ’cond_indirect_effects’-class object. See cond_indirect_effects() for details on this class.

Examples

library(lavaan)
dat <- modmed_x1m3w4y1
mod <-
"
m1 ~ x + w1 + x:w1
m2 ~ m1
y ~ m2 + x + w4 + m2:w4
"
fit <- sem(mod, dat, meanstructure = TRUE, fixed.x = FALSE, se = "none", baseline = FALSE)
est <- parameterEstimates(fit)

# Examples for cond_indirect():

subsetting_wlevels 111

# Conditional effects from x to m1 when w1 is equal to each of the levels

out1 <- cond_indirect_effects(x = "x", y = "m1",
wlevels = "w1", fit = fit)
out1[2, ]

# Conditional Indirect effect from x1 through m1 to y,

# when w1 is equal to each of the levels
out2 <- cond_indirect_effects(x = "x", y = "y", m = c("m1", "m2"),
wlevels = c("w1", "w4"), fit = fit)
out2[c(1, 3), ]

subsetting_wlevels Extraction Methods for a ’wlevels’-class Object

Description
For subsetting a ’wlevels’-class object. Attributes related to the levels will be preserved if appropri-
ate.

Usage
## S3 method for class 'wlevels'
x[i, j, drop = if (missing(i)) TRUE else length(j) == 1]

## S3 replacement method for class 'wlevels'

x[i, j] <- value

## S3 replacement method for class 'wlevels'

x[[i, j]] <- value

Arguments
x A ’wlevels’-class object.
i A numeric vector of row number(s), a character vector of row name(s), or a
logical vector of row(s) to be selected.
j A numeric vector of column number(s), a character vector of column name(s),
or a logical vector of column(s) to be selected.
drop Whether dropping a dimension if it only have one row/column.
value Ignored.

Details
Customized [ for ’wlevels’-class objects, to ensure that these operations work as they would be on
a data frame object, while information specific to a wlevels-class object modified correctly.
The assignment methods [<- and [[<- for wlevels-class objects will raise an error. This class of
objects should be created by mod_levels() or related functions.
112 summary.lm_list

Subsetting the output of mod_levels() is possible but not recommended. It is more reliable to
generate the levels using mod_levels() and related functions. Nevertheless, there are situations in
which subsetting is preferred.

Value
A ’wlevels’-class object. See mod_levels() and merge_mod_levels() for details on this class.

See Also
mod_levels(), mod_levels_list(), and merge_mod_levels()

Examples

data(data_med_mod_ab)
dat <- data_med_mod_ab
# Form the levels from a list of lm() outputs
lm_m <- lm(m ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m*w2 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m, lm_y)
w1_levels <- mod_levels(lm_out, w = "w1")
w1_levels
w1_levels[2, ]
w1_levels[c(2, 3), ]

dat <- data_med_mod_serial_cat

lm_m1 <- lm(m1 ~ x*w1 + c1 + c2, dat)
lm_y <- lm(y ~ m1 + x + w1 + c1 + c2, dat)
lm_out <- lm2list(lm_m1, lm_y)
w1gp_levels <- mod_levels(lm_out, w = "w1")
w1gp_levels
w1gp_levels[2, ]
w1gp_levels[3, ]

merged_levels <- merge_mod_levels(w1_levels, w1gp_levels)

merged_levels

merged_levels[4:6, ]
merged_levels[1:3, c(2, 3)]
merged_levels[c(1, 4, 7), 1, drop = FALSE]

summary.lm_list Summary of an lm_list-Class Object

Description
The summary of content of the output of lm2list().
terms.lm_from_lavaan 113

Usage
## S3 method for class 'lm_list'
summary(object, ...)

## S3 method for class 'summary_lm_list'

print(x, digits = 3, ...)

Arguments
object The output of lm2list().
... Other arguments. Not used.
x An object of class summary_lm_list.
digits The number of significant digits in printing numerical results.

Value
summary.lm_list() returns a summary_lm_list-class object, which is a list of the summary()
outputs of the lm() outputs stored.
print.summary_lm_list() returns x invisibly. Called for its side effect.

Functions
• print(summary_lm_list): Print method for output of summary for lm_list.

Examples

data(data_serial_parallel)
lm_m11 <- lm(m11 ~ x + c1 + c2, data_serial_parallel)
lm_m12 <- lm(m12 ~ m11 + x + c1 + c2, data_serial_parallel)
lm_m2 <- lm(m2 ~ x + c1 + c2, data_serial_parallel)
lm_y <- lm(y ~ m11 + m12 + m2 + x + c1 + c2, data_serial_parallel)
# Join them to form a lm_list-class object
lm_serial_parallel <- lm2list(lm_m11, lm_m12, lm_m2, lm_y)
lm_serial_parallel
summary(lm_serial_parallel)

terms.lm_from_lavaan Model Terms of an ’lm_from_lavaan’-Class Object

Description
It extracts the terms object from an lm_from_lavaan-class object.
114 total_indirect_effect

Usage
## S3 method for class 'lm_from_lavaan'
terms(x, ...)

Arguments
x An ’lm_from_lavaan’-class object.
... Additional arguments. Ignored.

Details
A method for lm_from_lavaan-class that converts a regression model for a variable in a lavaan
model to a formula object. This function simply calls stats::terms() on the formula object to
extract the predictors of a variable.

Value
A terms-class object. See terms.object for details.

See Also
terms.object, lm_from_lavaan_list()

Examples
library(lavaan)
data(data_med)
mod <-
"
m ~ a * x + c1 + c2
y ~ b * m + x + c1 + c2
"
fit <- sem(mod, data_med, fixed.x = FALSE)
fit_list <- lm_from_lavaan_list(fit)
terms(fit_list$m)
terms(fit_list$y)

total_indirect_effect Total Indirect Effect Between Two Variables

Description
Compute the total indirect effect between two variables in the paths estimated by many_indirect_effects().

Usage
total_indirect_effect(object, x, y)
total_indirect_effect 115

Arguments
object The output of many_indirect_effects(), or a list of indirect-class objects.
x Character. The name of the x variable. All paths start from x will be included.
y Character. The name of the y variable. All paths end at y will be included.

Details
It extracts the indirect-class objects of relevant paths and then add the indirect effects together
using the + operator.

Value
An indirect-class object.

See Also
many_indirect_effects()

Examples

library(lavaan)
data(data_serial_parallel)
mod <-
"
m11 ~ x + c1 + c2
m12 ~ m11 + x + c1 + c2
m2 ~ x + c1 + c2
y ~ m12 + m2 + m11 + x + c1 + c2
"
fit <- sem(mod, data_serial_parallel,
fixed.x = FALSE)

# All indirect paths, control variables excluded

paths <- all_indirect_paths(fit,
exclude = c("c1", "c2"))
paths

# Indirect effect estimates

out <- many_indirect_effects(paths,
fit = fit)
out

# Total indirect effect from x to y

total_indirect_effect(out,
x = "x",
y = "y")
Index

∗ datasets check_path, 6
data_med, 31 coef.cond_indirect_diff, 7
data_med_complicated, 31 coef.cond_indirect_diff(), 23, 69
data_med_mod_a, 32 coef.cond_indirect_effects, 8
data_med_mod_ab, 33 coef.cond_indirect_effects(), 20
data_med_mod_ab1, 34 coef.delta_med, 9
data_med_mod_b, 35 coef.delta_med(), 54, 55
data_med_mod_b_mod, 36 coef.indirect, 10
data_med_mod_parallel, 37 coef.indirect(), 20, 74
data_med_mod_parallel_cat, 38 coef.indirect_list, 12
data_med_mod_serial, 39 coef.indirect_proportion, 13
data_med_mod_serial_cat, 40 coef.indirect_proportion(), 76
data_med_mod_serial_parallel, 41 coef.lm_from_lavaan, 14
data_med_mod_serial_parallel_cat, cond_indirect, 15
42 cond_indirect(), 10, 11, 18–21, 28, 29,
data_mod, 43 55–58, 64, 68, 69, 71, 74, 79, 81, 82,
data_mod2, 43 85, 87, 102, 103
data_mod_cat, 44 cond_indirect_diff, 22
data_mome_demo, 45 cond_indirect_diff(), 7, 8, 23–25, 97, 98
data_mome_demo_missing, 46 cond_indirect_effects, 64
data_parallel, 47 cond_indirect_effects (cond_indirect),
data_sem, 48 15
data_serial, 49 cond_indirect_effects(), 8, 18–20, 22, 23,
data_serial_parallel, 50 25, 26, 55–58, 61, 63, 64, 68–70, 73,
data_serial_parallel_latent, 51 74, 78, 79, 83, 85, 87, 89, 90,
modmed_x1m3w4y1, 84 98–100, 110
simple_mediation_latent, 109 confint.cond_indirect_diff, 24
+.indirect (math_indirect), 81 confint.cond_indirect_diff(), 23, 69
-.indirect (math_indirect), 81 confint.cond_indirect_effects, 25
[.cond_indirect_effects confint.cond_indirect_effects(), 20
(subsetting_cond_indirect_effects), confint.delta_med, 26
110 confint.delta_med(), 54, 55
[.wlevels (subsetting_wlevels), 111 confint.indirect, 28
[<-.wlevels (subsetting_wlevels), 111 confint.indirect(), 20, 74
[[<-.wlevels (subsetting_wlevels), 111 confint.indirect_list, 29

all_indirect_paths, 4 data_med, 31
all_indirect_paths(), 4, 5, 19, 95 data_med_complicated, 31
all_paths_to_df (all_indirect_paths), 4 data_med_mod_a, 32
all_paths_to_df(), 4 data_med_mod_ab, 33

116
INDEX 117

data_med_mod_ab1, 34 index_of_momome(), 23, 69

data_med_mod_b, 35 indirect_effect (cond_indirect), 15
data_med_mod_b_mod, 36 indirect_effect(), 4, 5, 10, 11, 18–21, 28,
data_med_mod_parallel, 37 29, 55–58, 61, 63, 64, 68, 69, 71, 73,
data_med_mod_parallel_cat, 38 74, 78, 79, 81, 82, 85, 102, 103
data_med_mod_serial, 39 indirect_effects_from_list, 71
data_med_mod_serial_cat, 40 indirect_i, 73
data_med_mod_serial_parallel, 41 indirect_proportion, 75
data_med_mod_serial_parallel_cat, 42 indirect_proportion(), 13, 106
data_mod, 43
data_mod2, 43 lavaan, 6, 18, 68
data_mod_cat, 44 lavaan::lav_model_implied(), 54
data_mome_demo, 45, 47 lavaan::lav_model_set_parameters(), 54
data_mome_demo_missing, 46 lavaan::lavaan, 6, 17, 53, 61, 62, 66, 68, 73,
data_parallel, 47 76, 85
data_sem, 48 lavaan::lavaan(), 4, 80
data_serial, 49 lavaan::lavInspect(), 17, 54, 73
data_serial_parallel, 50 lavaan::parameterEstimates(), 6, 17, 66,
data_serial_parallel_latent, 51 73
delta_med, 52 lavaan::sem(), 4, 15, 19, 20, 56, 58, 60–62,
delta_med(), 9, 10, 26, 27, 101 66, 79
do_boot, 21, 55 lm(), 4, 6, 15, 17–19, 56, 66, 68, 73, 76, 78,
do_boot(), 18, 20, 53, 58, 61, 62, 68, 78, 96 79, 85, 94, 113
do_mc, 57 lm2boot_out, 77
do_mc(), 18, 20, 63, 69, 108 lm2boot_out(), 56, 57
lm2boot_out_parallel (lm2boot_out), 77
factor2var, 59 lm2list, 79
fit2boot_out, 60
lm2list(), 4, 5, 56, 68, 77, 78, 94, 107, 112,
fit2boot_out(), 56, 57, 61
113
fit2boot_out_do_boot (fit2boot_out), 60
lm_from_lavaan_list, 80
fit2boot_out_do_boot(), 56, 57, 61
lm_from_lavaan_list(), 14, 92, 93, 114
fit2mc_out, 62
fit2mc_out(), 59, 63
many_indirect_effects (cond_indirect),
gen_mc_est (do_mc), 57 15
get_one_cond_effect many_indirect_effects(), 5, 12, 19, 29, 30,
(get_one_cond_indirect_effect), 71, 72, 104, 105, 114, 115
64 math_indirect, 20, 81
get_one_cond_indirect_effect, 64 merge_mod_levels, 83
get_one_cond_indirect_effect(), 64 merge_mod_levels(), 19, 21, 23, 86, 87, 112
get_prod, 65 mod_levels, 85
ggplot2, 90 mod_levels(), 21, 23, 83, 86, 87, 111, 112
ggplot2::geom_point(), 90 mod_levels_list (mod_levels), 85
ggplot2::geom_segment(), 90 mod_levels_list(), 19, 83, 86, 87, 112
modmed_x1m3w4y1, 84
igraph::all_simple_paths(), 4
index_of_mome, 67 parallel::detectCores(), 18, 56, 61, 77
index_of_mome(), 23, 69 parallel::makeCluster(), 18, 56, 61, 77
index_of_momome (index_of_mome), 67 plot.cond_indirect_effects, 88
118 INDEX

plot.cond_indirect_effects(), 14, 81, 92,

93
predict.lm_from_lavaan, 91
predict.lm_from_lavaan_list, 81, 92
predict.lm_from_lavaan_list(), 81
predict.lm_list, 94
print.all_paths, 95
print.boot_out, 96
print.cond_indirect_diff, 97
print.cond_indirect_diff(), 23, 69
print.cond_indirect_effects, 98
print.cond_indirect_effects(), 20
print.delta_med, 100
print.delta_med(), 54, 55
print.indirect, 102
print.indirect(), 20, 74
print.indirect_list, 104
print.indirect_proportion, 106
print.indirect_proportion(), 76
print.lm_list, 107
print.lm_list(), 79
print.mc_out, 108
print.summary_lm_list
(summary.lm_list), 112
print.summary_lm_list(), 113

semTools::runMI(), 6, 17, 58, 62, 66, 68, 73,

76, 85
semTools::sem.mi(), 6, 15, 17, 58, 62, 66,
68, 73, 76, 85
simple_mediation_latent, 109
stats::lm(), 58
stats::predict(), 94
stats::terms(), 114
subsetting_cond_indirect_effects, 110
subsetting_wlevels, 111
summary(), 113
summary.lm_list, 112
summary.lm_list(), 79, 113

terms.lm_from_lavaan, 113
terms.object, 114
total_indirect_effect, 114