6

ASSESSING PLS-SEM
RESULTS PART III
Evaluation of the Structural Model
CASE STUDY ILLUSTRATION—HOW ARE
PLS-SEM STRUCTURAL MODEL RESULTS
REPORTED?
We continue with the extended corporate reputation model as introduced
in Chapter 5. If you do not have the PLS path model readily available in
SmartPLS 4, download the file Corporate Reputation.zip from the https://
www.pls-sem.net website and save it on your hard drive. Then, run the
SmartPLS software and click on Files → Import project from backup file in the
menu. In the box that appears on the screen, locate and open the Corporate
Reputation.zip file that you just downloaded. Thereafter, a new project ap-
pears with the name Corporate Reputation in the SmartPLS Workspace win-
dow on the left-hand side. This project contains several models (.splsm files)
labeled Simple model, Extended model, Redundancy analysis ATTR, Redundan-
cy analysis CSOR, and so forth, plus the data set Corporate reputation data.csv.
Alternately, you see in the main screen of the Workspace view, under Sample
projects, the Corporate reputation—PLS-SEM book (primer) example. After
clicking on the link with the label Install next to this sample project, the Ex-
ample—Corporate reputation (primer) project will appear in the Workspace.
Next, double-click on Extended model, and the extended PLS path model for
the corporate reputation example to open.
The assessment of the structural model builds on the results from the stan-
dard model estimation, the bootstrapping routine, and the PLSpredict proce-
2 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

dure. After running the PLS-SEM algorithm using the same algorithm and
missing values settings as in the previous chapters, SmartPLS shows the key
results of the model estimation in the Modeling window (Exhibit A6.1). Per
default, we see the path coefficients as well as the R2 values of the endogenous
constructs (shown in the circles).
For a more detailed assessment, we need to examine the SmartPLS results
report. Following the structural model assessment procedure (Exhibit 6.1),
we first need to check the structural model for collinearity issues by examin-
ing the VIF values of all sets of predictor constructs in the structural model.
To do so, go to Quality criteria → Collinearity statistics (VIF) and click on the
Inner model tab. The results table that opens (Exhibit A6.2) shows the VIF
values of all combinations of endogenous constructs (represented by the col-
umns) and corresponding exogenous (i.e., predictor) constructs (represented
by the rows). Specifically, we assess the following sets of (predictor) constructs
for collinearity: (1) ATTR, CSOR, PERF, and QUAL as predictors of COMP
(and LIKE); (2) COMP and LIKE as predictors of CUSA; and (3) COMP,
LIKE, and CUSA as predictors of CUSL. As can be seen in Exhibit A6.2, all
VIF values are clearly below the threshold of 5 and with two exceptions (i.e.,
the QUAL predictor) below 3. Since the two exceptions are close to 3, we
conclude that collinearity among the predictor constructs is not a critical is-
sue in the structural model, and we can continue examining the results re-
port.
The second step of the structural model assessment procedure (Exhibit 6.1)
involves assessing the significance and relevance of the structural model rela-
tionships. Starting with the relevance assessment, go to Final results → Path
coefficients, where we find the path coefficients as shown in the modeling
window in three formats: matrix, list and bar charts. Looking at the relative
importance of the driver constructs for the perceived competence (COMP),
one finds that the customers’ perception of the company’s quality of products
and services (QUAL) is most important, followed by its performance (PERF).
In contrast, the perceived attractiveness (ATTR) and degree to which the
company acts in socially conscious ways (CSOR) have very little bearing on
COMP. These two drivers are, however, of increased importance for establish-
ing a company’s likeability (LIKE). Moving on in the model, we also find that
likeability is the primary driver for the customers’ satisfaction and loyalty, as
illustrated by the increased path coefficients compared with those of COMP.
More interesting, though, is the examination of total effects. Specifically,
we can evaluate how strongly each of the four formative driver constructs
(ATTR, CSOR, PERF, and QUAL) ultimately influences the key target vari-
able CUSL via the mediating constructs COMP, LIKE, and CUSA. Total ef-
fects are shown under Final results → Total effects in the results report. We
read the table shown in Exhibit A6.3 column to row. That is, each column
represents a target construct, whereas the rows represent predecessor con-
structs. For example, with regard to loyalty, we can see that among the four
 Chapter 6 ■ Assessing PLS-SEM Results Part III 3

Exhibit A6.1 ■ Results in Modeling Window

4 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

Exhibit A6.2 ■ VIF Values in the Structural Model

Exhibit A6.3 ■ Total effects

exogenous driver constructs, quality has the strongest total effect on loyalty
(0.248), followed by corporate social responsibility (0.105), attractiveness
(0.101), and performance (0.089). Therefore, it is advisable for companies to
focus on marketing activities that positively influence the customers’ percep-
tion of the quality of their products and services. By also taking the con-
struct’s indicator weights into consideration, we can even identify which spe-
cific element of quality needs to be addressed. Looking at the outer weights
(Final results → Outer weights) reveals that qual_6 has the highest outer
weight (0.398). This item relates to the survey question “[the company] is a
reliable partner for customers.” Thus, marketing managers should try to en-
hance the customers’ perception of the reliability of their products and ser-
vices by means of marketing activities.
The analysis of the structural model relationships shows that several path
coefficients (e.g., COMP → CUSL) have rather low values. To assess whether
these relationships are significant (Exhibit 6.1), we run the bootstrapping
procedure. The extraction of bootstrapping results for the structural model
 Chapter 6 ■ Assessing PLS-SEM Results Part III 5

estimates is analogous to the descriptions in the context of formative mea-

surement model assessment (Chapter 5). To run the bootstrapping proce-
dure, go to Calculate → Bootstrapping in the SmartPLS menu or go to the
Modeling window and click on the Calculate icon, followed by Bootstrapping
(note that you first may need to go back to the Modeling window before the
Calculate icon appears). We retain all settings for missing value treatment and
the PLS-SEM algorithm as in the initial model estimation and select Do par-
allel processing option, 10,000 bootstrap samples and select the Complete
(slower) option. In the BT setup we choose Percentile Bootstrap as a Confidence
interval method, Two tailed testing, a significance level of 0.05, and select
Fixed seed. Next, we click Start calculation.
After running the procedure, SmartPLS shows the bootstrapping results
for the measurement models and structural model in the Modeling window.
Using the combo boxes available on the screen under the menu, you can
choose whether SmartPLS should display t values or p values in the Modeling
window. Exhibit A6.4 shows p values for the structural model relationships as
resulting from the bootstrapping procedure.
By going to the bootstrapping report, we get a more detailed overview of
the results. The table under Final results → Path coefficients provides us with
an overview of results, including standard errors, bootstrap mean values, t val-
ues and p values. Clicking on the Confidence intervals tab in the bootstrap-
ping results report shows the confidence interval as derived from the percen-
tile method without and with bias correction. Exhibit A6.5 shows the latter
result.
Finally, clicking on the Samples tab in the bootstrapping results report
shows the results of each bootstrap run as shown in Exhibit A6.6. The dis-
played table includes the estimates of all the path coefficients for all 10,000
subsamples. These estimates are used to compute the bootstrapping mean
values, standard errors, t values, and p values of all the path coefficients,
shown in the Mean, STDEV, T values, and P values table of the bootstrapping
results report.
Exhibit A6.7 provides a summary of the path coefficient estimates, t val-
ues, p values, and confidence intervals. Again, researchers usually report ei-
ther the t values (and their significance levels) or the p values or the confi-
dence intervals. We find that all criteria come to the same outcome for the
significance of path coefficients. Otherwise, we recommend relying on the
bootstrap confidence intervals for significance testing (see Chapter 5 for de-
tails). Exhibit A6.7 shows all results only for illustrative purposes.
Assuming a 5% significance level, we focus on the 95% bootstrap confidence
interval obtained by the percentile approach with bias correction and find that all
relationships in the structural model are significant, except PERF → LIKE, ATTR
→ COMP, CSOR → COMP, and COMP → CUSL (Exhibit A6.7). These results
suggest that companies should concentrate their marketing efforts on enhancing
their LIKE (by strengthening QUAL) rather than their COMP to maximize CUSL.
6 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

Exhibit A6.4 ■ Bootstrapping p values in the Modeling Window

 Chapter 6 ■ Assessing PLS-SEM Results Part III 7

Exhibit A6.5 ■ Percentile Confidence Intervals (with Bias Correction)

for the Path Coefficients

Exhibit A6.6 ■ Bootstrap Samples

8 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

Exhibit A6.7 ■ Significance Testing Results of the Structural Model

Path Coefficients

Path t Values p Values 95% Confi- Significancea

Coefficients dence Intervals (p < 0.05)?
(With Bias
Correction)

ATTR → COMP 0.086 1.579 0.114 [-0.016;0.195] No

ATTR → LIKE 0.167 2.666 0.008 [0.044;0.292] Yes

COMP → CUSA 0.146 2.173 0.030 [0.012;0.279] Yes

COMP → CUSL 0.006 0.103 0.918 [-0.100;0.114] No

CSOR → COMP 0.059 1.086 0.278 [-0.048;0.164] No

CSOR → LIKE 0.178 3.200 0.001 [0.067;0.284] Yes

CUSA → CUSL 0.505 11.960 0.000 [0.420;0.584] Yes

LIKE → CUSA 0.436 7.381 0.000 [0.316;0.545] Yes

LIKE → CUSL 0.344 6.207 0.000 [0.236;0.451] Yes

PERF → COMP 0.295 4.457 0.000 [0.162;0.418] Yes

PERF → LIKE 0.117 1.684 0.092 [-0.022;0.252] No

QUAL → COMP 0.430 6.400 0.000 [0.299;0.558] Yes

QUAL → LIKE 0.380 5.834 0.000 [0.246;0.500] Yes

a
We refer to the bootstrap confidence intervals for significance testing, as described in Chapter 5.

This is not surprising, considering that customers rated mobile network oper-
ators. As their services (provision of network capabilities) are intangible, af-
fective judgments play a much more important role than cognitive judgments
for establishing customer loyalty. Furthermore, we learn that ATTR and
CSOR only influence LIKE, which is also not surprising since these two driv-
er constructs are also more affective in nature.
To examine the bootstrapping results for the total effects, go to Final re-
sults → Total effects. Exhibit A6.8 summarizes the results for the total effects
of the exogenous constructs ATTR, CSOR, PERF, and QUAL on the target
constructs CUSA and CUSL taken from the Mean, STDEV, T values, P values
table of the bootstrapping results report. As can be seen, all total effects are
significant at a 5% level.
Next, we turn our attention to the assessment of the model’s explanatory
power as called for in the third step of the structural model assessment proce-
dure (Exhibit 6.1). To do so, we go back to the SmartPLS results report as
produced after running the PLS-SEM algorithm (not bootstrapping).
 Chapter 6 ■ Assessing PLS-SEM Results Part III 9

Exhibit A6.8 ■ Significance Testing Results of the Total Effects

Total Effect t Values p Values 95% Confi- Significancea

dence Intervals (p < 0.05)?
(With Bias
Correction)

ATTR → CUSA 0.086 2.817 0.005 [0.029;0.149] Yes

ATTR → CUSL 0.101 2.740 0.006 [0.030;0.176] Yes

COMP → CUSL 0.074 2.117 0.034 [0.006;0.145] Yes

CSOR → CUSA 0.086 3.142 0.002 [0.035;0.143] Yes

CSOR → CUSL 0.105 3.107 0.002 [0.042;0.175] Yes

LIKE → CUSL 0.220 6.282 0.000 [0.153;0.292] Yes

PERF → CUSA 0.094 2.454 0.014 [0.016;0.168] Yes

PERF → CUSL 0.089 2.034 0.042 [-0.001;0.174] Yes

QUAL → CUSA 0.228 6.189 0.000 [0.155;0.301] Yes

QUAL → CUSL 0.248 5.788 0.000 [0.160;0.331] Yes

a
We refer to the bootstrap confidence intervals for significance testing, as described in Chapter 5.

To start with, we examine the R 2 values of the endogenous latent variables,

which are available under Quality criteria → R-square (select the Overview tab
for the matrix view). Following our rules of thumb, the R 2 values of COMP
(0.631), CUSL (0.562), and LIKE (0.558) can be considered moderate,
whereas the R 2 value of CUSA (0.292) is rather weak.
To obtain the effect sizes f 2 for all structural model relationships, go to
Quality criteria → f-square (select the Matrix view). Exhibit A6.9 shows the
f 2 values for all combinations of endogenous constructs (represented by the
columns) and corresponding exogenous (i.e., predictor) constructs (repre-
sented by the rows). For example, LIKE has a medium effect size of 0.159 on
CUSA and of 0.138 on CUSL. On the contrary, COMP has no effect on
CUSA (0.018) or CUSL (0.000). Please note these results differ from a manu-
al computation of the f 2 values by using the aforementioned equation with
2
values for Rincluded 2
and Rexcluded . This difference results because SmartPLS uses
the latent variable scores of the model that includes all latent variables and
2
then internally excludes latent variables to obtain the Rexcluded . On the con-
2
trary, when manually computing the f values by estimating the model with
and without a latent variable, the model changes and, thus, so do the latent
variable scores. Hence, the difference of the manually computed f 2 values re-
sults from the changes in the latent variable scores due to a model modifica-
tion which is, however, incorrect.
10 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

Exhibit A6.9 ■ f 2 Effect Sizes

The fourth step of the structural model assessment procedure (Exhibit 6.1)
requires assessing the model’s predictive power using PLSpredict. To initiate the
procedure, go to Calculate → PLSpredict/CVPAT in the SmartPLS menu or
go to the Modeling window and click on the Calculate icon, followed by
PLSpredict/CVPAT. In the dialog box that opens, we retain the default set-
tings. That is, we run PLSpredict with 10 folds and 10 repetitions and select the
Fixed seed option. To initiate the analysis, click on Start calculation.

Exhibit A6.10 ■ PLSpredict Results Report

Exhibit A6.10 shows the PLSpredict results report. To access the PLS and
LM benchmarks model’s results, go to Final results → MV prediction summary
and select the Overview tab in the results report. We focus our analysis on the
model’s key target construct CUSL and consider the RMSE as the default
metric for interpreting the prediction error of the construct’s indicators. In an
initial step, we interpret the Q2predict values. The analysis shows that all three
 Chapter 6 ■ Assessing PLS-SEM Results Part III 11

2
indicators (i.e., cusl_1, cusl_2, and cusl_3) have Qpredict values larger than
zero, suggesting that the PLS path model outperforms the most naı̈ve bench-
mark. The following analyses require comparing the RMSE values produced
by the PLS-SEM analysis with those produced by the naı̈ve LM benchmark
model.
Comparing the RMSE values, we find that the PLS-SEM analysis pro-
duces smaller prediction errors (i.e., smaller RMSE values) than the LM for
all three CUSL indicators. Specifically, the analysis produces the following
RMSE values (PLS-SEM vs. LM):

) cusl_1: 1.300 vs. 1.310,

) cusl_2: 1.523 vs. 1.542, and
) cusl_3: 1.531 vs. 1.569.

These results suggest the model has high predictive power as the PLS-SEM
analysis outperforms the naı̈ve LM benchmark model for all CUSL indica-
tors. Note that the absolute size of the differences in RMSE values is of sec-
ondary importance for two reasons. First, the size of the RMSE values largely
depend on the measurement scale of the indicators. As the CUSL indicators
are measured on 7-point Likert scales, the range of possible RMSE differences
is quite limited. Second, the RMSE values generated by PLSpredict are highly
stable. Hence, even marginal differences in the RMSE values are typically sig-
nificant.
The results report after running PLSpredict/CVPAT in SmartPLS also in
includes the CVPAT results under Final results → CVPAT. In both CVPAT
results reports, PLS-SEM vs. Indicator average (IA) and PLS-SEM vs. Linear
model (LM), we obtain a negative average loss value difference for the Overall
model. This means that PLS-SEM has a lower average loss than the IA and
LM prediction benchmarks. Moreover, since the p value is below 0.05, we
conclude that PLS-SEM’s predictive capabilities are significantly better than
those of these two prediction benchmarks. Hence, the CVPAT results sup-
port high predictive power of the PLS-SEM results for the corporate reputa-
tion model.
In a final step, we compare different configurations of the reputation mod-
el. Drawing on Danks, Sharma, and Sarstedt (2020) and Sharma et al.
(2020), we compare the original model that serves as the basis for our prior
analyses (Model 1), with two more complex variants in which the four driver
constructs also relate to CUSA (Model 2) and CUSL (Model 3). Exhibit
A6.11 shows the three models under consideration.
To compare the models, we estimate each model using the PLS-SEM algo-
rithm and examine the BIC criterion, which can be accessed in the results re-
port under Quality criteria → Model selection criteria. Exhibit A6.12 shows
the BIC values for the five models under consideration.
12 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM)

Exhibit A6.11. Model comparisons

Exhibit A6.12 ■ BIC values

Model 1 Model 2 Model 3

BIC –261.602 –261.603 –245.038

Akaike weights (relative model likelihoods) 49.98% 50.01% 0.01%

Comparing the BIC values, we find that Model 2 yields the lowest BIC
value, closely followed by Model 1 and, with a greater difference, Model 3.
Considering the marginal difference in BIC values between Models 1 and 2,
however, the evidence in favor of the more complex model, which relates all
four driver constructs to CUSA is not very strong. To further explore the dif-
ference, we compute the BIC-based Akaike weights for the three models. To
do so, we first compute each delta score, which gives 0.001 for Model 1, 0 for
Model 2, and 16.565 for Model 3. We then compute e (–0.5 · delta) for each mod-
el, which gives 0.9995 for Model 1, 1 for Model 2, and 0.0003 for Model 3.
Dividing each value by (0.9995 + 1 + 0.0003) gives the Akaike weights
shown in Exhibit A6.12. Comparing the weights, we find a marginally higher
relative likelihood for Model 2 over Model 1. However, considering that
Model 1 is more parsimonious, we would opt for this model rather than the
more complex variant Model 2.