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CFA and SEM Fit Indices Guide

This document summarizes several common fit indices used to assess confirmatory factor analyses and structural equation models, including the chi-square test, GFI, NFI, TLI, CFI, RMSEA, SRMR, and AVE. It provides the descriptions, recommended cut-off values indicating good fit, and how to estimate these indices in R, SAS, and Stata. Kline suggests reporting the model chi-square, RMSEA, CFI, and SRMR at a minimum.

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Abhinav Nigam
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672 views2 pages

CFA and SEM Fit Indices Guide

This document summarizes several common fit indices used to assess confirmatory factor analyses and structural equation models, including the chi-square test, GFI, NFI, TLI, CFI, RMSEA, SRMR, and AVE. It provides the descriptions, recommended cut-off values indicating good fit, and how to estimate these indices in R, SAS, and Stata. Kline suggests reporting the model chi-square, RMSEA, CFI, and SRMR at a minimum.

Uploaded by

Abhinav Nigam
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We take content rights seriously. If you suspect this is your content, claim it here.
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Fit Indices commonly reported for CFA and SEM

There are more than a dozen different fit statistics researchers use to assess their confirmatory
factor analyses and structural equation models. Here we have assembled a list of the most
popular fit statistics used and recommended cut-offs that indicate a good fit.

Measure Name Description Cut-off for


good fit
Χ2 Model Chi- Assess overall fit and the discrepancy between p-value>
Square the sample and fitted covariance matrices. 0.05
Sensitive to sample size.
H0: The model fits perfectly.
(A)GFI (Adjusted) GFI is the proportion of variance accounted GFI ≥ 0.95
Goodness of Fit for by the estimated population covariance. AGFI ≥0.90
Analogous to R2. AGFI favors parsimony.
(N)NFI (Non) Normed- An NFI of .95, indicates the model of interest NFI ≥ 0.95
TLI Fit Index improves the fit by 95% relative to the null NNFI ≥ 0.95
model. NNFI is preferable for smaller samples.
Tucker Lewis Sometimes the NNFI is called the Tucker Lewis
index index (TLI)
CFI Comparative Fit A revised form of NFI. Not very sensitive to CFI ≥.90
Index sample size. Compares the fit of a target
model to the fit of an independent, or null,
model.
RMSEA Root Mean A parsimony-adjusted index. Values closer to RMSEA <
Square Error of 0 represent a good fit. 0.08
Approximation
(S)RMR (Standardized) The square-root of the difference between SRMR <0.08
Root Mean the residuals of the sample covariance matrix
Square Residual and the hypothesized model. If items vary in
range (i.e. some items are 1-5, others 1-7)
then RMR is hard to interpret, better to use
SRMR.
AVE Average Value The average of the R2s for items within a AVE >.5
(CFA only) Explained factor

Stephen Parry
Kline suggests that at a minimum the following indices should be reported:
1) The model chi-square
2) RMSEA
3) CFI
4) SRMR

How to estimate these fit indices:


• In R, use the FitMeasures function from the lavaan package.
• In SAS’s Proc Calis, specify the fitindex option with the particular indices you want.
• In Stata, after executing a CFA or SEM, use the command: estat gof, stats(all)

References:
Principles and Practice of Structural Equation Modeling. Rex B. Kline. 2005.
Structural Equation Modelling: Guidelines for Determining Model Fit. Daire Hooper, et al. 2008.

Stephen Parry

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