Fit Indices to Report for Confirmatory Factor Analysis and Structural Equation Modelling
3 min readMay 17, 2021
In this tutorial, I present a comprehensive tutorial on the fit indices reported in the Confirmatory Factor Analysis (CFA) and Structural Equation Modelling (SEM) analysis, to test the fitness of the model and variable constructs.
Present a discussion of the meaning of each fit index, its use and the threshold required
These are discussed below:
Chisq: The model Chi-squared assesses overall fit and the discrepancy between the sample and fitted covariance matrices.
Its p-value should be > .05 (i.e., the hypothesis of a perfect fit cannot be rejected). However, it is quite sensitive to sample size.GFI/AGFI: The (Adjusted) Goodness of Fit is the proportion of variance accounted for by the estimated population covariance.
Analogous to R2. The GFI and the AGFI should be > .95 and > .90, respectively.NFI/NNFI/TLI: The (Non) Normed Fit Index. An NFI of 0.95, indicates the model of interest improves the fit by 95\ NNFI (also called the Tucker Lewis index; TLI) is preferable for smaller samples.
They should be > .90 (Byrne, 1994) or > .95 (Schumacker & Lomax, 2004).CFI: The Comparative Fit Index is a revised form of NFI. Not very sensitive to sample size (Fan, Thompson, & Wang, 1999).
Compares the fit of a target model to the fit of an independent, or null, model. It should be > .90.RMSEA: The Root Mean Square…