# Evaluation of structural modeling *fit indices under misspecification conditions

#### Abstract

A simulation study was conducted to evaluate the performance of eight fit indices, including Chi-square/df ratio ($\chi\sp2$/df), Root Mean Squared Residuals (RMSR), Normed Fit Index (NFI), Nonnormed Fit Index (NNFI), Centrality m Index (MCI), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), and Multi-Fit Index (MFI). These indices were examined over four levels of model misspecification (the true model (M0), and three misspecified models (M1, M2, and M3)), four levels of sample size (75, 150, 300, and 900), two levels of Loading size (0.4 and 0.8), three levels of p/m ratio (2, 4, and 6), and two levels of factor correlations (0.3 and 0.6). Major findings from this study include: (1) Most of the fit indices were affected by the choice of estimator, with ML showing better results than GLS. (2) All fit indices were more sensitive to model misspecification when loading size was high. (3) $\chi\sp2$/df, NFI, and RMSR were affected by the p/m ratio. (4) $\chi\sp2$/df and MCI were not sensitively to the change in the degree of model misspecification for most conditions, and NFI, NNFI, RMSR, RNI, and MFI were sensitive to changes in the degree of model misspecification. (5) The consistency among the eight fit indices studied was weak under GLS estimation and strong under ML estimation. ^

#### Subject Area

Statistics|Psychology, Experimental|Psychology, Psychometrics

#### Recommended Citation

Lin Ding, "Evaluation of structural modeling *fit indices under misspecification conditions" (1996). Dissertations and Master's Theses (Campus Access). Paper AAI9702100.
http://digitalcommons.uri.edu/dissertations/AAI9702100

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