Effects of sample size, model misspecification and the number of indicators on fit indices for covariance structure modeling: A Monte Carlo study
This investigation studied the behavior of fit indices in covariance structure modeling (CSM) when sample size, model misspecification and the number of indicators per factor were varied. The results provide basic researchers with an extensive framework to examine fundamental uses of LISREL VI (i.e., performance of fit indices), and assist applied researchers in properly evaluating larger models using CSM by utilizing a variety of fit indices. Within this investigation covariance matrices, which form the basis for obtaining solutions in CSM, were generated according to the constraints of sample size and the number of indicators per factor for three six-factor models.^ Fifty sample covariance matrices were generated for sample sizes of 50, 100, 200 and 400 with one, two, and three indicators per factor and three degrees of misspecification. The issue of model error (misspecification) was introduced by attempting to fit one model, the target model, to the other two models. Moderate misspecification was represented by fitting the target model to a model consisting of two additional relationships among the factors. The third model represented extensive misspecification by consisting of five additional relationships to the target model.^ From the LISREL VI analyses, 15 fit indices (including stand-alone, incremental and parsimonious fit indices) were provided or calculated from these results. These fit indices and whether the solutions were nonconvergent and improper served as the dependent variables.^ A 4 (sample size) x 3 (degree of misspecification) x 3 (number of indicators per factor) analysis of variance (ANOVA) was conducted to determine which of the three independent variables or any combination thereof contributed to the resulting behavior of the fit indices. Since large sample sizes were used, $\omega\sp2$ was estimated. In addition to the analysis of variance, a log-linear analysis was conducted on the frequency of improper and nonconvergent solutions.^ The results of this study have both supported and contradicted previous findings. The limitations of this study can be categorized as due to decisions made in the sampling design and specification of the population model. Recommendations for the use of the fit indices were made within the constraints of the study. ^
Patelis, Thanos, "Effects of sample size, model misspecification and the number of indicators on fit indices for covariance structure modeling: A Monte Carlo study" (1994). ETD Collection for Fordham University. AAI9425202.