Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of non-normality is considered. We conducted a Monte Carlo simulation manipulating the underlying multivariate distribution to assess the effect of the source of non-normality (latent, error, and marginal conditions with either multivariate normal or non-normal marginal distributions) on different measures of fit (empirical rejection rates for the likelihood-ratio model test statistic, the root mean square error of approximation, the standardized root mean square residual, and the comparative fit index). We considered different estimation methods (maximum likelihood, generalized least squares, and (un)modified asymptotically distribution-free), sample sizes, and the extent of non-normality in correctly specified and misspecified models to investigate their performance. The results show that all measures of fit were affected by the source of non-normality but with varying patterns for the analyzed estimation methods.
RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The story they tell depends on the estimation methods
