The effects of mixing metrics and distributions simultaneously in structural equation modeling: A simulation stud

This study compared the performance of mean- and variance-adjusted robust weighted least squares (WLSMV) and robust maximum likelihood (MLR) in M plus for estimating the parameters in a small and medium covariance structure model using a mixture of continuous and categorical observed variables. To emulate real data applications, mixtures of data types and data distributions within and across latent constructs were manipulated. The performance of fit statistics, parameter estimates, and standard errors under various conditions of nonnormality, sample size, and model size were examined.;The results of this study confirmed widely known previous findings that increasing nonnormality and decreasing sample size can have adverse effects on fit statistics and standard errors. In terms of chi-squared fit statistics, WLSMV had good Type I error control for a correctly specified model. For WLSMV, mixing data types reduced bias in fit compared to when all indicator variables were ordinal. With WLSMV, other fit statistics were fairly insensitive to the study conditions except for lower sample size in conjunction with moderate nonnormality and a fairly substantial effect of model size on both TLI and CFI. Overall, bias in factor loading and structural parameter estimates with WLSMV were acceptable. Whereas WLSMV produced substantial bias in some factor loading standard errors, it retrieved the estimated standard errors of structural parameters fairly well given the study conditions.;On the other hand, MLR was frequently found to be adversely affected when ordinal data were introduced into the model. For MLR, assessment of model fit with mixtures of continuous and ordinal data was inconclusive because Mplus did not produce the usual fit statistics; however, given the substantial bias seen in parameter estimation and the instability in estimation of standard errors, the findings for MLR with mixed data types were not promising.;The primary hypothesis that parameter estimates, standard errors, and fit statistics would not perform well when some indicator variables were continuous and others were ordinal was supported by the current study. The most striking finding was that at least under some conditions where fit statistics suggested overall good model fit, some of those were the same conditions where parameter estimates and/or standard errors were most biased.