Statistical estimation of structural equation models with a mixture of continuous and categorical observed variables.

In the social and behavioral sciences, observed variables of mixed scale types (i.e., both continuous and categorical observed variables) have long been included in structural equation models. However, little is known about the impact of mixed continuous and categorical observed variables on the performance of existing estimation methods. This study compares two popular estimation methods with robust corrections, robust maximum likelihood (MLR) and diagonally weighted least squares (DWLS), when mixed continuous and categorical observed data are analyzed, evaluating the behavior of DWLS and MLR estimates in both measurement and full structural equation models. Monte Carlo simulation was carried out to examine the performance of DWLS and MLR in estimating model parameters, standard errors, and chi-square statistics. Two population models, a correlated three-factor measurement model and a five-factor structural equation model, were tested in combination with 36 other experimental conditions characterized by the number of observed variables' categories (2, 3, 4, 5, 6, and 7), categorical observed distribution shape (symmetry and slight asymmetry), and sample size (200, 500, and 1000). Data generation and analysis were performed with Mplus 8. Results reveal that (1) DWLS yields more accurate factor loading estimates for categorical observed variables than MLR, whereas DWLS and MLR produce comparable factor loading estimates for continuous observed variables; (2) inter-factor correlations and structural paths are estimated equally well by DWLS and MLR in nearly all conditions; (3) robust standard errors of parameter estimates obtained by MLR are slightly more accurate than those produced by DWLS in almost every condition, but the superiority of MLR over DWLS is not clearly evident once a medium or large sample is used (i.e., n = 500 or 1000); and (4) DWLS is systematically superior to MLR in controlling Type I error rates, but this superiority is attenuated with increasing sample size. The article concludes with a general discussion of the findings and some recommendations for practice and future research.