The Impact of Unmodeled Heteroskedasticity on Assessing Measurement Invariance in Single-group Models

This study compared two single-group approaches for assessing measurement invariance across an observed background variable: restricted factor analysis (RFA) and moderated nonlinear factor analysis (MNLFA). In MNLFA models, heteroskedasticity can be accounted for by allowing the common-factor variance and the residual variances to differ as a function of the background variable. In contrast, RFA models assume homoskedasticity of both the common factor and the residuals. We conducted a simulation study to examine the performance of RFA and MNLFA under common-factor and residual homoskedasticity and heteroskedasticity. Results suggest that MNLFA and RFA with product indicators outperform RFA with latent moderated structural equations in conditions with heteroskedastic common-factors, and MNLFA outperforms RFA in conditions with residual heteroskedasticity. We provide an explanation for the robustness of RFA with product indicators to violations of common-factor homoskedasticity.