The Impact of Unmodeled Heteroskedasticity on Assessing Measurement Invariance in Single-group Models. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Kolbe, Laura; Jorgensen, Terrence D.; Molenaar, Dylan
• Is Part Of: Structural equation modeling. Volume 28:Issue 1(2021)
• Page Start: 82
• Page End: 98
• Publication Date: 2021-01-02
• Subjects: Heteroskedasticity -- measurement Invariance -- moderated Nonlinear Factor Analysis -- restricted Factor Analysis -- product Indicators; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2020.1766357
• Languages: English
• ISSNs: 1070-5511

Abstract

ABSTRACT: 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.