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

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.

The moderating effect of coworkers’ training participation on the influence of peer support in the transfer process

“…This approach is a well-performing alternative to latent moderated structural equations (LMS, which are only available in Mplus; Muthén and Muthén, 2012). PI is also robust to heteroskedasticity (Kolbe et al, 2020), which obtains similar power, but lower Type 1 error rates than LMS (Kolbe and Jorgensen, 2019), can be implemented into any software program, and provides more traditional SEM fit indices that are not available when using LMS in Mplus (Kolbe and Jorgensen, 2018). Following the recommendations of , the component approach inspired joint-significance testing of multiple parameter estimates was applied to identify the presence of the indirect effect in moderated mediation.…”

Assessing measurement invariance with moderated nonlinear factor analysis using the R package OpenMx.

“…In almost all MNLFA models in this tutorial, the common-factor means, common-factor variances, common-factor covariance, and indicators’ residual variances are allowed to vary as a function of gender and age 2 . Such models are also referred to as heteroskedastic MNLFA models (see Kolbe et al, 2021).…”

“…The difference between these methods and MGCFA is that the data are aggregated over the groups. We therefore refer to these methods as single-group methods (Kolbe et al, 2021), the most flexible of which is MNLFA, described below. For details about the differences between the single-group methods see Bauer (2017) and Kolbe et al (2021).…”

Testing and Interpreting Latent Variable Interactions Using the semTools Package

“…In contrast, LMS does not yield the standard test statistic or fit indices used to evaluate data-model correspondence, and fit indices have only recently been proposed for MCMC estimation of SEMs [32] and incorporated into blavaan and Mplus [33]. Product indicators can also accommodate heteroskedasticity in situations where LMS assumes homoskedasticity [34]. There are also some disadvantages, such as product indicators are assumed to be continuous by virtue of multiplying their values, whereas LMS and MCMC are flexible enough to incorporate ordinal indicators.…”

“…However, perfectly symmetric data are rare in practice, and with the availability of nonnormality corrections to SEs and test statistics [38], it may be safer to freely estimate the factor covariances with the latent interaction. Doing so can also account for unmodeled heteroskedasticity of factor scores [34].…”