Testing Measurement Invariance Across Unobserved Groups: The Role of Covariates in Factor Mixture Modeling

Abstract

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed.

Robustness of Latent Profile Analysis to Measurement Noninvariance Between Profiles

“…Although BIC, LMR, and aLMR performed well in class enumeration, saBIC yielded higher correct enumeration rates with unequal proportions and small factor mean difference, which is consistent with the finding of previous simulation studies (e.g., Henson et al, 2007;E. S. Kim et al, 2016;Wang et al, 2020). When saBIC did not identify the correct number of profiles in LPA, overextraction of profiles occurred when factor mean difference was large and underextraction occurred when factor mean difference was small.…”

“…For large MNI conditions, difference in loadings and intercepts increased to .40 and .50, respectively, for noninvariant items. These sizes of MNI were consistent with previous methodological studies (e.g., E. S. Maij-de Meij et al, 2010;Stark et al, 2006;Wang et al, 2020).…”

“…When saBIC did not identify the correct number of profiles in LPA, overextraction of profiles occurred when factor mean difference was large and underextraction occurred when factor mean difference was small. AIC tended to overextract the number of profiles, which has been consistently documented in methodological studies (Cho & Cohen, 2010;Henson et al, 2007;Nylund et al, 2007;Wang et al, 2020).…”

“…When the amount of MNI was 40%, two items from each measurement model (the 4th, 5th, 9th, 10th, 14th, 15th, 19th, and 20th items) had MNI, which resulted in a total of eight noninvariant items. These two percentages, corresponding to a small and large number of noninvariant items, are aligned with both applied and methodological studies on MI testing or detection of noninvariant items (e.g., Cho & Cohen, 2010;Davidov et al, 2012;Jak et al, 2013;Maij-de Meij et al, 2010;Wang et al, 2020).…”

“…This can be explained by the fact that these conditions would generally lead to substantial improvement in class enumeration across models, including LPA that ignored MNI across profiles (Dias, 2004;E. S. Kim et al, 2016;Lubke & Neal, 2006, 2008Wang et al, 2020).…”