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Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This Monte Carlo simulation study examines the issue of measurement invariance testing with FMM, specifically with the presence of covariate effects. First, this study investigates the impact of excluding and misspecifying covariate effects on the class enumeration of FMM. Second, the impact of excluding and misspecifying covariate effects on the measurement invariance testing will be studied. This study considers the exclusion and misspecification of various covariate effects, including the effects on the latent class membership and the factor. This study aims to provide implications for applied researchers regarding the appropriate way to include covariates in the measurement invariance testing with FMM.