Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This Monte Carlo simulation study examined the issue of measurement invariance testing with FMM when there are covariate effects. Specifically, this study investigated the impact of excluding and misspecifying covariate effects on the class enumeration and measurement invariance testing with FMM. Data were generated based on three FMM models where the covariate had impact on the latent class membership only (population model 1), both the latent class membership and the factor (population model 2), and the latent class membership, the factor, and one item (population model 3). The number of latent classes was fixed at two. These two latent classes were distinguished by factor mean difference for conditions where measurement invariance held in the population, and by both factor mean difference and intercept differences across classes when measurement invariance did not hold in the population. For each of the population models, different analysis models that excluded or misspecified covariate effects were fitted to data. Analyses consisted of two parts. First, for each analysis model, class enumeration rates were examined by comparing the fit of seven solutions: 1-class, 2-class configural, metric, and scalar, and 3-class configural, metric, and scalar. Second, assuming the correct solution was selected, the fit of analysis models with the same solution was compared to identify a best-fitting model. Results showed that completely excluding the covariate from the model (i.e., the unconditional model) would lead to under-extraction of latent classes, except when the class separation was large. Therefore, it is recommended to include covariate in FMM when the focus is to identify the number of latent classes and the level of invariance. Specifically, the covariate effect on the latent class membership can be included if there is no priori hypothesis regarding whether measurement invariance might hold or not. Then fit of this model can be compared with other models that included covariate effects in different ways but with the same number of latent classes and the same level of invariance to identify a best-fitting model.

A Monte Carlo simulation study on class enumeration with latent class regression models. / Latent class regression (LCR) is a statistical method used to identify qualitatively different groups or latent classes within a heterogeneous population and commonly used in the behavioural, health, and social sciences. Despite the vast applications, an agreed fit index to correctly determine the number of latent classes is hotly debated. To add, there are also conflicting views on whether covariates should or should not be included into the class enumeration process. We conduct a simulation study to determine the impact of covariates on the class enumeration accuracy as well as study the performance of several commonly used fit indices under different population models and modelling conditions. Our results indicate that of the eight fit indices considered, the aBIC and BLRT proved to be the best performing fit indices for class enumeration. Furthermore, we found that covariates should not be included into the enumeration procedure. Our results illustrate that an unconditional LCA model can enumerate equivalently as well as a conditional LCA model with its true covariate specification. Even with the presence of large covariate effects in the population, the unconditional model is capable of enumerating with high accuracy. As noted by Nylund and Gibson (2016), a misspecified covariate specification can easily lead to an overestimation of latent classes. Therefore, we recommend to perform class enumeration without covariates and determine a set of candidate latent class models with the aBIC. Once that is determined, the BLRT can be utilized on the set of candidate models and confirm whether results obtained by the BLRT match the results of the aBIC. By separating the enumeration procedure of the BLRT, it still allows one to use the BLRT but reduce the heavy computational burden that is associated with this fit index. Subsequent analysis can then be pursued accordingly after the number of latent classes is determined. / Thesis / Master of Science (MSc)