Modeling Predictors of Latent Classes in Regression Mixture Models

Abstract

The purpose of the current study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that the step-1 of the three-step approach shows adequate results in class enumeration, we suggest using an alternative approach: 1) decide the number of latent classes without predictors of latent classes and 2) bring the latent class predictors into the model with the inclusion of hypothesized direct covariates effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed.

Fitting latent variable mixture models

“…There is now a considerable body of literature concerning whether or not to include covariates when deciding on the number of classes (Asparouhov & Muthen, 2014; Kim, Vermunt, Bakk, Jaki, & Van Horn, 2016; Li & Hser, 2011; Nylund-Gibson & Masyn, 2016; Vermunt, 2010). Results of simulation studies seem to converge to the conclusion that is not necessary to include covariates to detect the correct number of classes.…”

“…It avoids the inflated Type I errors that occur when carrying out model selection and statistical testing of parameters in a single sample (Lubke & Campbell, 2016; Lubke et al, 2016). Grimm et al (2016) propose to use k -fold cross validation which also leads to correct Type-I error in the selected model. However, splitting the total sample into for instance 5 folds severely decreases the power to detect classes.…”

A Comparison of Methods for Uncovering Sample Heterogeneity: Structural Equation Model Trees and Finite Mixture Models

“…This is the current recommended approach because including covariates during the estimation allows these variables to inform class formation. The main issue is that a proper model must be specified for the covariates and this is a complicated process with inherent challenges (Kim, Vermunt, Bakk, Jaki, & Van Horn, 2016). When estimating a mixture with covariates in the model, we might expect more similar results to that of SEM Trees because associations between the covariates and outcomes are part of the search for latent classes; however, given the potential for the covariates to be poorly distributed, there is the potential for the covariates to dominate the formation of the latent classes.…”

Measurement Invariance and Differential Item Functioning Across Gender Within a Latent Class Analysis Framework: Evidence From a High-Stakes Test for University Admission in Saudi Arabia

“…The measurement parameters of the latent classes are held fixed (step 1) while accounting for classification error (step 2), and then the covariate is introduced in the model, and its relationship to the latent class variable is estimated (step 3) (see Nylund-Gibson et al, 2014 for a detailed description). However, even though this approach has been recently criticized for not being robust to avoid misspecifications in the latent class enumeration process (i.e., determining the optimal number of classes) and obtain accurate estimates of the covariates' effects on latent class membership (Kim et al, 2016;Masyn, 2017).…”