Impact of an equality constraint on the class-specific residual variances in regression mixtures: A Monte Carlo simulation study

Abstract

Regression mixture models are a novel approach for modeling heterogeneous effects of predictors on an outcome. In the model building process residual variances are often disregarded and simplifying assumptions made without thorough examination of the consequences. This simulation study investigated the impact of an equality constraint on the residual variances across latent classes. We examine the consequence of constraining the residual variances on class enumeration (finding the true number of latent classes) and parameter estimates under a number of different simulation conditions meant to reflect the type of heterogeneity likely to exist in applied analyses. Results showed that bias in class enumeration increased as the difference in residual variances between the classes increased. Also, an inappropriate equality constraint on the residual variances greatly impacted estimated class sizes and showed the potential to greatly impact parameter estimates in each class. Results suggest that it is important to make assumptions about residual variances with care and to carefully report what assumptions were made.

Modeling Predictors of Latent Classes in Regression Mixture Models

“…Four types of regression mixture models were analyzed to investigate the optimal strategy for including the latent class predictor(s) in the model: (1) correctly specified one-step model, (2) omitting the direct effect of y on z in one-step model, (3) three-step approach excluding the direct effect of y on z (4) adjusted three-step approach including the direct effect of y on z at step 1. The class-specific residual variances are estimated for all four approaches given that a previous study show that equality constraint on the residual variances across classes has a substantial impact on the bias in class enumeration and parameter estimates (Kim et al, In press). Determining the appropriate number of latent classes is the first step of estimating a regression mixture model, which involves testing a series of models with an increasing number of latent classes in order to assess the fit of the model.…”

Box-Counting Dimension Revisited: Presenting an Efficient Method of Minimizing Quantization Error and an Assessment of the Self-Similarity of Structural Root Systems

“…For the local estimator, we tested the null hypothesis that the local slope estimates of each plant have a single common mean (the plant's true box-count dimension) and variance that can be estimated from the data, i.e., H 0 : V i , j ~ N ( D j , σ j ) for i = 1..4 local estimates and j = 1..36 plants, which follows in Reeve's ( 1992 ) method of differences from the assumption that log( N ( s )) ∝ log( s ). We used the Games-Howell test for one-way ANOVA (Games and Howell, 1976 ) on local slope data pooled for all 36 plants to do pairwise comparisons of the means of local slopes in four groups by scale. The Games-Howell test has lower power than classic ANOVA, but is designed specifically for groups with non-homogeneous variances and was used because the variance was observed to increase with scale.…”

Using Multilevel Mixture Models in Educational Research: An Illustration with Homework Research

“…Chen, Bollen, Paxton, Curran, & Kirby, 2001), which had unequal means and class-invariant variances. Before deciding which modeling strategy to apply, we compared models with unequal variances and equal variances because previous findings had suggested that the specification of LPAs with unequal variances yields less biased results (e.g., Kim et al, 2016;Peugh & Fan, 2013). When we allowed the variances to be freely estimated across classes, improper solutions resulted.…”