Right Model, Wrong People: Correct Class Assignment in Latent Class Assignment

• In Event: 61.063 - Mixture Modeling in Practice

Abstract

Researchers and practitioners often use Latent Class Analysis (LCA) and Latent Profile Analysis (LPA) to create profiles or typologies of individuals, based on their responses to a set of response variables. The model parameters from the mixture-model characterize the probability of an observed response given membership in a latent class. Examination of such parameters is suggestive of what typologies the classes might “represent”. However, using those model parameters to classify observations into classes can be highly error prone. Therefore, although we may have a good sense of what the classes are, we may have a much harder time determining who belongs in which class. Exploring correct class assignment is a question of exploring the consequential validity of LCA. This study explores the consequential validity of using LCA/LPA to classify individuals for diagnostic purposes.
The extant literature on LCA has examined how accurately the correct number of latent classes be recovered (Lo, Mendell, & Rubin, 2001; Nylund, Asparouhov, & Muthén, 2007), how distal outcomes and covariates can be incorporated in LCA (Vermunt, 2010; Lanza, Tan, & Bray, 2013; Asparouhov & Muthén, 2014a,b), and how parameter estimation could be biased in LCA (Steinley & Brusco, 2011; Bray, Lanza, & Tan, 2015). Yet, few studies have examined how accurately correct class assignment can be recovered (cf. Tueller & Lubke, 2010; Lubke & Tueller, 2010; Steinley & Brusco, 2011). To fill this gap, we investigate the accuracy of the mixture-model clustering technique LCA, or more precisely LPA, to correctly assign individuals to the class which they belong under varying conditions known to influence LCA. Specifically, we evaluate correct class assignment in LCA varying: 1) with-class variance, 2) between-class separation, 3) the number of response variables, and 4) latent class proportions. We used a Monte Carlo simulation to evaluate correct class assignment in LCA. All data were generated and analyzed in Mplus 7.4 (Muthén & Muthén, 2015). The large-scale latent variable analysis in Mplus was facilitated using the MplusAutomation (Hallquist & Wiley, 2011) package in R 3.4.0 (R Development Core Team, 2018). The true number of classes in the population was fixed at three. Equal and unequal (0.50, 0.35, and 0.15) latent class proportions were evaluated. The latent classes were identified by 3 or 6 response variables. We evaluated within-class variances of 0.5, 0.7, 1, or 1.4. The separation between classes was calculated using the standardized distance between mean values on the response variables. The distance between response variables across adjacent classes was 0.5, 1, or 1.5, representing medium, large, and very large effect sizes (Cohen, 1988). Statistical summaries and visual depictions of class assignment are used to evaluate correct class assignment across the design factors, emphasizing both the positive (correct assignment) and negative (incorrect assignment) inferences. Our results indicate that LPA performed best when within-class variance was small, between-class separation was large, the number of observed variables was large, and latent class proportions were equal. The findings of this study have implications for applied researchers using LCA/LPA, and we provide guidance for researchers who wish to use LPA/LCA to assign individuals to latent classes.

Authors

• Dakota Wayne Cintron, Neag School of Education, University of Connecticut

• D. Betsy Mccoach, University of Connecticut