The Role of Class Separation in Class Enumeration for Latent Profile Analysis with Nested Data

• In Event: Advancing Mixture Modeling Methodology: Model Specification, Class Enumeration, and Measurement Invariance for Complex Data Structures

Abstract

This study evaluates how the nested structure of data affects class enumeration and parameter estimation in latent profile analysis (LPA), with a specific focus on rethinking how class separation is operationalized. We conceptualize profile separation using Euclidean distance in two-dimensional space and assess how these distances interact with varying levels of intraclass correlation (ICC) and class imbalance. The aim is to determine the effectiveness of Mplus’s TYPE=COMPLEX option relative to TYPE=MIXTURE and TYPE=TWOLEVEL MIXTURE models for identifying latent profiles in multilevel data.
Mixture modeling techniques like LPA are increasingly used in social science research to identify unobserved subgroups. However, educational data are often hierarchically structured (e.g., students nested in classrooms), and failure to account for this nesting can result in biased estimates and misclassification (Kaplan & Keller, 2011; Chen et al., 2012). Prior simulation studies have addressed nesting in latent class analysis (Kaplan & Keller, 2011) and growth mixture models (Chen et al., 2012), but few have rigorously evaluated LPA under conditions of realistic, interpretable profile separation in nested data. This study addresses that gap by conceptualizing separation using Euclidean distances mapped to Cohen’s d, improving the interpretability of class distinctions.
The Monte Carlo simulation utilized Mplus and the MplusAutomation R package. Data were generated for three latent profiles based on two continuous indicators. Four class separation conditions were tested using fixed Euclidean distances between centroid coordinates: (1) all centroids far apart, (2) two far apart with one close to both, (3) two moderately apart with one close to both, and (4) all moderately distant. Cohen’s d was used to calibrate the distance magnitude. Two ICC levels (.05 and .25) and three mixing proportions (balanced, moderately unbalanced, and severely unbalanced) were crossed with the four distance conditions, yielding 24 design cells. Each condition included 500 replications.
The simulated data consisted of 12,000 datasets (24 conditions × 500 replications), with each dataset containing 1,000 individuals nested within 40 clusters. Analyses evaluated model convergence, information criteria (BIC, SSA-BIC), classification accuracy (entropy, modal class assignment), and parameter recovery (mixing proportions, conditional means, standard errors) under three model types.
Preliminary findings suggest that for well-separated classes, TYPE=TWOLEVEL consistently identifies the correct number of profiles and provides more accurate parameter estimates, particularly at higher ICC levels (Authors, 2024). In contrast, TYPE=COMPLEX tends to overestimate standard errors and occasionally overextract classes, while ignoring nesting underestimates standard errors and leads to biased class proportions. These discrepancies are amplified as class separation decreases or when mixing proportions are highly unbalanced.
This study advances methodological understanding of how nested data structures interact with class separation and imbalance in LPA. By using a geometrically grounded and statistically interpretable measure of profile distance, it offers a better framework for simulating and evaluating latent profiles. The findings inform best practices for LPA in multilevel research and highlight the limitations of commonly used modeling shortcuts like TYPE=COMPLEX when profiles are not well separated.

Authors

• Angela D. Starrett, University of South Carolina

• Katherine E. Masyn, Georgia State University