Modeling Unobserved Heterogeneity Using Latent Profile Analysis: A Monte Carlo Simulation

Abstract

Latent profile analysis (LPA) has become a popular statistical method for modeling unobserved population heterogeneity in cross-sectionally sampled data, but very few empirical studies have examined the question of how well enumeration indexes accurately identify the correct number of latent profiles present. This Monte Carlo simulation study examined the ability of several classes of enumeration indexes to correctly identify the number of latent population profiles present under 3 different research design conditions: sample size, the number of observed variables used for LPA, and the separation distance among the latent profiles measured in Mahalanobis D units. Results showed that, for the homogeneous population (i.e., the population has k = 1 latent profile) conditions, many of the enumeration indexes used in LPA were able to correctly identify the single latent profile if variances and covariances were freely estimated. However, for a heterogeneous population (i.e., the population has k = 3 distinct latent profiles), the correct identification rate for the enumeration indexes in the k = 3 latent profile conditions was typically very low. These results are compared with the previous cross-sectional mixture modeling studies, and the limitations of this study, as well as future cross-sectional mixture modeling and enumeration index research possibilities, are discussed.

Keywords:

• cross-sectional heterogeneity
• latent class analysis
• latent profile analysis
• Monte Carlo simulation
• numeration indexes
• population heterogeneity

Notes

¹Shaded row (k = 1) represents the true data generation model.

²Entropy and NEC (and the LRT Derivatives) are undefined if k = 1.

¹Shaded row (k = 1) represents the true data generation model.

²Entropy and NEC are undefined if k = 1.

Shaded row (k = 1) represents the true data generation model.

¹Shaded row (k = 1) represents the true data generation model.