Statistical Power to Detect the Correct Number of Classes in Latent Profile Analysis

TLDR

Little research has examined factors influencing statistical power to detect the correct number of latent classes using latent profile analysis (LPA). The study simulated power to detect the correct number of latent classes in LPA as a function of interclass distance, true class count, sample size, and number of indicators. Seven model selection methods were evaluated in the simulations. Power was inadequate for small or medium class separation, but for very large separation (d = 1.5) the Lo–Mendell–Rubin test, adjusted LMR, bootstrap likelihood ratio test, BIC, and sample‑size‑adjusted BIC reliably selected the correct number of classes; for large separation (d = 0.8) power varied with indicator count and sample size, while AIC and entropy consistently failed to select the correct number of classes.

Abstract

Little research has examined factors influencing statistical power to detect the correct number of latent classes using latent profile analysis (LPA). This simulation study examined power related to interclass distance between latent classes given true number of classes, sample size, and number of indicators. Seven model selection methods were evaluated. None had adequate power to select the correct number of classes with a small (Cohen's d = .2) or medium (d = .5) degree of separation. With a very large degree of separation (d = 1.5), the Lo–Mendell–Rubin test (LMR), adjusted LMR, bootstrap likelihood ratio test, Bayesian Information Criterion (BIC), and sample-size-adjusted BIC were good at selecting the correct number of classes. However, with a large degree of separation (d = .8), power depended on number of indicators and sample size. Akaike's Information Criterion and entropy poorly selected the correct number of classes, regardless of degree of separation, number of indicators, or sample size.