Bayesian Latent Class Analysis: Sample Size, Model Size, and Classification Precision

The current literature includes limited information on the classification precision of Bayes estimation for latent class analysis (BLCA). (1) Objectives: The present study compared BLCA with the robust maximum likelihood (MLR) procedure, which is the default procedure with the M plus 8.0 software. (2) Method: Markov chain Monte Carlo simulations were used to estimate two-, three-, and four-class models measured by four binary observed indicators with samples of 1000, 750, 500, 250, 100, and 75 observations, respectively. With each sample, the number of replications was 500, and entropy and average latent class probabilities for most likely latent class membership were recorded. (3) Results: Bayes entropy values were more stable and ranged between 0.644 and 1. Bayes’ average latent class probabilities ranged between 0.528 and 1. MLR entropy values ranged between 0.552 and 0.958. and MLR average latent class probabilities ranged between 0.539 and 0.993. With the two-class model, BLCA outperformed MLR with all sample sizes. With the three-class model, BLCA had higher classification precision with the 75-sample size, whereas MLR performed slightly better with the 750- and 1000-sample sizes. With the 4-class model, BLCA underperformed MLR and had an increased number of unsuccessful computations, particularly with smaller samples.