A Monte Carlo simulation was used to generate data based on the contextual multilevel model, where sample size, effect size, and intraclass correlation (ICC) of the predictor variable were varied. The effects of simulation factors on parameter bias, parameter variability, and standard error accuracy were assessed. Parameter estimates were in general unbiased. Power to detect the slope variance and contextual effect was over 80% for most conditions, except some of the smaller sample size conditions. Type I error rates for the contextual effect were also high for some of the smaller sample size conditions. Conclusions and future directions are discussed.
The purpose of this study was to examine in which way adding more indicators or a covariate influences the performance of latent class analysis (LCA). We varied the sample size (100 ≤ N ≤ 2000), number, and quality of binary indicators (between 4 and 12 indicators with conditional response probabilities of [0.3, 0.7], [0.2, 0.8], or [0.1, 0.9]), and the strength of covariate effects (zero, small, medium, large) in a Monte Carlo simulation study of 2- and 3-class models. The results suggested that in general, a larger sample size, more indicators, a higher quality of indicators, and a larger covariate effect lead to more converged and proper replications, as well as fewer boundary parameter estimates and less parameter bias. Furthermore, interactions among these study factors demonstrated how using more or higher quality indicators, as well as larger covariate effect size, could sometimes compensate for small sample size. Including a covariate appeared to be generally beneficial, although the covariate parameters themselves showed relatively large bias. Our results provide useful information for practitioners designing an LCA study in terms of highlighting the factors that lead to better or worse performance of LCA.