As mentioned in Topic A of Session 2, in traditional or ‘fixed effects’ regression, a common set of regression coefficient estimates apply to all cases. In contrast, random effects regression models allow for heterogeneity to exist in the coefficients, so that each case may have its own set of regression coefficients.
A standard random effects regression model, frequently estimated using Bayesian methods and referred to as Hierarchical Bayes (BB) — assumes that the underlying heterogeneity is continuous and yields separate individual-level coefficients for each case. LC regression assumes that the underlying heterogeneity is discrete and provides separate coefficients for each latent class. See Topic E for one important application of CFactors.