Unifying regression models through maximum likelihood: gsem as a teaching tool

Most commonly used parametric regression models share a common foundation: maximum likelihood estimation. Viewing them this way lets researchers build from simple models to complex specifications using a single statistical principle. We begin with linear regression recast as Gaussian regression, then extend it to generalized linear models for binary, count, and positive continuous outcomes. Next, we add latent variables, including hierarchical random effects, to obtain generalized multilevel models. Throughout, we illustrate each step with Stata’s gsem command for generalized structural equation modeling.