Studies in the social and behavioral sciences often involve categorical data, such as ratings, and define latent constructs underlying the research issues as being discrete. In this article, models with discrete latent variables (MDLV) for the analysis of categorical data are grouped into four families, defined in terms of two dimensions (time and sampling) of the data structure. A MATLAB toolbox (referred to as the “MDLV toolbox”) was developed for applying these models in practical studies. For each family of models, model representations and the statistical assumptions underlying the models are discussed. The functions of the toolbox are demonstrated by fitting these models to empirical data from the European Values Study. The purpose of this article is to offer a framework of discrete latent variable models for data analysis, and to develop the MDLV toolbox for use in estimating each model under this framework. With this accessible tool, the application of data modeling with discrete latent variables becomes feasible for a broad range of empirical studies.