Latent Variable Hybrids: Overview Of Old And New Models

The conference that this book builds upon contained many different special topics within the general area of modeling with categorical latent variables, also referred to as mixture modeling. The many different models addressed at that conference and within this volume may overwhelm a newcomer to the field. In fact, however, there are really only a small number of variations on a common theme. This chapter aims to distinguish the different themes, show how they relate to each other, and give some key references for further study. Some new mixture models are also proposed. Table 1.1 gives a summary of different types of latent variable models. An overview discussion of the models of Table 1.1 was presented in Muthén (2002). The entries of the table are types of models, with the rows dividing the models into cross-sectional and longitudinal and the columns dividing models into traditional models with continuous latent variables, models