Nowadays, latent class (LC) and other types of finite mixture models belong to the standard research toolbox of social and behavioural scientists. These methods provide elegant solutions to common statistical problems, such as clustering, scaling, and dealing with unobserved heterogeneity, and software for simple and complicated mixture modelling is generally available, e.g., LEM, Mplus, PANMARK, WINMIRA, GLLAMM, GLIMMIX, and Latent GOLD.

The traditional application of LC analysis is cluster analysis with categorical response variables (indicators). LC cluster models can, however, not only be used with categorical indicators, but also with continuous indicators and counts, as well as with combinations of indicators of different scale type.

A less well-known variant of the LC model is the LC or mixture regression model, which has been simultaneously proposed in the academic marketing and the statistical literature. The LC regression model is a regression model for two-level data structures. Depending on the scale type of the dependent variable, one uses another type of model from the generalized linear modelling (GLM) family; that is: a standard linear, a binary, multinomial, ordinal, conditional or exploded logistic, or a (truncated) Poisson regression model.

The data has the form of a two-level data set in which dependent observations belonging to the same unit are linked by an ID variable. These replications can arise from lower-level observations that are nested within a higher-level observation, repeated measures taken from the same individual, or responses on various indicators. The fact that multiple indicators can also be seen as repeated measures illustrates that the LC regression model contains the LC cluster model as a special case.

The basic idea of LC regression modelling is that latent classes (of higher-level units) differ with respect to the size of the regression coefficients. In other words, regression coefficients are assumed to vary across observations. The mixture regression model is, in fact, a random-coefficients model or, more precisely a nonparametric random-coefficients model. It has various advantages over standard two-level modelling approaches, such as imposing less restrictive distributional assumptions and providing much faster and stable estimation with non-linear regression models.

In this workshop, I will introduce the LC regression model using several interesting application types, such as multilevel modelling, longitudinal, growth and survival analysis, and the analysis of data collected by choice experiments and structured tests or questionnaires. I will also show the connection with LC cluster analysis, multilevel regression analysis, and item response theory modelling, as well as illustrate how restrictions yield variants such as zero-inflated and mover-stayer models and models with several latent variables. I will also pay attention to recent developments, such as models combining discrete (classes) and continuous (traits) forms of unobserved heterogeneity, the three-level extension of the LC regression model, and procedures for dealing with complex sampling designs. During the workshop I will make use of the newest versions of the Latent GOLD and Latent GOLD Choice programs.

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