A new formulation for latent class models

Latent class, or finite mixture, modelling has proved a very popular, and relatively easy, way of introducing much-needed heterogeneity into empirical models right across the social sciences. The technique involves (probabilistically) splitting the population into a finite number of (relatively homogeneous) classes, or types. Within each of these, typically, the same statistical model applies, although these are characterised by differing parameters of that distribution. In this way, the same explanatory variables can have differing effects across the classes, for example. A priori, nothing is known about the behaviours within each class; but ex post, researchers invariably label the classes according to expected values, however defined, within each class. Here we propose a simple, yet effective, way of parameterising both the class probabilities and the statistical representation of behaviours within each class, that simultaneously preserves the ranking of such according to class-specific expected values and which yields a parsimonious representation of the class probabilities.