Latent Variable Mixture Models

Latent variable mixture models serve to investigate heterogeneous populations consisting of two or more clusters of subjects. For instance, a population may consist of subjects who master a study topic and are therefore prepared to take an exam, and subjects who are not well-prepared. Similarly, in a longitudinal setting, there may be groups of subjects who differ with respect to their developmental trajectories. The observed data from a potentially heterogeneous population are modeled using a mixture distribution rather than a single distribution. A mixture distribution is a weighted sum of component distributions, and each of the component distributions is usually assumed to correspond to a cluster of subjects. Model parameters can be specific for each component distribution, and can therefore be used to model differences between the clusters.