Latent Profile Model

The latent profile model is a latent variable model with a categorical latent variable and continuous manifest indicators. It was introduced in 1968 by Lazarsfeld and Henry. Although under different names, very similar models were proposed in the same period by Day and Wolfe. Over the past ten years, there has been renewed interest in this type of latent variable model, especially as a tool for cluster analysis. The latent profile model can be seen as a probabilistic or model-based variant of traditional non-hierarchical cluster analysis procedures such as the K-means method. It has been shown that such a model-based clustering procedure outperforms the more ad hoc traditional methods. It should be noted that only a few authors use the term latent profile model. More common names are mixture of normal components, mixture model clustering, model-based clustering, latent discriminant analysis, and latent class clustering. Possible social sciences applications of the latent profile model include building typologies and constructing diagnostic instruments. A sociologist might use it to build a typology of countries based on a set of socio-economic and political indicators. A psychologist may apply the method to combine various test scores into a single diagnostic instrument. As in latent class analysis, latent profile analysis assumes that the population consists of C unobserved subgroups that can be referred to as latent profiles, latent classes, or mixture components. Because the indicators are continuous variables, it is most natural to assume that their conditional distribution is normal. The most general model is obtained with unrestricted multivariate normal distributions; that is,