Disentangling Continuous and Discrete Structure Within Data

When fitting models to data, general assumptions are frequently made automatically without much consideration for their implication on subsequent interpretations.  For instance, fitting a standard factor model often presupposes an underlying set of continuous, latent factors.  Likewise, when searching for group structure, mixture models (e.g., latent profile analysis, latent class analysis) or cluster analysis are implemented and assume a a set of discrete latent ``classes''.  Usually, the type of model that is fit to the data is governed by the theoretical notions underpinning the substantive question of interest.  In this talk, it is shown that both types of structures can be present and correspond to different subsets of the data.  A general strategy is discussed for extracting both class structure and factor structure.  Demonstrations are given on a data set of internet habits of collegiate students.