A Cautionary Note about Having the Right Mixture Model but Classifying the Wrong People

Mixture models can be used for explanation or individual prediction and classification. In practice, researchers are often tempted to make the class membership manifest by classifying cases according to their class of maximum posterior probability and using the "observed" class membership directly or as a variable in follow-up analyses to predict distal outcomes. This study revisits the issue of correct class assignment in latent profile analysis by providing an example where the number of classes is known (3-classes), sampling variability is eliminated, and precise estimates of classification indices are provided. This pseudo-population study design assumes the data-generating mechanism is known and provides a "best-case" scenario for evaluating correct class assignment. We use a variety of classification indices and graphical displays to show that correct classification may be poor despite relatively high entropy and overall correct class assignment metrics (e.g., percent correct). Our study serves as a reminder of the risks associated with trying to make latent class memberships manifest.