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

Abstract

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.

Keywords:

• Latent class and profile analysis
• mixture modeling
• correct class assignment

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 The question of whether latent classes should be thought of as separate entities or not is a matter of ongoing debate. Some authors suggest that latent classes are merely a heuristic device not to be taken literally (Nagin & Tremblay, 2005). Others emphasize the necessity of prediction for identifying separate latent classes (Wendt et al. 2019).

2 An important point to note here is that we assumed that the separation between classes was equivalent. It may be the case that in practice the smallest class is often more separated (“further away”) from all other classes. An important area for future research may be evaluating how far away the smallest class needs to be to accurately recover members of the class, and whether this is a function of the size of the smallest class as well.