A Note on the Use of Mixture Models for Individual Prediction

Abstract

Mixture models capture heterogeneity in data by decomposing the population into latent subgroups, each of which is governed by its own subgroup-specific set of parameters. Despite the flexibility and widespread use of these models, most applications have focused solely on making inferences for whole or subpopulations, rather than individual cases. This article presents a general framework for computing marginal and conditional predicted values for individuals using mixture model results. These predicted values can be used to characterize covariate effects, examine the fit of the model for specific individuals, or forecast future observations from previous ones. Two empirical examples are provided to demonstrate the usefulness of individual predicted values in applications of mixture models. The first example examines the relative timing of initiation of substance use using a multiple event process survival mixture model, whereas the second example evaluates changes in depressive symptoms over adolescence using a growth mixture model.

Keywords:

• growth mixture models
• individual prediction
• mixture models
• person-centered analysis

ACKNOWLEDGMENTS

The authors would like to thank Danielle Dean and Jolynn Pek for helpful comments on this article.

FUNDING

This work was supported by National Institutes of Health Grants F31 DA040334 (Fellow: Veronica Cole) and R01 DA034636 (PI: Daniel Bauer). The content is solely the responsibility of the authors and does not represent the official views of the National Institute on Drug Abuse or the National Institutes of Health.

Notes

¹ Note that here and throughout the article, the term marginal is applied when marginalizing with respect to the latent variables, although the expression remains conditional on the observed exogenous covariates.

Additional information

Funding

This work was supported by National Institutes of Health Grants F31 DA040334 (Fellow: Veronica Cole) and R01 DA034636 (PI: Daniel Bauer). The content is solely the responsibility of the authors and does not represent the official views of the National Institute on Drug Abuse or the National Institutes of Health.