Investigating population heterogeneity with factor mixture models.

TLDR

Population heterogeneity can arise from observed factors such as gender or from unobserved sources, and while latent class models address the latter, factor mixture models combine latent classes with common factors to explore such heterogeneity, allowing covariates to be incorporated in various conceptual ways and positioning the approach relative to other methods for heterogeneous data. The paper discusses in detail how factor mixture models can be applied to explore unobserved population heterogeneity and the role of covariates. A step‑by‑step example using data from the Longitudinal Survey of American Youth demonstrates how factor mixture models can be applied in an exploratory fashion to single‑time‑point data.

Abstract

Sources of population heterogeneity may or may not be observed. If the sources of heterogeneity are observed (e.g., gender), the sample can be split into groups and the data analyzed with methods for multiple groups. If the sources of population heterogeneity are unobserved, the data can be analyzed with latent class models. Factor mixture models are a combination of latent class and common factor models and can be used to explore unobserved population heterogeneity. Observed sources of heterogeneity can be included as covariates. The different ways to incorporate covariates correspond to different conceptual interpretations. These are discussed in detail. Characteristics of factor mixture modeling are described in comparison to other methods designed for data stemming from heterogeneous populations. A step-by-step analysis of a subset of data from the Longitudinal Survey of American Youth illustrates how factor mixture models can be applied in an exploratory fashion to data collected at a single time point.