Addressing heterogeneous populations in latent variable settings through robust estimation

Individuals routinely differ in how they present with psychiatric illnesses and in how they respond to treatment. This heterogeneity, when overlooked in data analysis, can lead to misspecified models and distorted inferences. While several methods exist to handle various forms of heterogeneity in latent variable models, their implementation in applied research requires additional layers of model crafting, which might be a reason for their underutilization. In response, we present a robust estimation approach based on the expectation-maximization (EM) algorithm. Our method makes minor adjustments to EM to enable automatic detection of population heterogeneity and to recognize individuals who are inadequately explained by the assumed model. Each individual is associated with a probability that reflects how likely their data were to have been generated from the assumed model. The individual-level probabilities are simultaneously estimated and used to weight each individual's contribution in parameter estimation. We examine the utility of our approach for Gaussian mixture models and linear factor models through several simulation studies, drawing contrasts with the EM algorithm. We demonstrate that our method yields inferences more robust to population heterogeneity or other model misspecifications than EM does. We hope that the proposed approach can be incorporated into the model-building process to improve population-level estimates and to shed light on subsets of the population that demand further attention. (PsycInfo Database Record (c) 2023 APA, all rights reserved).