Assessing qualitative individual differences with Bayesian hierarchical latent-mixture models

How do individuals vary in psychological experiments? Understanding how and why an effect differs across individuals provides a cornerstone for the development of precise psychological theories. Particularly important is the distinction between qualitative and quantitative differences: Does the manipulation affect all people in the same way or do some people show no or even a reversed effect? To address these questions, we develop a Bayesian hierarchical latent-mixture model where trial-by-trial observations are modeled with a linear model and critical true effect parameters for individuals are modeled as a mixture of three latent classes of positive effects, negative effects, and null effects. We use Bayesian inference, implemented via parameter-expanded Markov chain Monte Carlo integration, to derive Bayes factors for evaluating the number and types of latent classes, classify individuals, and regularize individual effect estimates based on class membership. We demonstrate the usefulness of the model through simulations and applications to extant data and show that the approach is computationally efficient, aligns well with the structure in data, and provides clear, interpretable insights about substantive hypotheses. Thus, it offers an attractive method for assessing qualitative individual differences in experimental psychology.