Efficient Bayesian Hierarchical Factor Analysis for Model-Based Psychological Research

Studying individual differences in psychology often involves examiningcorrelations across various measures. However, research involving high-dimensional data—such as in task batteries or neuroscience—often targetslatent constructs rather than individual correlations. Furthermore, the num-ber of correlations grows quadratically with increasing dimensionality, po-tentially leading to overfitting and spurious inference. Therefore, researcherscommonly use factor analysis to study individual differences. However, con-ventional approaches ignore the hierarchical structure of the data and over-look measurement error, leading to attenuated factor loadings. In this pa-per, we introduce a Bayesian framework that integrates hierarchical mod-eling to account for measurement error with factor analysis to infer latentstructures. We employ a post-hoc processing algorithm that removes theneed for conventional constraints on factor loadings, thereby avoiding po-tential bias in their estimation. Additionally, we utilize a shrinkage priorto automatically identify and exclude unsupported factors. The accompa-nying software enables the creation of generative models at the individuallevel, supporting a wide range of hypotheses—from descriptive to theory-driven models—and facilitating robust group-level inferences grounded inpsychological theory. Through simulations and empirical applications, wedemonstrate that our hierarchical factor analysis method flexibly and reli-ably estimates latent structures in high-dimensional data, offering a valuabletool for individual-differences research in psychology and neuroscience.