Hierarchical Factor Models For Experimental Designs

It is challenging to study individual differences in experimental tasks because performance on these tasks is highly noise prone. This excessive noise if unaccounted results in attenuated correlations, overstated confidence, and increased residuals in factor models. One advantage in using experimental tasks is that they are comprised of many repeated trials allowing for a separate modeling of trial noise and individual variation. Here, we develop a set of hierarchical factor models for experimental tasks. We show that these models disattenuate correlations, provide for more clear assessments of factor structures, and have bona-fide measures of uncertainty for observed and latent variables. Attention is paid to computational issues including mixing and rotational ambiguity, and code is available for analysis in R with JAGS. The methods are illustrated through explorations of individual differences in two domains: visual illusions and cognitive control.