Bayesian hierarchical modelling for between-subject analysis

Cognitive models are more and more frequently applied to test both within- and between-subject hypotheses, however, the latter has generally suffered from the lack of statistical methods to answer such questions. A common approach to testing between-subject hypotheses is to perform a second step of analysis on the estimated parameters of the model to answer whether, for example, drift rate differs with age, or between people with schizophrenia and controls. However, a lot of statistical power is lost in such two-step analyses. Here we propose to include linear models such as ANOVA, regression, and by extension mixed effect models, in the hierarchical framework in which cognitive models are usually estimated. With such a hierarchical linear model we omit the two-step analysis. Furthermore, we supply methods with which we can estimate Bayes factors between the null and the proposed model. Our work gives researchers the option to formalize different types of hypotheses for between-subject research, with the added benefit of maintaining a more parsimonious parameter space.