Joint Bayesian Inference Reveals Model Properties Shared between Multiple Experimental Conditions

Statistical modeling produces compressed and often more easily interpretable descriptions of experimental data in form of model parameters. When experimental manipulations target selected parameters, it is necessary for their interpretation that other model components remain constant. For example, psychophysicists use dose rate models to describe how behavior changes as a function of a single stimulus variable. The main interest is on shifts of this function induced by experimental manipulation, assuming invariance in other aspects of the function. Combining several experimental conditions in a joint analysis that takes such invariance constraints into account can result in a complex model for which no robust standard procedures are available. We formulate a solution for the joint analysis through repeated applications of standard procedures by allowing an additional assumption. This way, experimental conditions can be analyzed separately such that all conditions are implicitly taken into account. We investigate the validity of the supplementary assumption through simulations. Furthermore, we present a natural way to check whether a joint treatment is appropriate. We illustrate the method for the specific case of the psychometric function; however the procedure applies to other models that encompass multiple experimental conditions.