Inclusion Bayes Factors for Mixed Hierarchical Diffusion Decision Models

Cognitive models provide a substantively meaningful quantitative description of latent cognitive processes. The quantitative formulation of these models supports cumulative theory building and enables strong empirical tests. However, the nonlinearity of these models and pervasive correlations among model parameters pose special challenges when applying cognitive models to data. Firstly, estimating cognitive models typically requires large hierarchical data sets that need to be accommodated by an appropriate statistical structure within the model. Secondly, statistical inference needs to appropriately account for model uncertainty to avoid overconfidence and biased parameter estimates. In the present work, we show how these challenges can be addressed through a combination of Bayesian hierarchical modeling and Bayesian model averaging. To illustrate these techniques, we apply the popular diffusion decision model to data from a collaborative selective influence study. Translational AbstractCognitive models use mathematical equations to describe how observable human behavior, such as the speed and accuracy of a person's answers on a knowledge test, relate to the underlying unobservable cognitive processes, such as retrieving information from memory. The numerical values of the parameters of these equations quantify different aspects of a person's cognitive processes in a given situation. Applications of cognitive models to data face two challenges. First, estimating the model parameters typically requires repeatedly measuring the behavior of several persons in a given situation. Hence, such data are subject to uncertainty about the repeated measurements of each individual as well as uncertainty about the differences in the unobservable cognitive processes between individuals, and all sources of uncertainty need to be appropriately accounted for statistically. Second, the same data can be described by different competing cognitive models but the correct model is unknown to scientists. Using an incorrect model can lead to misleading quantitative descriptions of a person's cognitive processes and to incorrect conclusions. Hence, uncertainty about the correct model needs to be appropriately accounted for statistically. In the present work, we show how Bayesian hierarchical modeling can address the first challenge by statistically separating different sources of uncertainty in the data. Moreover, we show how Bayesian model averaging can address the second challeng