Joint Bayesian Modeling of Binomial and Rank Data for Primate Cognition

In recent years, substantial effort has been devoted to methods for analyzing data containing mixed response types, but such techniques typically do not include rank data among the response types. Some unique challenges exist in analyzing rank data, particularly when ties are prevalent. We present techniques for jointly modeling binomial and rank data using Bayesian latent variable models. We apply these techniques to compare the cognitive abilities of non-human primates based on their performance on 17 cognitive tasks scored on either a rank or binomial scale. In order to jointly model the rank and binomial responses, we assume that responses are implicitly determined by latent cognitive abilities. We then model the latent variables using random effects models, with identifying restrictions chosen to promote parsimonious prior specification and model inferences. Results from the primate cognitive data are presented to illustrate the methodology. Our results suggest that the ordering of the cognitive abilities of species varies significantly across tasks, suggesting a partially independent evolution of cognitive abilities in primates.