Joint Bayesian Modeling of Binomial and Rank Data for Primate Cognition

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 nonhuman primates based on their performance on 17 cognitive tasks scored on either a rank or binomial scale. 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.