Joint Bayesian Modeling of Binomial and Rank Data for Primate Cognition

Abstract

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 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. 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. Supplementary materials for this article are available online.

• Interanimal variability
• Latent performance
• Mixed response

Additional information

Notes on contributors

Bradley J. Barney

Bradley Barney is Assistant Professor, Department of Statistics and Analytical Sciences, 1000 Chastain Rd. #1601, Kennesaw State University, Kennesaw, GA 30144 (E-mail: [email protected]).

Federica Amici

Federica Amici is Postdoctoral Fellow, Department of Developmental and Comparative Psychology, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany D-04103 (E-mail: [email protected]).

Filippo Aureli

Filippo Aureli is Investigator, Instituto de Neuroetología, Universidad Veracruzana, Xalapa, Veracruz, Mexico and Professor, Research Centre in Evolutionary Anthropology and Palaeoecology, Liverpool John Moores University, Liverpool, United Kingdom (E-mail: [email protected]).

Josep Call

Josep Call is Professor, School of Psychology and Neuroscience, University of St. Andrews, St. Andrews, United Kingdom and Director, Wolfgang Köhler Primate Research Center, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany D-04103 (E-mail: [email protected]).

Valen E. Johnson

Valen Johnson is Professor and Head, Department of Statistics, Texas A&M University, College Station, TX 77843-3143 (E-mail: [email protected]).