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 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.

近年来，学界已针对含混合响应类型（mixed response types）的数据开展了大量分析方法研究，但此类技术通常未将排序数据（rank data）纳入响应类型范畴。针对排序数据的分析存在独特挑战，尤其是当结（ties）大量存在时。本文提出基于贝叶斯隐变量模型（Bayesian latent variable models）的二项分布与排序数据联合建模方法。我们将该方法应用于通过17项认知任务的表现对比非人灵长类动物（nonhuman primates）的认知能力，每项任务的评分采用排序量表或二项分布量表。为实现排序与二项分布响应的联合建模，我们假设响应值由潜在认知能力（latent cognitive abilities）隐式决定。随后我们采用随机效应模型（random effects models）对隐变量进行建模，并通过设定可识别约束以实现简约的先验设定与模型推断。我们通过灵长类认知数据集的分析结果对所提方法进行演示说明。研究结果表明，不同任务下物种认知能力的排序存在显著差异，这暗示灵长类的认知能力演化存在部分独立性。本文的补充材料可在线获取。