A Novel Multivariate Generalized Circular Mixed Model for Count Data: Classical & Bayesian Inferences

Abstract

This paper introduces a novel multivariate generalized circular mixed model (GCMCM) framework for analyzing count data with underlying directional components. The proposed methodology addresses gaps in traditional count models that overlook angular dependencies by integrating circular distributions with count-based observations. We develop a generalized mixed-model framework, integrating multivariate circular data and count responses through logical and rigorous Bayesian inference. The model is particularly applicable in fields such as ecology and neuroscience. The theoretical properties, estimation techniques, and applications are discussed in detail, highlighting computational challenges and advancements.