Bayesian factor zero-inflated Poisson model for multiple grouped count data

TL;DR

This paper introduces a Bayesian factor model tailored for grouped count data that efficiently captures complex associations across multiple dimensions, utilizing advanced augmentation techniques for improved computation.

Contribution

It presents a novel Bayesian factor model with a link function approach for grouped count data, incorporating data augmentation and Pólya-Gamma techniques for efficient posterior inference.

Findings

Model effectively captures associations within and between counts and at-risk probabilities.

Demonstrated superior computational efficiency through data augmentation techniques.

Validated on simulated and real data involving youth participation in illegal activities.

Abstract

This paper proposes a computationally efficient Bayesian factor model for multiple grouped count data. Adopting the link function approach, the proposed model can capture the association within and between the at-risk probabilities and Poisson counts over multiple dimensions. The likelihood function for the grouped count data consists of the differences of the cumulative distribution functions evaluated at the endpoints of the groups, defining the probabilities of each data point falling in the groups. The combination of the data augmentation of underlying counts, the P\'{o}lya-Gamma augmentation to approximate the Poisson distribution, and parameter expansion for the factor components is used to facilitate posterior computing. The efficacy of the proposed factor model is demonstrated using the simulated data and real data on the involvement of youths in the nineteen illegal activities.