# A multivariate correlated poisson generalized inverse gaussian regression model for dependent count data: Estimation and testing procedures

## TL;DR

This paper introduces a new statistical model for analyzing multivariate count data with correlation and overdispersion, improving accuracy in public health applications.

## Contribution

The novel MCPGIGR model integrates random effects and log-link functions for flexible and robust analysis of dependent count data.

## Key findings

- MCPGIGR outperforms Multivariate Poisson Regression in model fit for maternal and neonatal mortality data.
- Simulation studies confirm the consistency and performance of the proposed Maximum Likelihood Estimation and testing procedures.

## Abstract

Regression modeling for multivariate count data often struggles with assumption of overdispersion and correlation among response variables. To address these issues, this study proposes a new model called Multivariate Correlated Poisson Generalized Inverse Gaussian Regression (MCPGIGR), which integrates random effects through common shock variables and allows for flexible mean structures via a log-link function. This research develops a Maximum Likelihood Estimation (MLE) and Maximum Likelihood Ratio Tests (MLRT) to evaluate both simultaneous and partial significance of predictors. We conduct simulation studies to assess the consistency and performance of the proposed estimators. Furthermore, in an application to maternal and neonatal mortality across 38 districts/cities in East Java (Indonesia), MCPGIGR substantially improves model fit relative to a Multivariate Poisson Regression (MPR) baseline (AICc decreases from 2378.63 to 1924.60 for γ=−1/2). The proposed framework provides a practical and flexible tool for analyzing correlated, overdispersed multivariate counts in public health and related domains. The highlights of this research are:

• The MCPGIGR model introduces a correlated multivariate count regression framework with exposure adjustment.

• It provides robust parameter estimation and hypothesis testing via MLE and MLRT.

• MCPGIGR demonstrates improved model fit and practical interpretability in public health applications.

Image, graphical abstract