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Mixed Poisson regression models with covariate dependent rates.

P Wang¹, M L Puterman, I Cockburn

¹Nanyang Business School, Nanyang Technical University, Singapore 2264.

|June 1, 1996

Summary

This study introduces a flexible Poisson mixture model incorporating covariates. The methodology offers robust tools for analyzing count data, demonstrated with seizure and salmonella assay examples.

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Area of Science:

Statistics
Biostatistics
Statistical Modeling

Background:

Count data analysis often requires flexible modeling beyond standard Poisson regression.
Poisson mixture models offer a powerful framework for handling overdispersion and complex data structures.
Incorporating covariates into the rates of mixture models enhances their applicability to real-world phenomena.

Purpose of the Study:

To develop and investigate a class of Poisson mixture models that accommodate covariates in the rate parameters.
To provide a comprehensive framework including estimation, model selection, and diagnostic procedures.
To demonstrate the practical utility of the proposed methodology through real-world data analyses.

Main Methods:

Utilized the Expectation-Maximization (EM) algorithm and quasi-Newton methods for parameter estimation.
Developed a model selection procedure for choosing among competing Poisson mixture models.
Applied residual analysis and goodness-of-fit tests for model validation.

Main Results:

The proposed Poisson mixture models encompass standard Poisson regression and independent Poisson mixtures as special cases.
A Monte Carlo simulation study evaluated implementation and model selection aspects.
The methodology was successfully applied to analyze seizure frequency and Ames salmonella assay data.

Conclusions:

The developed Poisson mixture models with covariates in rates provide a versatile and effective tool for count data analysis.
The estimation and diagnostic procedures are robust and suitable for practical applications.
The methodology offers significant advantages over traditional models for complex count data scenarios.