Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference

Version 1 : Received: 22 April 2021 / Approved: 22 April 2021 / Online: 22 April 2021 (08:55:29 CEST)

How to cite: Tovissodé, C.F.; Glèlè Kakaï, R.L. A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference. Preprints 2021, 2021040592 (doi: 10.20944/preprints202104.0592.v1). Tovissodé, C.F.; Glèlè Kakaï, R.L. A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference. Preprints 2021, 2021040592 (doi: 10.20944/preprints202104.0592.v1).

Abstract

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

Subject Areas

Flexible count regression ; balanced discrete gamma distribution ; deviance statistic ; latent equidispersion ; likelihood ratio

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