Tests for zero-inflation and overdispersion

TL;DR

This paper introduces a flexible new methodology for detecting zero-inflation and overdispersion in count data, applicable to various models, and demonstrates its effectiveness through simulations and real data analysis.

Contribution

It develops a novel, general testing framework based on sample extremes comparison for zero-inflation and overdispersion detection, including specific tests for structural zeros and model discrimination.

Findings

Zero-inflated Poisson model rejected for fetal lamb data

Negative binomial model not rejected, indicating appropriate dispersion

Method performs well in simulation studies

Abstract

We propose a new methodology to detect zero-inflation and overdispersion based on the comparison of the expected sample extremes among convexly ordered distributions. The method is very flexible and includes tests for the proportion of structural zeros in zero-inflated models, tests to distinguish between two ordered parametric families and a new general test to detect overdispersion. The performance of the proposed tests is evaluated via some simulation studies. For the well-known fetal lamb data, we conclude that the zero-inflated Poisson model should be rejected against other more disperse models, but we cannot reject the negative binomial model.