Counting on count regression: overlooked aspects of the Negative Binomial specification

TL;DR

This paper critically examines the Negative Binomial regression specification in empirical research, revealing overlooked mathematical issues that impact statistical inference and offering recommendations for more rigorous methodology.

Contribution

It uncovers errors in common analytical approaches to Negative Binomial regression and provides detailed computational clarifications to improve methodological accuracy.

Findings

Identified problems with gamma function derivatives affecting Fisher Information

Revealed potential inaccuracies in statistical testing procedures

Provided detailed computational recommendations for better practice

Abstract

Negative Binomial regression is a staple in Operations Management empirical research. Most of its analytical aspects are considered either self-evident, or minutiae that are better left to specialised textbooks. But what if the evidence provided by trusted sources disagrees? In this note I set out to verify results about the Negative Binomial regression specification presented in widely-cited academic sources. I identify problems in how these sources approach the gamma function and its derivatives, with repercussions on the Fisher Information Matrix that may ultimately affect statistical testing. By elevating computations that are rarely specified in full, I provide recommendations to improve methodological evidence that is typically presented without proof.