Counting on a miracle: Problems with negative binomial analysis

• In Event: Methodology Section Open Call Paper Session

Abstract

Many sociological outcomes of interest are count in nature (e.g., crime/deviance, HIV, death). Because many of these are overdispersed, it is common for sociologists to utilize negative binomial models as an alternative to Poisson when attempting to explain variations in these counts. We found that the overwhelming majority of studies published in top general and specialized journals using count outcomes employ negative binomial regression to test their hypotheses. But negative binomial regression requires a number of assumptions be met in order to produce accurate parameter estimates—specifically, that the overdispersion is, in fact, negative binomial. In this paper, we use simulated data to show how violations to these assumptions can lead to issues of parameter estimation and inferences. Specifically, we find that in data where overdispersion does not follow a negative binomial, gamma distribution estimates of regression coefficients demonstrate substantial bias, even flipping signs. We further find that negative binomial models tend to substantially underestimate the precision around an estimate, what we call a “false efficiency” problem. In simulations with a small effect and large standard error, the negative binomial often produces substantially smaller standard errors than what is theoretically specified, often leading one to reject the null when the null should not be rejected. We then also demonstrate that fixed effects negative binomial models are not true within estimators, and that unobserved heterogeneity correlating with the overdispersion parameter can lead to substantially biased estimates. We demonstrate that quasi-Poisson models are generally robust to these concerns. Although the quasi-Poisson model may lead to larger standard errors and thus increase the likelihood of Type II error, we argue that this is a worthwhile tradeoff in order to elicit accurate regression coefficients and limit the likelihood of Type I error.

Authors

• Kyle Thomas, University of Missouri-St. Louis

• Greg Midgette, University of Maryland