Rank-Poisson Transformation for Use with Count Data in Poisson Regression

Count outcomes are commonly analyzed using Poisson regression, but empirical data often exhibit overdispersion, excess ties, heaping, or other departures from the Poisson distribution. This paper evaluates a rank-Poisson transformation, denoted poisrank, designed to map observed counts onto Poisson quantiles before fitting a Poisson regression model. Our goal is to test whether a rank-Poisson transformation offers a useful general-purpose strategy when count data do not satisfy Poisson assumptions. Using an empirical example and a Monte Carlo simulation study with Poisson, overdispersed, rounded, and gapped count distributions, we compared Poisson regression on raw counts, Poisson regression after the poisrank transformation, quasi-Poisson regression, and additional comparison approaches. Although the transformation made the marginal distribution more similar to a Poisson distribution, it generally did not outperform standard alternatives for inference. In particular, quasi-Poisson regression more consistently maintained appropriate rejection rates with overdispersion whereas poisrank tended to be conservative and often reduced power. These findings suggest that the rank-Poisson transformation is better understood as an exploratory robustness device than as a preferred replacement for established count-data methods.