Modelling Underdispersed Count Data: Relative Performance of Poisson Model and its Alternatives

Count data are common in many fields and often modelled with the Poisson model. However, the equidispersion assumption (variance = mean) related to the Poisson model is often violated in practice. While much research has focused on modelling overdispersed count data, underdispersion has received relatively little attention. Alternative models are therefore needed to handle overdispersion (variance > mean) and underdispersion (variance < mean). This study assessed the relative performance of the Poisson model and its alternatives (COM-Poisson, Generalized Poisson Regression, Double Poisson and Gamma Count) to model underdispersed count data. Using a Monte Carlo experiment, the simulation plan considered various underdispersion levels (k (variance/mean) = 0.2, 0.5 and 0.81), k=1 as a control, and sample sizes (n=20, 50, 100, 300 and 500). Results showed that the Poisson model is not robust to handle underdispersion but it is the best performer when k=1. The COM-Poisson model best fitted severe underdispersed data (k=0.2). It is also the best performer model for moderate underdispersed count data (k=0.81). However, when k=0.5, the Double Poisson model and Generalized Poisson model outperformed other models for relatively large sample sizes (n=100, 300 and 500). Our finding suggests that none of the models suits all situations. Therefore, in practice, several of these models need to be tested to select the best one.