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