A data transformation to deal with constant under/over-dispersion in Poisson and binomial regression models

This paper proposes a data transformation to deal with the presence of constant under/over-dispersion relative to the Poisson or binomial assumptions. The proposed methodology is very simple as it does not require to replace the Poisson or binomial by more complex regression models based on more flexible distributions. The new approach consist of a transformation of the response variable, followed by the analysis of its relation with the covariates by applying to the transformed variable the usual Poisson or binomial regression models. The transformation depends on a tuning parameter, which can be easily chosen using a straightforward criterion. The efectiveness of the proposed approach is illustrated by simulation experiments and by analyzing six real data sets.