A flexible count regression model with varying precision

In this paper, we formulate mean and dispersion submodels for the class of Bell-Touchard regression models, and so we introduce the Bell-Touchard regression model with varying precision for count response variables. This regression model is, in some aspects, similar to the double generalized linear model framework, allowing for parameter interpretation in terms of the response variable in its original scale. We also provide an iterative process to estimate the regression coefficients in the mean and dispersion submodels, and develop diagnostic measures for this class of regression models. The methods developed are applied in a real data set for illustrative purposes.