Detecting over- and under-dispersion in zero inflated data with the hyper-Poisson regression model

The zero inflated hyper-Poisson regression model permits count data to be analysed with covariates that determine different levels of dispersion and that present structural zeros due to the existence of a non-users group. A simulation study demonstrates the capability of the model to detect over- and under-dispersion of the potential users group of the dataset in relation to the value of covariates, and to estimate the proportion of structural zeros with great accuracy. An application of the model to fit the number of children per family in relation to several covariates confirms the presence of structural zeros in fertility data at the same time as it detects under-dispersion in most of the levels determined by the covariates.