A quasi-negative binomial regression with an application to medical care data

This paper introduced a Quasi-Negative Binomial Regression as an extension of Quasi-Negative Binomial to handle response count datasets modulated with covariates. In some literature, Poisson regression is assumed to model the count data appropriately with exemption of excess-zero and over-dispersion more than other identical models. Nevertheless, in the presence of excess-zero and over-dispersion, the Negative Binomial regression and Generalized Poisson regression and their zero-inflation provided some respite. If the data were highly skewed, with long tail, they fit the data incorrectly. Therefore, Quasi-Negative Binomial is recommended even though it cannot accommodate data modulated with covariates, hence the proposed Quasi-Negative Binomial Regression model and its zero-inflated model. The estimates of the model parameters were derived using maximum likelihood method and the performance of the model was examined using simulation study. Also, the adequacy of the model was established by comparison with other competing models’ information criteria. The results showed that the proposed models outperformed the competing models.