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The Poisson regression is a popular approach in modeling count data. However, in many situations often the variance of data is greater than the mean (over-dispersed data) and the generalized Poisson or mixed Poisson models such as the Poisson gamma (negative binomial), Poisson inverse Gaussian, Poisson lognormal, and Poisson Lindley have been proposed as the alternatives to the Poisson for describing over-dispersed count data. In some situations, the source of over-dispersion is the large percentage of zeros in the dataset. In the other words, the dataset involves an excessive number of zeros than are expected in the common discrete distributions which are known as the zero-inflated events. In order to analyze these data, zero-inflated models such as the zero-inflated Poisson, zero-inflated generalized Poisson, and zero-inflated negative binomial have been applied. This work proposes the functional form and the regression model of the zero-inflated Poisson quasi-Lindley (ZIPQL) and then, beside the alternative models, it was fitted and compared to US National Medical Expenditure Survey data.

Zero-inflated poisson quasi-Lindley regression for modeling number of doctor visit data