Abstract
For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.
Highlights
Poisson Hurdle model (GPHR), which simultaneously deals with count data that are both zero-inflated/zero-deflated and over-/under-dispersed, and utilizes generalized method of moments (GMM) to estimate the parameters
If α > 0, the variance is greater than the mean, which is known as overdispersion; if α < 0, the variance is less than the mean, which is known as under-dispersion; and if α = 0, the generalized Poisson distribution degenerates to a Poisson distribution
According to the basic principle of the Hurdle model, if the second process is in a zero-truncated generalized Poisson distribution, the Generalized Poisson Hurdle Regression model can be proposed as follows: (
Summary
Count data are common in various areas, such as public health, insurance, traffic, and epidemiology. The use of generalized Poisson distribution is proposed for over- or under-dispersed count data [1]. For count data with an excess of zeros, zero-inflated regression models, such as zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB), have been proposed [7,8]. Bocci et al generalized the usual Hurdle regression model by specifying a multiple inflated truncated negative binomial distribution for the positive responses and applied it to the tourism behavior of Italian residents [22]. Sarvi et al studied the use of the GEE-based generalized Poisson Regression model for over- and under-dispersed clustered count data with excess zeros [27]. Poisson Hurdle model (GPHR), which simultaneously deals with count data that are both zero-inflated/zero-deflated and over-/under-dispersed, and utilizes GMM to estimate the parameters.
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