| Summary: | 碩士 === 國立臺北大學 === 統計學系 === 100 === In the public health, social science, engineering science, agricultural science and other disciplines, it is common to use the Poisson (POI) regression to analyze discrete count data. However, excessive zeros often occur in the data and then cause over-dispersion. Therefore, Lambert (1992) proposed the zero-inflated Poisson (ZIP) regression model to fit such data.
In this research, we extend the zero-inflated Poisson regression model to the zero-and-K-inflated Poisson (ZKIP) regression model. The ZKIP model can be applied to count data, which contains extra zeros and Ks, where K is a non-zero positive integer. For example, a survey question inquiring the number of times that young adults visited a dentist in two years resulted in zero time (zero) or one time (K) for most people, this is so-called zero-and-K-inflated data.
In the simulation study, it compares the goodness of fit for ZKIP, ZIP and POI models, and discusses the best timing of using these models in the data. We also explores the effect of different sample size, zero proportion, k proportion and mean in Poisson distribution on data fitting for these considered models
The simulation study shows that ZKIP has better fit than POI and ZIP in all simulation configurations. In the empirical study, we use 2005 national health interview survey data to compare the performance of data fitting for the three models. The results show that the zero-and-K-inflated Poisson regression model outperforms the other two models.
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