Zero-and-K Inflated Poisson Model And Its Application

Zero inflated regression model has been widely used in many fields such as disease research,medical statistics and social economy.In fact,in addition to a lot of zeros,there may be more positive integer K in the count data.This phenomenon is called Zero-and-K inflated.The Zero inflated model has been unable to estimate the count data accurately in this case.In this paper,Zero inflated Poisson model is used as an example to establish Zero-and-K inflated Poisson model.And then two cases of the distribution model without covariates and the regression model with covariates are discussed.Firstly,establish Zero-and-K inflated Poisson regression model on the basis of Zero inflated regression model,and use Newton-Raphson method and EM algorithm of maximum likelihood estimation to estimate the parameter of Zero-and-K Inflated Poisson Model.Secondly,the numerical simulation analysis was performed to verify the fitting effect of the new model.The comparison between Zero-and-K inflated Poisson distribution model and Zero-and-K inflated Poisson regression model reveals that regression model not only more fit the count data,but also can reflect the influence of covariates.By contrast,the fitting effect of the Newton-Raphson method and the EM algorithm is similar,while the EM algorithm converges faster.Finally,this paper analyzes the partial data of tuberculosis infection in various schools in D city from 2014 to 2016.We take the number of tuberculosis infection as the response variable and take other variables as the covariant.The regression results of the Zero-and-K inflated Poisson regression model with covariates shows that the influence of dormitory density,PPD strong positive rate,and exposure time of infectious sources on tuberculosis infection was relatively significant except the influence of air speed.In this way,we can take better preventive measures and effective control of the disease,which is a very high infectious disease.The analysis shows that the Zero-and-K inflation Poisson regression model is more suitable for data fitting and influencing factors analysis of tuberculosis.Therefore,the Zero-and-K inflated Poisson regression model has research significance and practical value.