Variable Selection Of Regression Model For Zero-Inflated Conway-Maxwell-Poisson Distribution

The zero-inflated counting model has been applied in many fields such as social economy,medical treatment,and criminal investigation.The zero-inflated Conway-Maxwell-Poisson regression model,as one of the commonly used zero-inflated counting models,can solve the problems of overdispersion and underdispersion in data.The variable selection method can process a large amount of longitudinal data and extract useful information from it for statistical analysis to obtain satisfactory results.A type of variable selection method based on the penalty function has attracted wide attention from statisticians.In the existing literature,there are few studies on variable selection methods of zero-inflated CMP regression models.Considering that the penalized generalized estimation equation method is convenient for accuracy and efficiency in many aspects such as variable selection,it does not need to rely on complex joint likelihood function for calculation,and can also consider the correlation between data groups.Therefore,applying this method to the zero-inflated CMP regression model can play more useful value.Characteristics of the mean value affected by dispersion parameters in the zero-inflated CMP regression model,in this paper,a modified ES(Expectation-Solution)algorithm is selected for iteration.It includes the EM(Expectation Maximization)algorithm and the generalized estimation equation method.The advantage is that different parameters can be treated differently to analyze longitudinal data.Based on the modified ES algorithm,a variable selection method of the model-the penalized generalized estimation equation method is proposed,that is,a SCAD penalty function that satisfies oracle characteristics is added to the generalized estimation equation.Use k-fold cross-validation to select tuning parameters,and give a complete iterative algorithm and the concrete form of the sandwich method variance estimation to achieve the goal.In the Monte Carlo simulation study,the proposed method has a stable and good performance in the variable selection effect,which is more advantageous than the unpenalized model.The penalized generalized estimation equation method with the correct working correlation matrix under a limited sample allows the model to obtain an effective estimate.Provide a feasible reference for the analysis of complex and diverse data in the future.