Bayesian Variable Selection For Quantile Regression Model With Strong Heredity Constraints

Variable selection is an important problem in regression research.For general linear models,there are many variable selection methods,such as AIC criterion,BIC criterion,stepwise regression and so on.These variable selection methods have good performance in solving linear regression problems without interaction terms.However,in many cases,the linear model without interaction terms can not fit the actual data well,so it is necessary to consider the interaction terms,that is to say,in the linear regression problem with correlated predictors,it is necessary to select and estimate variables by maintaining the hierarchical relationship between predictors.The socalled heritability(this paper only refers to strong heritability)means that if and only if the main item in the model exists,its interaction item has the possibility of existence,and when one of the main items does not exist,the interaction item with the main item must not exist.Quantile regression model can explain the dependent variable from different quantiles,and it can describe the conditional distribution of the explained variable more comprehensively.Even if the error term is non normal distribution,the parameters of quantile regression can be well estimated.For quantile regression model without considering interaction effect,scholars have also proposed many variable selection methods and parameter estimation methods,but there are few studies on variable selection of quantile regression model with interaction term and genetic effectThis paper presents a variable selection method for quantile regression model with genetic effect.By introducing quantile model and considering a hierarchical prior with strong heredity,the model with the highest posterior is selected according to the posterior mean value of the calculated model.The variable selection method used in this paper is an improved random variable selection(SSS)method based on the random variable search method and fully considering the strong heredity.This variable selection method can avoid traversing all possible models,and the model space can move to the region with high a posteriori probability.The random search algorithm can traverse the model space quickly and effectively even when there are many variables in the model.In the study of data simulation,the variable selection method proposed in this paper is applied to the quantile regression model with genetic effect,by comparing the result of variable selection with that of mean regression model with genetic effect,we can see that the result of quantile regression model is better than that of mean regression model.At the end of the paper,a case study of prostate cancer data is carried out.From the comparison results of the cases,it can be seen that the variable selection results of quantile regression model with genetic effect have more practical significance.