Meta Analysis Based On Random Lasso

Variable selection plays a pivotal role in statistics.When the model contains disturbance variables,in order to improve the interpretability and predictability of the model,it is necessary to eliminate the disturbance variables,so the variable selection method should be applied in the model.The Random Lasso method breaks through the limitations of Lasso.Compared with several variable selection methods such as Elastic-Net,Adaptive Lasso,and Relaxed Lasso,this method can select all highly correlated variables or eliminate them altogether,especially when the influence and symbols of variables are different.This method has obvious advantages in the flexibility of coefficient estimation,and the Random Lasso method is superior to other variable selection methods in predicting performance.So,for the Meta-analysis of multiple datasets,we apply the Random Lasso method for variable selection.The main contents of this paper are as follows:First,in a linear model in which both explanatory variables and response variables are continuous variables,the Random Lasso method is used to select explanatory variables for Meta-analysis of multiple data sets,this method is called Meta-analysis based on Random Lasso in continuous data sets.The process of using Random Lasso for variable selection have two steps: In the first step,the sum of the importance measures of the variables in the multiple data sets is used as the comprehensive importance measure,so that the probability of each explanatory variable being extracted is given in the second step of the variable selection;the second step is to select the explanatory variables and estimate the coefficients.Among them,the comprehensive importance measure generated by the first step will make the importance of important variables more significant,and eventually the chance of being selected as important variables will be greater.The simulation results show that this method has better effect on the estimation of coefficients and the elimination of unimportant variables than the Random Lasso method in a single data set although it has the same effect on the selection of important variables as the Random Lasso method.Then,based on the constructed Lasso-Poisson model that its explanatory variables are continuous variables,while the response variables are discrete variables subject to Poisson distribution,Random Lasso method is used to select variables for Meta-analysis of multi-data sets,this method is called Meta-analysis based on random Lasso in Lasso-Poisson regression model.The simulation studies results show that although this method has the same effect on the selection of important variables as the Random Lasso method in a single data set,it has better effect on the estimation of coefficients and the elimination of unimportant variables than the Random Lasso method in a single data set.