Variable Selection Of Mixed Model Based On Penalty Likelihood Function

Longitudinal data widely exists in statistical study,and mixed models are commonly used for processing longitudinal data.There exists methods in the literature,some of which just model parts of mixed model and select variables.There may be misspecification of the partial covariance structure,resulting in some parameter estimates to be biased.This dissertation combines the mixid model with the penalty function,which simplifies the model and promotes the research process of variable selection of the mixed model,and has practical application for solving real problems.The research contents are as follows:Firstly,all parts of the mixed model joint modeling were included in the variable selection scope,variable selection is performed for 5 parameters simultaneously,but the model is more complicated at this time,and it’s difficult to estimate the penalty likelihood of the parameters directly using the Newton-Raphson algorithm.Therefore,this dissertation considers adding penalty terms to the conditional expectation of the log-likelihood to constitute penalized likelihood function,then use the cross-validation method to select the five adjustment parameters of the three parts of the mean,random effect and random error covariance model.Finally use this optimal adjustment parameter combination for parameter estimation and variable selection.Secondly,the feasibility of variable selection of mixed model based on penalized likelihood function is verified by simulation and empirical analysis.The simulation results show: that the larger sample size,the better variable selection effect,the weaker effect of the covariance structure part;the important explanatory variables of the mean model can better selected by the method proposed in this dissertation,its parameter estimation and model fitting effect are better,and the scope of application is wider;different penalty functions have their own advantages in fitting effect and parameter validity.Finally,the dissertation summarizes the problems studied in this dissertation and follow-up research content.