Simulation Comparison Of Three Linear Regression Multiple Imputation

In the fields of social statistics research,non-response problem has occurred frequently.Non-response problem will affect the authenticity and reliability of statistical analysis results,thus affecting the quality of the survey data.Therefore,the handle of non-response in the actual investigation and study is very important.There are two main ways to deal with non-response problem:one is to take precautions before the actual investigation.Although this method can reduce the frequency of non-response,but the cost of investigation is higher and it can not completely eliminate non-response.And the other is,after the investigation,using different methods to remedy the incomplete data set.These a variety of methods will reduce the error in survey and enhance the reliability of survey data,also decrease the cost.Imputation method is one of the most desirable methods in dealing with non-response data.The multiple imputation methods use different imputation values for non-response data set,so the result of imputation data set is highly reliable,thus improving the accuracy of the survey results.Under a variety of interpolation multiplicities,non-response rates and non-response mechanisms,this paper simulates coefficients estimators of linear model based on the Ordinary linear regression multiple imputation,Bayesian linear regression multiple imputation,Bayesian bootstrap linear regression under the condition of non-response.The simulation results show that the three multiple imputation methods significantly improve the imputation results,using the linear relationship between the non-response and explanatory variables.When the number of imputations are selected for 5,using three multiple imputation methods respectively can give better estimate of the regression coefficients,the absolute values of the bias and mean squared error of the coefficients estimators are significantly smaller than the ones using the PMM and DA imputation methods;the difference with the ones using the EMB imputation method is small.With the increase of non-response rate,the absolute values of the deviation and mean squared error of the coefficients estimators present a small increasing trend.Under non-response dependent variable of non-random at non-response mechanism,the absolute values of the bias and mean squared error of the intercept estimators are larger,the absolute value of the deviation and the mean square error of the other coefficients estimators are relatively small.Under the non-random non-response mechanism of the non-response variable,the intercept term has alarge deviation absolute value and mean square error,and the absolute value and mean square errors of the other coefficient estimators are relatively small.At the same time,the deviation of the coefficients and the mean square error are different from those of the normal distribution.The kurtosis value is negative,and the data are more dispersed than the normal distribution.