On Estimators Of Coefficients Of Linear Regression Models Based On Data Augmentation Multiple Imputation

Non-response frequently encountered in the social survey, and it is an important factor affecting the quality of survey data. Non-response is difficult to avoid in our survey practice, it could cause a systembias ofparameter estimation, and the bias does not decrease by increasing sample size. The cautious preventive measures before survey can effectively reduce the non-response rate, But cannot solve the non-response thoroughly. Additional investigation unit for non-response can lead to the costs increased and the time prolonged. Imputation method can take full advantage of sample information, and it is one of the important method to solve non-response currently. Imputation method includes single and multiple imputation. Single imputation method gives one value to non-response, and it cannot estimate the error of the parameter estimators. Multiple imputation gives several values to non-response, The emergence of multiple imputation makes up the defects of single imputation method, we can estimate the error of the parameter estimators. Data Augmentation imputation is one of the most commonly used multiple imputation method.This paper summarizes the goodness of the commonly used imputation methods, and simulates the statistics property of the MCMC multiple imputation. For the non-response, we firstly impute the non-response using Data Augmentation imputation, thenestimate the coefficients of the liner models, finally we calculate the bias and mean square error of the coefficients estimators. We simulate coefficients estimators of linear regression model when non-response mechanism, non-response rate, and number of imputation are given. Non-response mechanisms including the completely at random, at random, and not an random. The non-response rate choose from 5% to 45%, The interval length is 10%. The number of imputation is selected as 5,15,25,35,45. Simulation results show, when the number of imputation are relatively small, the amount of bias and mean square error of the coefficients estimators are small at non-response completely at random mechanism. As the increasing of the number of imputation, the decreasing amplitude ofbias and mean square error of the coefficients estimator are very small. The number of imputation is recommended to select the number of 5-15. At non-response at random mechanism, the amount of bias and mean square error of the regression coefficient estimators show increasing trend as the increasing of non-response rate. The amount of bias and mean square error of the coefficient estimators shows decreasing trend as the increasing of the number of imputation. In this case, we will get a better estimator if we select a higher number of imputation, the number of imputation is recommended to select the number of 35-45. At not non-response at random mechanism, the accuracy of the estimator is relatively better when the number of imputation is 5. the accuracy of the estimators do not show decreasing trend as the increasing of the number of imputation. At this point, it is recommended to consider several number of imputations to make comparison.