基于PMM多重插补法的线性模型系数估计量的模拟研究

On Estimators of Coefficients of Linear Regression Model Based on PMM Multiple Imputation

在利用含无回答的经济数据建立线性回归模型之前,选择PMM多重插补法给出无回答的插补值。模拟结果显示,在任意无回答机制下,随着插补重数增大,系数估计量的偏差和均方误差减小不显著。对于任意无回答率,建议插补重数为5。在完全随机无回答机制下,随着无回答率增加,系数估计量的偏差或均方误差增大往往不显著。然而,在随机无回答机制下或在非随机无回答机制下,随着无回答率增加,系数估计量的偏差和均方误差增大往往显著。

This paper estimates the coefficients of linear regression model by using the economics data containing the non-response, and selects PMM multiple imputation to give imputed values of the non-response. The simulation shows that under every non-response mechanism, the bias and mean squared error of the coefficients estimators do not obviously reduce as the multiplicity of imputation increases. The multiplicity of imputation is suggested as 5 for any non-response rate. Under completely random non-response mechanism, the bias and mean squared error of the coefficients estimators do not always obviously increase as non-response rate becomes large. However, under random non-response mechanism or under non-response not at random mechanism, the bias and mean squared error of coefficients estimators often significantly increase as the non-response rate becomes large.