The Simulation Of Coefficients Estimators Of Linear Regression Model Used PMM Imputation Method

In the field of social, medical and economic actual investigation and study, non-response often appears, and it is difficult to avoid, will affect the quality of survey data. So it is very necessary to study the solution of non-response.Dealing with non-response, we usually engaged in prevention and remedy of two point of view. Prevention is just making the investigation work rigorous and careful, reducing the non-response rate, but not completely eliminate the non-response,The remedy is intended to reduce the bias of estimation and increase reliability.Imputation method is one of the better way to solve non-response currently. And this method includes single imputation and multiple imputation.Single imputation method just give one value to each non-response, but this method can not estimate the parameter estimation error. Multiple imputation means give several values to each non-response, and we can estimate the error of the parameter estimators. Multiple imputation method for single imputation method, Multiple imputation method to make up for the shortcomings of the single imputation method. Because it considers the uncertainty of the data, this method constructs multiple interpolation values is to simulate distribution estimator under a certain condition, make more effective statistical inference.Among them, Predictive Mean Matching imputation method is a widely used method of multiple imputation method, through a simulation study for this method, the result of simulation can be used for multiple imputation method in practice,and provide theoretical suggestions and reference.This paper mainly simulate the statistics property of the PMM multiple imputation.For the non-response, firstly we impute the non-response using Predictive Mean Matching imputation method, then we estimate the coefficients of the linear regression model, at last we calculate the amount of deviation and mean square error of coefficients estimators.The factor considered in this paper include:number of imputation,non-response mechanism, non-responserate. The number of imputation in this paper was set as 5,15,25,35, 45,and the non-response rate is set to 5%,15%,25%,35%,45%, and in view of non-response mechanisms,we consider three mechanisms, they are the completely at random, at random, and not an random.According to the final simulation results, we can see that no matter under any non-response mechanisms, when the number of imputation is gradually increasing, The estimators of coefficients of the linear regression model, their deviation and mean square error show no significant decreasing trend. For any non-response rate, this paper suggeste to choose 5 times as the best imputation multiplicity. When the non-response mechanism is completely random, if non-response rate is large, the deviation and mean square error of the estimators of coefficients of the linear regression model, they often do not significantly increase. However, when non-response mechanism is at random and not at random, if non-response rate is bigger, coefficient of deviation and mean square error estimators are often shown to increase significantly.