不可忽略的无回答机制下的校准研究

Calibration for Nonignorable Unit Nonresponse

在实际调查工作中,由于客观条件的限制,难以完全避免无回答情况的出现。当无回答已经产生,且单元作答情况与目标变量本身有关系时,缺失数据机制不可忽略,需要在数据分析阶段弥补无回答对估计产生的负面影响。现有方法多假定缺失数据机制为随机缺失,少数非随机缺失机制下的方法基于模型进行推断,但因其对模型假设和模型识别的较强要求造成了应用上的局限性。校准估计已在抽样推断中得到了广泛应用,它在利用辅助信息提高样本代表性的同时,控制了无回答误差。采用RGRG法将模型校准法与准随机化的响应模型相结合,解决非随机缺失下的权数调整和总体估计问题。对RGRG法的估计过程和估计优势进行了理论分析和实证研究。结果表明,在不可忽略的无回答机制下,通过RGRG法的调整降低了最终权数的变异性;加权估计量具有更小的偏差、标准误差和均方误差根,具有渐进无偏性和渐近一致性。同时,该方法是稳健的,对无回答具有双重保护作用,允许响应模型和超总体模型仅在一定程度上拟合总体,降低了对模型识别的敏感度。

In the actual sampling survey,it is difficult to completely avoid the non-response due to the limitation of objective conditions.When the nonresponse has occurred,which is related to the target variable,the missing data mechanism cannot be ignored,and it is necessary to compensate for the negative impact of the nonresponse on the estimation in the data analysis stage.The existing methods mostly assume that the missing data mechanism is random missing;a few methods under non-random missing mechanism are model-based.However,due to its strong requirements for model assumptions and model recognition,it has limited application.Calibration has been widely used in sampling inference.It uses the auxiliary information to improve the representativeness of the sample,and controls the nonresponse error.The RGRG method used here combines the model-based calibration method with a quasi-randomized response model to solve the weight adjustment and estimation problems in the absence of non-randomness.The paper conducts theoretical analysis and empirical research of the RGRG method.The results show that under the nonignorable nonresponse mechanism,adjustment of the RGRG method reduces the variability of the final weights.The weighted estimator has smaller bias,standard errors and root mean square errors,and is progressively unbiased and gradually nearly consistent.At the same time,the method is robust and has double protection for no answer,allowing the response model and the super-population model to fit the population only in some sense,reducing the sensitivity to model identification.