遺失資料之多重插補法模擬比較研究

Abstract

本研究重點為探討拔靴法（bootstrap method）、資料擴增法（data augmentation）與多重插補法（multiple imputation）對遺失資料（missing data）進行區間估計的成效。一般處理遺失值的方式有很多種，但插補法則較多統計學者使用，插補法可分為單一插補法（single imputation）及多重插補法。在早期因為單一插補法較為方便，所以較為多人所使用，而今日許多軟體漸漸提供多重插補法，讓使用者可以爲遺失值填入多個比單一插補法更有效的值。本研究利用模擬資料，同時用三種方法進行平均數的區間估計，以證明多重插補法的參數估計能力，可以達到與拔靴法的同樣效果。 本研究模擬三種型態的多元常態分布資料，並且設定不同的遺失比例，分別進行拔靴法、資料擴增法與多重插補三種方法的信賴區間估計。結果發現拔靴法在信賴區間估計上，無論樣本大小或是遺失資料比例為何，其估計能力都有一定的水準；資料擴增法則是在小樣本的信賴區間估計較大樣本好，但無論遺失比例為何，資料擴增法都是三種方法中出現最多錯誤估算的；多重插補法的估計效果和拔靴法相當，無論樣本大小或是遺失比例為何，信賴區間幾乎都涵蓋母體參數，尤其在遺失比例高達50%時，多重插補法依舊能準確地估計母體參數，顯示多重插補法所產生的參數估計是可以信賴的。

The purpose of this study is to compare the difference between the method of bootstrap, a data augmentation and multiple imputation for estimating the confidence interval of missing data. In general, there are several methods dealing with missing data, but imputation method is usually used by statisticians. The imputation method can be divided into single imputation and multiple imputation. In early years, single imputation is more convenient. Now lots of software provides the procedure of multiple imputation. The confidence intervals for mean were established by the three methods. Then we show that the multiple imputation is as efficient as bootstrap method. We simulate data from multivariate normal distribution with three different sample sizes, and set different missing rates it was found that the coverage probability for bootstrap method is approximate to the confidence coefficient. The data augmentation is inferior to both bootstrap method and multiple imputation. The result of the multiple imputation is similar to the bootstrap method. The multiple imputation still estimates the parameters accurately even for high missing rate.