問卷分析遺失值估計問題的探討

Abstract

遺失值在處理資料上是一個普遍的問題。因此，恢復資料的完整性是一個重要的議題。本文探討在問卷裡遺失值的估計問題，而且我們比較了四種估計方法。此四種方法分別是KNN，Pearson相關性線性迴歸估計，James-Stein的相關性線性迴歸估計，以及考慮自變數相互作用的線性迴歸估計。我們模擬各種情況去比較在不同條件下的估計平均絕對誤差，如不同的共變異矩陣以及不同的受訪人數。此外我們在真實數據上應用此四種方法，並且比較和模擬結果的差異。 我們發現會隨著變異數變大估計誤差會變大，而相關係數變大誤差則會變小。四個方法在模擬的比較結果分別是KNN誤差最大，correlation for linear regression、James-Stein for linear regression與stepwise linear regression次之。

The missing value occurrence is a common problem for processing data. Therefore, missing value estimation is an important issue for restoring data. This thesis considers the missing value estimation problem in questionnaire, and we compare four methods for imputing missing value. These four methods are KNN, Pearson correlation coefficient for linear regression, James-Stein estimate for linear regression and stepwise linear regression respectively. We use simulation study to compare mean absolute error on different situations such as different variance-covariance matrix or different number of respondents. In addition, we apply four estimation methods in a real data example. We find that mean absolute error decreases as the correlation increases or variance decreases. In addition, we find KNN method has the largest mean absolute error in all situations, and the other methods have similar mean absolute errors in our simulation.