貝氏方法在多選題排序上的應用

Abstract

在許多調查研究中，問卷調查是一個很重要的工具。許多文獻上對於可複選的問題分析不如研究單選問題那麼的深入。Wang (2008a)在frequentist 的架構下，提出針對複選題作排序的方法。但是在實際的情況下，對於各個選項也許存在著事前分配，所以建立新的方法結合過去資料與新的資料作排序在問卷調查中是必要的課題。在本篇研究中，我們根據貝式多重檢定的方法，藉由控制後驗的錯誤發生率來得到在貝式架構下的排序。除此之外，我們也將用模擬的方法去比較這些方法的差異及恰當的拒絕區域。

In many studies, the questionnaire is an important tool for surveying. In the literature, the analyses of multiple-choice questions are not established as in depth as those for single-choice question. Wang (2008a) proposed several methods for ranking the Responses in Multiple-Choice Questions under the usual frequentist setup.However in many situations, there may exist prior information for the ranks of the responses, therefore, establishing a methodology combining the update survey data and the past information for ranking the responses is an essential issue for the questionnaire data analysis. In this paper, we based on several Bayesian multiple testing procedures to develop the Bayesian ranking methods by controlling the posterior expected false discovery rate. In addition, a simulation study is conducted to make a comparison of these approaches and to derive the appropriate rejection region for the testing.