多選題排序應用的演算法

Abstract

問卷調查在很多研究中是一項常用的調查工具，其中複選題是問卷中常見到的題型。近年來，很多研究提出了一些模型和方法針對複選題的資料做分析，但複選題選項排序的問題是目前主要有興趣的議題。Wang (2008) 提出了一些方法用來檢定任兩個選項被選到的機率是否相等，然而，當選項的個數太多時，根據這些方法來做排序將會使得排序過程變得複雜費時。因此，在本篇文章裡，我們提出了一個演算法進而寫成一個程式，使得不管選項個數的多寡，都能迅速排序 出結果。此外，為了減少排序上不一致性問題的情況發生，我們提出採用False Discovery Rate 的檢定準則來做排序。根據我們模擬的結果，證明這樣的方法可以減少不一致性現象的出現。

In many studies, the questionnaire is a common tool for surveying. A multiple response question is a commonly used question designed in a questionnaire. Recently, many studies proposed models and approaches for analyzing data of a multiple response question. Ranking responses problem may be the primary issue in the analysis of a multiple response question. Wang (2008) proposed methodologies for testing the equality of selected probabilities for two responses. Since it is possible that the number of responses is large, it leads to a complicated situation to rank the responses based on these approaches. In this study, we develop algorithms for ranking responses for any response number. In addition, to diminish the ranking inconsistent situation, we propose adopting the false discovery rate testing criterion for ranking. A simulation study shows it can reduce the frequency of ranking inconsistent phenomenon.