成對比較資料中個別差異模型結構之分類

Abstract

人類的決策與選擇行為是生活中常見的心理活動，故為心理學所廣泛探討與應用的議題之一，成對比較是目前探討選擇行為常用的方法。而在成對比較資料的分析上，主要的模型可分為塞斯通(Thurstone)以及Bradley-Terry-Luce (BTL)兩大類。 探討這兩類模型的文獻很多，但很少將此兩種模型做完整的分類比較，我們試圖從模型中看待或考量個別差異的結構之不同，將這些模型進行清楚的分類。本篇論文首先介紹了塞斯通以及BTL兩種成對比較模型及其發展， 並將文獻中與其相關或延伸的模型進行分類來區別它們在考慮個別差異上之異同，另外我們選用了R、Mplus、LatentGold三種統計軟體來進行模型估計，利用模擬研究的方法， 經由比較估計量的偏差以及均方誤差去檢視這三種軟體在各類模型的估計表現。我們並且分析了兩筆關於與名人交談以及選擇大學的實際成對比較資料，使讀者對於本文所提之模型分類及其功用能更加清晰。 最後我們依本文之模型分類，整理出目前常用的一些統計軟體可運用於分析成對比較資料的現況，以期能夠提供未來進行成對比較研究的人員作為參考。Making decisions and choices are common psychological activities in our daily lives, and therefore choice behavior has been widely studied and discussed in psychology. There are two major classes of models in analyzing paired comparison data, namely the Thurstonian and the Bradley-Terry-Luce models. Although there has been quite a few theoretical development and applications of these two models throughout the literature, these works were seldom compared or integrated to provide a comprehensive overview. In this thesis, we first formulated a taxonomy of paired comparison models based on how they account for individual differences in judgment. Secondly, three statistical softwares, including R, Mplus, and LatentGold were used for estimation of models within such a taxonomy and their performance in parameter recovery were evaluated and compared through empirical bias and mean square error in simulation studies. Moreover, two paired comparison datasets of “`choosing from celebrities to have a conversation with’’ and “choosing university to attend’’ were analyzed to better illustrate the use of such a taxonomy. Finally, we gave a summary on statistical softwares capable of analyzing paired comparison data and we hoped to facilitate better use or analysis of paired comparison data for researchers.