文化共識理論結合 Luce-Krantz 閾值理論處理次序類別資料：模擬研究

Abstract

文化共識理論（cultural consensus theory, CCT），係由 Batchelder 與其同事於 1980 年代中期發展出一套認知基底的方法學來評估出受訪者們之間的共識，與傳統的測驗理論不同在於，研究者對於所謂的文化「共識/正確」答案事前是未知的。CCT 最主要的目的在於揭露某一文化群體下的成員們所共有的文化知識、偏好或是信念。在受訪者們有相同文化共識下，General Condorcet Model（GCM，CCT 架構下的模型之一），卻只能專門處理二元變項的回答資料（如：真/假）。本研究延伸原先 GCM 的模型架構，並結合 Luce-Krantz 的閾值理論而提出一個新的廣義模型，命名為 General Condorcet-Luce-Kranztz model（GCLK），進而處理次序類別型的資料（包括：用李克特量表的問卷資料），此次序類別回答選項允許受訪者針對不同道題目，在回答上能表達不同的信心程度。除了找出問卷題目的共識答案外，GCLK 同時能估計出回答題目時的各項特徵，包括：題目難度、受訪者的能力與猜測偏誤。在 GCLK 公理化的設定下，本研究證明出的理論能幫助研究者偵測在同一筆的資料中存有多少組共識群體；本研究也利用階層式貝氏模型結合馬可夫鏈蒙地卡羅隨機取樣法，來估計出各項參數的後驗分配，並做了後驗預測檢驗來確認模型假設的合理性。本研究最終透過一系列的模擬研究，展示 GCLK 的可行性，以及利用貝氏估計方法印證此模型也有良好的參數回復能力。

Cultural consensus theory (CCT), developed by Batchelder and colleagues in the mid-1980s, is a cognitively driven methodology to assess informants' consensus in which the culturally correct answers are unknown to researchers in prior. The primary goal of CCT is to uncover the cultural knowledge, preference, or beliefs shared by group members. One of the CCT models, called the General Condorcet Model (GCM), deals with dichotomous (e.g., true/false) response data which were collected from a group of informants who share the same cultural knowledge. I propose a new model, called the General Condorcet-Luce-Kranztz model (GCLK), which incorporates the GCM with the Luce-Krantz threshold theory. The GCLK accounts for ordinal categorical data (including Likert-type questionnaires) in which informants can express different confidence levels when answering the items/questions. In addition to finding out the consensus truth to the items, the GCLK also estimates response characteristics, including the item difficulty and the informant's competency and guessing bias. I axiomatize the GCLK and develop a theory that can help researchers detect the number of cultures for a given data set. I utilize the hierarchical Bayesian modeling approach and the Markov chain Monte Carlo sampling method for estimation; a posterior predictive check is established to verify the central assumptions of the model. Through a series of simulation studies, I evaluate the model's applicability and find that the GCLK performs well on parameter recovery.