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系統識別號 U0026-2007201612532100
論文名稱(中文) 具有遺漏值列聯表之最大概似估計
論文名稱(英文) Maximum Likelihood Estimation of Contingency Table Probabilities with Missing Values
校院名稱 成功大學
系所名稱(中) 心理學系
系所名稱(英) Department of Psychology
學年度 104
學期 2
出版年 105
研究生(中文) 胡文馨
研究生(英文) Wen-Hsin Hu
學號 u76031019
學位類別 碩士
語文別 中文
論文頁數 40頁
口試委員 指導教授-黃柏僩
口試委員-鄭中平
口試委員-李俊霆
中文關鍵字 順序變項  列聯表細格機率  結構方程模型  遺漏值 
英文關鍵字 Ordinal Variable  Contingency Table Cell Probability  Structure Equation Modeling  Missingness 
學科別分類
中文摘要 在進行順序變項的結構方程模型分析時,一個常用的方法是先將資料以列聯表的方式表徵,利用列聯表的配對細格機率求得資料的多元類別關聯,再將此多元類別關聯做為共變異數矩陣進行結構方程模型分析。在實務應用上實徵資料的研究常會面臨遺漏值的問題,雖然在連續變項的結構方程模型的遺漏值已經有了完善的發展,然而在以結構方程模型分析順序變項時的遺漏值處理法卻尚未有一個好的流程。本研究試圖使用階層對數模型結合 Poisson 廣義線性模型提出一個求得列聯表配對細格機率估計值的方法,並推導其漸進估計標準誤,做為一個處理順序變項結構方程模型的遺漏值問題的初探。本研究亦以一個模擬資料比較此方法和列刪除法、配對刪除法於偏誤值、變異數與 95% 信賴區間覆蓋率之表現,結果顯示最大概似法在整體的表現上優於其他兩者,不但具有較小的偏誤和變異數,同時 95% 信賴區間覆蓋率的表現也符合預期,本文亦於最後說明如何將此法應用於結構方程模型方法。
英文摘要 When using structural equation modeling (SEM) to analyze ordinal data, analysts first obtain a polychoric correlation matrix and the data then treat it as covariance matrix in SEM. Once the original ordinal data has missing values, the modification of the process
of estimating polychoric correlation correctly may be an issue. The quality of polychoric correlation estimates relies on the quality of pairwise contingency table cell probability estimates. This article proposed a procedure of maximum likelihood (ML) method of obtaining the estimates of contingency table cell probabilities and derived the of asymptotic covariance matrix of contingency table cell probability estimates. The article also conducted a simulation research to compare the performances of the proposed method, listwise deletion and pairwise deletion. The results suggested that when data is missing completely at random, all of the three methods performed well. On the contrary, only maximum likelihood method had an acceptable performance when the data is missing at random.
論文目次 摘要 i
英文摘要 ii
目錄 v
表目錄 vi
圖目錄 vii
第一章. 緒論 1
第一節. 研究背景 1
第二節. 結構方程模型 2
第三節. 遺漏機制 3
第四節. 遺漏值處理法 5
第五節. 研究問題 7
第二章. 模型與求解 9
第一節. 模型架構 9
第二節. 最大概似估計法 12
1 牛頓法 12
2 ECM 算則 13
第三節. 訊息矩陣與漸進共變異數矩陣 14
第三章. 模擬研究 18
第一節. 模擬設計 18
第二節. 結果 22
第四章. 討論 34
第一節. 研究貢獻 34
第二節. 給實徵資料分析者的建議 35
第三節. 最大概似法於順序變項 SEM 中之應用 36
第四節. 研究限制 36
參考文獻 38
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