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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/141007
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/141007


    Title: 多群體試題反應理論樹狀模型之統計推論與應用
    Statistical Inference and Applications of a Multiple-group Item Response Theory Tree Model
    Authors: 楊承鑫
    Yang, Cheng-Xin
    Contributors: 張育瑋
    Chang, Yu-Wei
    楊承鑫
    Yang, Cheng-Xin
    Keywords: 貝氏估計
    差異試題功能
    試題反應樹狀模型
    遺失值
    spike-and-slab 先驗分佈
    Bayesian estimation
    Differential item functioning
    Item Response Theory tree model
    Missing data
    Spike-and-slab priors
    Date: 2022
    Issue Date: 2022-08-01 17:15:40 (UTC+8)
    Abstract: 本研究將文獻上的一個試題反應理論樹狀模型推廣至可以處理多群體的模型,可以同時考慮問卷或成就測驗中的群體差異與遺失值的效應。有別於大多數差異試題功能檢驗的研究需要先尋找定錨題再偵測具差異試題功能的題目,以在成就測驗中去掉這類的題目進而達到測驗的公平性,本研究透過貝氏估計搭配使用 spike-and-slab 先驗分佈 (Ishwaran 與 Rao 2005; Rockova 與 George 2018) 在特定參數,並使用吉氏採樣與 Metroplis-Hastings 演算法等計算技巧,可以同時完成差異試題功能的檢驗與模型的參數估計。本文亦將呈現對於提出模型建議的估計流程,並以模擬研究展現參數估計的不偏性與均方根誤差,及差異試題功能檢驗的成效。最後將本文提出的方法應用至一筆實際資料。
    In the current study, we extend an Item Response Theory tree model with four end nodes (TR4) in the literature to accommodate group difference. The extended model takes the group difference and missing data in questionnaire or achievement test into consideration. Different from most of present differential item functioning (DIF) studies where one has to select anchor items and then detect DIF items, we achieve DIF detection and parameter estimation simultaneously through applying some spike-and-slab priors (Ishwaran and Rao 2005; Rockova and George 2018) in full Bayesian inference. The suggested estimation procedure for the Multiple-group TR4 model is presented. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real data set for illustration.
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    Description: 碩士
    國立政治大學
    統計學系
    109354015
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0109354015
    Data Type: thesis
    DOI: 10.6814/NCCU202200971
    Appears in Collections:[統計學系] 學位論文

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