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題名:國立臺中教育大學教育測驗統計研究所博士論文
作者:陳姿良
作者(外文):Chen, Tzu-Liang
校院名稱:國立臺中教育大學
系所名稱:教育測驗統計研究所
指導教授:許天維
永井正武
學位類別:博士
出版日期:2014
主題關鍵詞:粗糙集結構模型法粗糙集理論決策屬性檢驗程序可達矩陣再配置矩陣階層式結構圖RSMRough Set Theoryprogram of testing decision attributereachable matrixRe-configuration Matrixhierarchical structural graph
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本研究的目的為提出粗糙集結構模型法(Rough Structural Modeling, RSM)改良粗糙集理論(Rough Set Theory),使其結構化與可視化,以及提出決策屬性檢驗程序,解決粗糙集分析法中決策屬性由專家主觀判斷的缺點,並應用於教育測量領域。透過三個範例(迷思區分析、敏感性分析、課程結構分析)的實證資料分析,不但驗證研究方法的可行性與信賴性,更為無母數統計的研究領域提出了客觀且創新的研究方式。RSM是一種適用於可達矩陣運算的結構分析方式,此分析法結合粗糙集理論和形式概念分析法(Formal Concept Analysis, FCA),根據二元概念格算法來構造概念格,透過生成再配置矩陣(Re-configuration Matrix)以及可達矩陣的運算,以建立不同概念群中概念之間的階層式結構圖。將RSM應用在迷思區分析、敏感性分析、課程結構分析時,透過決策屬性的訂定,不但可建立不同概念群間的結構圖,更可精簡結構圖,以凸顯出不同決策屬性之物件在結構上的差異。決策屬性檢驗程序結合ROC(Receiver Operating Characteristic)分析及無母數的卡方檢定(Chi-square Test),有別於傳統相對誤差的判斷方式,不論研究對象數量多寡,此檢驗程序皆適用。將此檢驗程序應用在迷思區分析時,可比較不同Gamma值所決定出來的迷思區,改良迷思區分析法;應用在敏感性分析時,可檢驗Gamma值和排序的切截點,改良ROC分析法中專家主觀判斷的缺點。受限於研究時間與人力等客觀因素,本研究可能之限制如下:(一)本研究所提供應用於教育測量之三個範例,研究對象均為立意取樣。(二)本研究在生成形式背景以及所提出的二元概念格算法,均為二元資料。
The purposes of this study are to propose Rough Structural Modeling (RSM) to improve structure and visualization of Rough Set Theory in educational measurement, to propose program of testing decision attribute for solving shortcoming of decision attribute that is subjective judged by experts in Rough Set Theory. Through three empirical examples (analyses of Misconceptions’ Domain, sensitivity, and curriculum’s structure), the objective and innovative method with verified feasibility and reliability is proposed in nonparametric statistical. RSM is a method of structural analysis that combined Rough Set Theory and Formal Concept Analysis (FCA) with operation of reachable matrix. It generates Re-configuration Matrix to establish hierarchical structural graph based on operation of binary concept lattice. The graph of different decision attributes can be applied in analyses of Misconceptions’ Domain, sensitivity, and curriculum’s structure. Program of testing decision attribute is applicable regardless of the amount of participants that combines Receiver Operating Characteristic (ROC) and Nonparametric Chi-square Test. Applying the program in analysis of Misconceptions’ Domain with different Gamma value for improving related method. For sensitivity analysis, shortcoming of subjective judged by experts in ROC can be improved by evaluating cut-off points of Gamma value and sorting. Because of objective factors, limitations of the study are as follows: (a) The sampling methods are purposive sampling. (b) The data are both binary data in formal context and operation of binary concept lattice.
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