The Integrated Model of Fuzzy Latent Knowledge Space and Its Application

本研究結合無參數試題反應理論（item response theory of non-parameter）、模糊理論（fuzzy theory）和潛在類別模式（latent class model），提出適合心理計量資料的「模糊潛在知識空間模式」（fuzzy latent knowledge space model）。本研究的整合模式，除了保有一般知識空間模式的特色和意義之外，亦改進了Yamamoto（1987）、Tatsuoka（1995）模式的缺失，並擴展山下、勝又、津田（1994）的方法和模式。所以，本研究的整合模式特色包括：（1）呈現受試者對知識狀態類別的隸屬度（membership）；（2）以試題近似三值圖（approximate ternary graph）呈現知識空間中類別之間的試題發展關係；（3）以試題分割樹形圖（partition tree graph）呈現各類別內試題的類似結構（similarity structure）；（4）呈現知識空間中每個類別的典型反應組型（ideal response pattern ）、能力值和精熟距離（distance of master）；（5）試題可採二元、多元或混合計分；（6）試題不須有局部獨立性（local independence）之假設。 本研究主要可分為實例分析和資料模擬兩大部分，在實例分析方面，分別以「國小四至六年級數學技能與解題能力的學習進展指標試題」和「國小高年級除法概念試題」二個實例，進行資料分析，說明「模糊潛在知識空間模式」的分析過程。在資料模擬方面，主要探討兩個類別在不同之人數比例和平均數接近度的情形下，分析模糊分割演算的特性。本研究提出的整合模式，期待可提供心理計量學亟待發展的類神經網路（neural networks），或人工智慧（artificial intelligence）電腦化認知診斷（computerized cognition diagnosis）工具之基礎。根據實例分析和資料模擬的結果，本研究提出結論和建議。同時，對於「模糊潛在知識空間模式」，亦提出有待發展與改進的相關主題。The purpose of this study is to combine "item response theory of non-parameter", "fuzzy theory" and "latent class model" to develop a newintegrated model called "fuzzy latent knowledge space".The integrated model is suitable for analyzing psychometrical data. In addition to having the traditional features and meanings of knowledge space, the integrated model also improves some defects of Yamamoto(1987) and Tatsuoka(1995), and enhances the method of Yamashita, Katsumata, & Tsuda(1994). Therefore, the features of the integrated model are as follows: (1)showingthe membership of task-takers with respect to each latent class; (2)showing the developmental relationship between each latent class by approximate ternary graph; (3)showing the similarity structure of items in each latent class by partition tree graph; (4)showing the ideal response pattern, ability, and distance of master of each latent class; (5)the items could be dichotomous,polytomous, or mixed scoring; and (6)there is no restriction of "local independence" between items.There are two major parts in this study. They are real data analysis and data simulation. As to the real data analysis, the researcher uses two datasets of "indicators of mathematics learning progress" and "concepts ofpartitive word problems". We can realize the features of the integrated modelaccording to the process of analyzing data. As to the data simulation, under the manipulated two factors-- "distance of mean" and "proportion of population", we can understand the characteristics of fuzzy partition.According to the real data analysis and the data simulation, the inuegrated model could be developed for tool of computerized cognitiondiagnosis or neural networks cognition diagnosis, which is very useful for psychom etrics. Based upon the findings of this study, recommendations for further research are suggested