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Please use this identifier to cite or link to this item: http://ir.ncue.edu.tw/ir/handle/987654321/15196

Title: 無母數參數估計在IRT真分數等化法的應用與分析
Nonparametric ICC Estimation with Application to IRT True Score Equating
Authors: 李信宏
Contributors: 數學系
Keywords: 等化;IRT 真分數等化;試題反應模式
Kernel smoothing;BILOG 3;Equating;Item Response Theory(IRT) Model;IRT True Score Equating;Kernel Smoothing
Date: 2000
Issue Date: 2013-01-07T09:04:06Z
Publisher: 行政院國家科學委員會
Abstract: 等化是指利用統計方法來轉換兩個或者多個試卷分數的過程。這裡所指的多個試卷,實際上其測驗內容以及所欲測量的潛在能力是一致的,可以視為同一測驗的數個版本(same test but different forms)。這些試卷可以在不同日期施測,或者在同一時間對不同受試者施測,藉由等化過程,這些試卷的測驗結果亦即受試者的表現,就可以直接互相比較。
一般常用的等化方法包括了傳統的線性等化、百分位數等化以及IRT 真分數等化和觀察分數等化等。其中IRT 真分數等化乃是經由累加的試題反應模式函數值,來求取兩個試卷的同等分數,在這個轉換分數的過程中,必須使用統計方法來估計試題反應模式中的試題參數。一般而言,參數估計大部分採用聯合最大概似估計法、邊際最大概似估計法或者貝氏估計法等。這些方法一方面要考慮到試題反應模式的選擇是否適用於測驗資料,另一方面由於概似函數的複雜,試題參數估計值大都是藉由數值方法遞回計算來獲得,其結果應用於等化可能無法轉換成比較精確的同等分數。
本研究建議使用kernel smoothing來估計試題特徵曲線並應用於IRT真分數等化。此方法是一種無參數的分析方法,不需要先假設某一模式,而是根據實際作答結果,選擇適當的權數將作答資料做加權平均,進而估計試題特徵曲線。此外,計畫中也將設計各種不同狀況來實施模擬研究,特別是當測驗資料並不符合二參數以及三參數對數模式時,以強調使用無母數方法的優點。最後,研究的成果將和使用BILOG 3軟體估計參數進而實行等化的結果對照分析,希望藉此充分瞭解計畫所提方法的各種性質,進一步而能夠應用於實際的測驗資料。
Equating is a statistical process that is used in situation where several alternate forms of a test exist and scores earned on different forms are compared to each other. Currently, a number of procedures have been developed in equating. For example, linear equating, equipercentile equating, IRT true score equating as well as observed score equating. Typically, after the item parameters are estimated and converted to be on the same scale, the IRT true score equating can be employed to transform scores between different forms. However, this method is based on strong model assumptions, which likely do not hold precisely in certain real testing situations. The proposed procedure used nonparametric regression methods such as kernel smoothing to estimate item 2 characteristics curves (ICCs) for each item. The estimated ICCs then are added together resulting in an estimated true score from which the IRT true score equating can be utilized. A full-scale simulation study is design to investigate the performance of our procedure, especially for equating errors. Meanwhile, the comparisons of behaviors of our method with other equating approaches is reported and carefully discussed.
Relation: 國科會計畫, 計畫編號: NSC89-2118-M018-005; 研究期間: 8908-9007
Appears in Collections:[數學系] 國科會計畫

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