在測驗含有題組(testlet)結構時，由於違反了試題反應理論(Item Response Theory, IRT)中局部獨立性的假設，使得IRT的估計方法產生偏誤，過去研究的解決方式為在IRT模型中多加入一個參數，將題組的影響力納入模型中，此即為題組反應理論(Testlet Response Theory, TRT)，在貝氏(Bayesian)的架構下，此方法的計算則可透過SCORIGHT軟體來達成。本研究旨在透過另一種方法，即廣義方程式(Generalized Estimation Equation, GEE)去處理測驗中的題組效果。GEE過去常被使用於分析縱貫式(longitudinal)的資料，本研究使用此方法來捕捉題組測驗下作答結果的相關性，並經重新參數化調整係數後使其能對受試者能力值進行估計。 電腦模擬的結果顯示GEE能有效的處理題組效果帶來的影響。在GEE和貝氏題組模型的比較上，GEE對於程度好和程度差的受試者有較佳的估計效果；而貝氏題組模型則對於程度中等的受試者表現較好，此外我們也針對GEE的估計效率進行了實驗，結果顯示先將受試者依能力分組再進行GEE估計能提升GEE的估計效率。 在文章中，我們也展示了使用GEE計算題組訊息量的方式，做為題組式測驗下評估該測驗對於各能力區間的受試者在估計準確度上的參考。 / If the tests have testlet structure, the bias may arise when using traditional Item Response Theory(IRT) estimation methods due to the violations to the assumption of local independence. To deal with the testlet effect, previous studies introduced a new parameter to the classical IRT model which called Testlet Response Theory(TRT). Under the Bayesian framework, the estimation can be accomplished on the SCORIGHT program. The purpose of this paper is to use another method named Generalized Estimation Equation(GEE) to model testlet response data. GEE was commonly used to analyze the longitudinal data. We use this method to capture the information from the correlated items and estimated ability of the examinees through re-parametrization. Simulation results indicate that GEE can deal with the testlet effect effectively. On the comparison between GEE and Bayesian testlet model, GEE does better on estimation of the examinees who have high or low ability level. In contrast, Bayesian testlet model does better on estimation of medium ability level. In addition, we design the experiment to test the efficiency of GEE. The results show that group the examinees according to their ability before doing the GEE estimation can improve the efficiency of GEE. In this paper, we also demonstrate the method to calculate testlet information using GEE which can be taken as reference for assessing estimation accuracy of each ability level in testlet-based testing.

本文在古典測驗的概念下，賦予題組適當機率模式，探討難度指標與鑑別度指標的計算公式；且以九十六年第二次國中基測英語科試題為驗證實例，並與傳統模式之計算結果相互比較。 / Modeling a testlet with a probability structure, we investigate the computational formulas of the difficulty index and the discrimination index. Data taken from the English test items of the second basic competence test for junior high school students in 2007 are used for empirical verification and the result is compared with that obtained by the traditional method.

題組題是依據所提供之新情境和資料作答的試題類型，它能測量到學生的理解、應用、分析或評鑑能力，一般來說，同一題組內各子題有某種程度的關聯性。由於題組題是近幾年國民中學基本學力測驗常見的試題類型，且目前各種鑑別度定義僅針對單一試題作鑑別度分析，若將其應用在分析題組型試題鑑別度時，除了無法計算題組本身的鑑別度之外，甚至會忽略題組內各子題之間的關聯性。此外，目前題組鑑別度的相關研究並不多，故本論文以複相關係數的觀點探討其鑑別度，提供新的研究方向。本文先分析獨立型試題鑑別度，並將其研究結果拓展至題組型試題。對於獨立型試題，本文驗證了以點二系列相關為定義的鑑別度是以相關係數為定義的鑑別度之特例。對於題組型試題，在蒐集測驗結果資料後，本文運用迴歸分析的技巧計算「題組本身」鑑別度，同時，為了探求在排除同一題組內前面各子題影響力後的子題鑑別度對於該題組鑑別度的貢獻程度，故本文提出「淨得分」與「淨鑑別度」的新概念，並發現題組鑑別度與各子題淨鑑別度之間有密切的關聯性；再者，本文亦提供了檢定各子題淨鑑別度是否顯著的統計方法。最後，以99年第一次國中基測英語科試題為例，利用本文研究結果計算其獨立型試題鑑別度以及題組試題之題組鑑別度、各子題鑑別度與各子題淨鑑別度，並與其它有關試題鑑別度的研究作比較與分析。 / For testlet, it is answered by the provided new situation and information, can measure the student’s understanding, application, analysis and judging ability. Generally speaking, a relation exists in each item within testlet. In the recent years, testlet is an usual type in the Basic Competence Test for Junior High School. Moreover, current all definitions of discrimination index are only focusing on the single item. When these definitions are applied to analyze the discrimination index of testlet directly, not only the discrimination index of testlet can not be calculated but the relation between items within testlet will be neglected. Furthermore, due to the lack of the discrimination index study on testlet, this thesis investigates the discrimination index of testlet by regression analysis with the view point of multiple correlation coefficient and provides a new direction for the following study. This thesis is investigating the discrimination index of independent items, and this result is applied to testlet. For individual items, this study proves that point-biserial correlation is a special case of correlation coefficient. For testlet, after data collection, this study calculates the discrimination index of testlet itself by regression analysis. In the meantime, for investigating the contribution of the discrimination index of testlet of item within testlet which is getting rid of the influence of the previous items in the same testlet, this study proposes a new concept of “net score” and “net discrimination”. First, this study finds the close relation between the discrimination index of testlet and item within testlet. Second, this study states how to find the “net” discrimination index of item within testlet is remarkable or not by statistics. Finally, this study takes the English test items of the First Basic Competence Test for Junior High School Students in 2010 as example to calculate their discrimination index of individual item, testlet, item with testlet, and the net discrimination index of item within testlet, separately, by the deduced formula. A comparison and analysis between this and related study also have been taken into process in this study.