試題反應理論 (item response theory;IRT)藉由受試者的實際試題反應結果,對受試者的能力進行推估,受試者的能力估計不會受到題目特性所影響。因此,本文主要藉由「擴張高低鑑別指數核平滑化無參數估計法」、「點二相關鑑別指數核平滑化無參數估計法」及「核平滑化無參數常態轉換改進估計法」三種不同IRT模式之模擬實驗,進行能力值之估計分析研究,從而驗證三種模式之估計精準度。 本研究以MATLAB軟體進行程式撰寫,產生模擬實驗資料,各項參數之設定分別為:試題鑑別度(a)、試題難度(b)和受試者能力值(θ)為常態分配,猜測參數(c)為均勻分配。試題數分為20題、30題、40題共三種,受試者人數則分為400人、800人、1200人之三種組合樣本,故共得九種組合樣本以進行能力值估計,根據研究所得結果,獲致以下幾項結論: 一、在能力值估計之精準度方面,不論是MSE值或相關係數值之檢驗,「常態轉換改進估計」之模式有最佳表現,「點二相關鑑別指數」模式其次,而「擴張高低鑑別指數」模式則最不理想。 二、在「常態轉換改進估計」模式中,可獲知當人數愈多時,所求得之MSE愈小,故知在樣本數愈大時,估計之精準度愈高。
Modern test theory is the core of the Item Response Theory. According to the actual result of item response for examinees to estimate the ability value. The estimate for item parameter is not influenced by the ability of examinees.Furthermore, the estimate for ability of examinees is not influenced by the item characteristic either . Therefore, the main purpose of this study rely on simulation to compare the accuracy of ability estimated value of three IRT Models, i.e.Upper-lower item discrimination index、Point-Biserial Correlation Item Discrimination、improve estimating value of normal transformed Kernel smoothing approaches to nonparametric. We use MATLAB in the generation and simulation of data in this study. Parameters set up as below. Discrimination、difficulty and ability value obey normal distribution. Guess paramete obey uniform distribution. We design three different sets of items amount:twenty,thirty and forty question;three different sets of examinees amount:four hundred, eight hundred and one thousand two hundred examinees. Nine different combinations type to estimate ability value.The result of the study is as below. 1. The accuracy of ability estimated value of improve estimating value of normal transformed is the best, secondly Point-Biserial Correlation Item Discrimination, upper-lower item discrimination index is the most unsatisfactory. 2. In improve estimating value of normal transformed model, when number of people is the more the smaller the MSE tried to get is, so know to count in the sample when being the bigger the higher the accuracy estimated is.