能力估計方法對多向度電腦化適性測驗測量精準度的影響

The Influences of the Ability Estimation Methods on the Measurement Accuracy in Multidimensional Computerized Adaptive Testing

本研究旨在分析不同能力估計方法對多向度電腦化適性測驗（multidimensional computerized adaptive testing， MCAT ）測量精準度的影響。研究分為兩階段：第一階段先找出在MCAT 中貝氏期望後驗法（expected a posteriori， EAP ）的最佳節點數（quadrature point）；第二階段是比較最大概似法（maximum likelihood， ML）、期望後驗法（EAP ）與最大後驗法（maximum a posteriori， MAP ）在不同向度（二向度與四向度）及不同相關性（低相關與高相關）的情況下，進行不同題數（20 題、40 題、60 題、80 題）MCAT 時的能力估計信度、偏誤（bias） 以及均方根誤（root mean square of error， RMSE）。階段一的結果顯示，隨著EAP 節點數的增加（從5~30 點）與能力向度的增加，其選題所需的時間會明顯地增加。在考量到選題時間又不致影響到測量精準度的情況下，在MCAT 中將EAP 的節點數訂為10 是理想的選擇。階段二的結果顯示，MAP 法與EAP 法比ML 法的能力估計信度高，均方根誤較低。在平均偏誤方面此三種方法則無明顯差異，不過MAP 法會有明顯的.歸性偏誤。這些現象在能力間相關較高、能力向度數量較多以及題數較少時會更明顯。整體而言，三種方法各有其優缺點，其中MAP 法的.歸性偏誤、EAP 法的選題時間以及ML 法的信度與測量誤差是未來進行MCAT 時需要改善的問題。

The goal of the research was to investigate the influences of ability estimation methods on multidimensional computerized adaptive testing. In stage 1， different quadrature points of the Baysian expected a posteriori (EAP) estimation were manipulated in order to find out the appropriate quadrature point of EAP in multidimensional computerized adaptive testing (MCAT). In stage 2， the maximum likelihood (ML) estimation， the Bayesian maximum a posteriori (MAP) estimation， and the EAP estimation methods were used in two kinds of ability dimensions (two and four dimensions) and two kinds of correlations between dimensions (high correlations and low correlations). The target item numbers of MCAT were 20， 40， 60， and 80. The dependent variables were the average reliability， bias， and the root mean square of error (RMSE) in all ability dimensions. Results in stage 1 indicated that the higher the quadrature point and the ability dimensions， the much higher the estimation time of MCAT. Ten points was appropriate in less than 4 dimensions of MCAT when the estimation time and the reliability of ability estimation were taken into consideration. Results of stage 2 indicated that MAP and EAP methods resulted in higher reliability and lower RMSE than ML method， especially in the conditions of high correlation between abilities， more ability dimensions， and fewer MCAT items. There were advantages and disadvantages in the three estimation methods. The regression bias of MAP， the estimation times of EAP， and the reliability and RMSE of ML were the problems that should be resolved when executing MCAT.