- 學位論文
廣義隱藏式馬可夫模型與核平滑化無參數試題反應理論整合模式之蒙地卡羅模擬研究
The Monte Carlo Simulation Study of The Hybrid Model of Generalized Hidden Markov Model and Kernel smoothing based Item Response Theory
摘要
試題特徵曲線是試題反應理論的中心概念，其估計精準度無法以數理統計方法或邏輯法來推導證明其優劣。本文主要藉由模擬實驗來比較參數試題反應理論、基於廣義隱藏式馬可夫模型之IRT 混和模式、核平滑化無參數試題反應理論與廣義隱藏式馬可夫模型與核平滑化無參數試題反應理論整合模式四種模式之試題特徵曲線估計精準度。 模擬實驗使用MATLAB撰寫程式及產生模擬資料，並且假設鑑別度參數、難度參數和受試者能力參數為常態分配，猜測參數為均勻分配，試題數25題，受試者人數共分為100、200、500、1000、1500、2000人六種情形。根據本研究所得之結果，獲得以下結論： 一、試題特徵曲線的估計，以廣義隱藏式馬可夫模型與核平滑化無參數試題反應理論整合模式最佳。 二、在加入廣義隱藏式馬可夫模型後，無論參數或無參數型試題反應理論模式試題特徵曲線估計精準度都更為精確。 三、受試者人數會影響試題特徵曲線估計精準度，受試者人數愈多，試題特徵曲線估計精準度愈高。
並列摘要
Item characteristic curve is the central concept of the item response theory, the accuracy of ICC estimation of IRT model that is unable to prove better or not with mathematical or statistical method or the logic rule. The main purpose of this study rely on simulation to compare the accuracy of ICC estimation of four IRT Models, i.e. three-parameter logistic IRT model, the hybrid model of GHMM and 2PL-IRT, kernel smoothing based IRT, the hybrid model of GHMM and kernel smoothing based IRT. Simulation utilized MATLAB software to develop programs and simulate the data needed. Supposing discrimination parameter, difficulty parameter and ability parameter are normal distribution, guessing parameter is uniform distribution, item numbers are 25, there are six different numbers of examinees : 100,200,500,1000,1500 and 2000. According to this study, several findings have been concluded as follows: 1. The hybrid model of GHMM and kernel smoothing based IRT is better than the other’s IRT models for the accuracy of ICC estimation. 2. No matter parameter or nonparameter IRT model with GHMM is more accurate for the accuracy of ICC estimation. 3. The size of examinees will influence the accuracy of ICC estimation, more examinees are more accurate.