類神經網路在試題反應理論之研究

古典測驗理論是目前測驗學界使用與流通最廣的理論模式；但其理論有一些先天的缺失，測驗學者為彌補古典測驗理論的缺點於是有現代測驗理論誕生；而試題反應理論(Item Response Theory，簡稱為IRT）又是其中的精隨。試題反應模式表示受試者能力與受試項目反應間關係的數學描述，其模式使用無參數試題反應模式預估，其函數可呈現更多樣化、更真實性的優點。因此，本研究基於此種模式進行試題特徵曲線的估算，這是現代測驗理論之IRT非常重要的工作。而本論文主要是運用類神經網路的通用迴歸類神經網路進行試題反應理論的試題特徵曲線的估計，並與傳統的常用估計法－三次曲線尺平滑插補做比較。研究中比較各種不同方法在不同情況之預估受試者能力精確度，模擬實驗中所考量的影響因素有：試卷試題數、受試者人數、受試者能力分布及受試者的答題情況，所採用的比較率則有RMSE，SSE，MSE，RS等四種誤差量尺。實驗結果顯示當受試者的答題為階梯情況時，通用迴歸類神經網路插補法有最小的誤差值；三次曲線尺平滑插補法如同預期，在各種情形下都有不錯的預估精率度。

關鍵字

試題反應理論；試題特徵曲線；通用迴歸類神經網路；三次曲線尺平滑插補法

並列摘要

Classical test theory is the most popular and useful model in the nowadays. Unfortunately, there are some natural defects in this theory. Testing experts try to solve these disadvantages so a modern test theory was born and Item Response Theory (IRT) is the kernel of it. IRT relates characteristics of items and characteristics of individuals to the probability of a positive response. If a non-parameter model was used, the estimated function will be more multiform and real. Therefore this research is based on non-parameter model to estimate the Item Characteristic Curve (ICC) and the work is very important in the IRT. Generalized Regression Neural Network (GRNN) is the main approach to estimate ICC in the IRT in this paper. The simulation results were compared with cubic spline interpolation. In this research various methods were applied under different conditions to compute accuracy of estimating examinee's ability. Some factors which include the number of test items, the number of examinees, the distribution of examinee's ability, and the probability of answering are consider in the simulation and RMSE, SSE, MSE, RS are used to measure error. The simulation results show that when the probability distribution of answering is a step-wise function, there are the best performance using GRNN approach. The results as we desired that no matter under what conditions the performance of cubic spline interpolation is not bad.