無參數加權認知診斷模式

A Nonparametric Weighted Cognitive Diagnosis Model

認知診斷模式可以用來了解受試者在技能或概念上的精熟與否，近年來也已經 被應用到不同領域中。其中，無參數認知診斷模式可透過「觀察作答反應」與「理 想作答反應」之間的距離，搭配最近鄰分類器，來決定受試者的認知反應組型（技 能具備與否）。因為無參數認知診斷模式不需要估計參數，故其適用於小樣本，模 式判別所需要的時間也非常短暫。但是無參數認知診斷模式並未考慮到受試者在作 答時可能會疏忽答錯或猜測答對，僅僅比對觀察作答反應與理想作答反應可能會受 到疏忽或猜測影響，造成誤判受試者的認知反應組型。故本研究提出「無參數加權 認知診斷模式」，利用疏忽權重與猜測權重，搭配理想作答反應，計算出加權中 心。最後，再比對「觀察作答反應」與「加權中心的距離」來決定受試者的認知反 應組型。模擬資料結果顯示，在受試者樣本數較少的情況下，無參數加權認知診斷 模式的估計優於無參數認知診斷模式與DINA（Deterministic Input， Noisy “And” Gate Model）模式，特別是整體辨識率的一致性。透過「分數乘法」實證資料也驗 證，無參數加權認知診斷模式可以提供較準確的認知反應組型估計，也更適用於目 前小班制的教學現場。

Cognitive Diagnosis Models (CDMs) can help teachers or researchers to understand the skills that have been mastered or those have not. Hence， some models have been applied to many areas recently. A nonparametric CDM (NCDM) was proposed to estimate the attribute profile vectors of examinees by the nearest neighborhood classifier through the distances from the observed responses to the ideal responses.Moreover， NCDM does not require the parameter estimation and is more appropriate to the small sample size problem than parametric CDMs such as DINA (Deterministic Input， Noisy “And” Gate Model) model. In addition， it costs only a few CPU times for estimating examinees’ attribute profile vectors by applying NCDM. However， observed responses of examinees on an item are influenced by the slipping or guessing of examinees. Furthermore， NCDM does not take them into account. In this study， a nonparametric weighted CDM (NWCDM) was proposed， and it uses weighted means based on the slipping and guessing weights instead of the ideal responses of NCDM. The estimated attribute profile vectors of examinees are classified by the nearest neighborhood classifier through the distances from the observed responses to the weighted means. From the experimental results of simulated data sets， NWCDM outperforms than NCDM and DINA on estimating attribute profile vectors when the sample size is small. According to the results on a real data set， NWCDM can provide more accurate estimations， and is more suitable for recently small class teaching.