G-DINA模型考慮順序限制下之參數估計

Abstract

測驗的目的在於評估學生的學習狀況，但是不論是百分制還是量尺分數都沒有辦法對於學生掌握了哪些概念提供足夠的訊息。為了讓老師和學生能從測驗的結果中得到更完整的資訊，認知診斷模型在這方面提供了很大的幫助。其中，DINA模型概念簡單，也容易解釋，它的一般化形式G-DINA模型則提供了更彈性的參數估計。然而，G-DINA原則上允許即使掌握的概念較多，也可能在試題的答對率上不如掌握概念較少的學生。這篇論文對於參數空間受限制的G-DINA模型，提供了上移和下移兩種參數估計的算法，藉此避免在實際應用認知診斷模型時會發生上述被認為是違反直覺的現象。透過模擬研究，在參數空間確實在受限制之範圍時，我們比較這兩種參數估計方法與原本的估計方法在參數估計上的準確度以及受試者認知組型的辨識率。結果顯示我們所提出的上移法表現較其它兩個方法好。因此不論受試者的認知組型、題目的類型或樣本大小為何，本文都建議使用這個方法。

The purpose of a test is to assess student learning, but the percentile or the total score of the test does not seem to provide enough information as for whether the students master all or some attributes the test intends to evaluate. In order to obtain a better understanding of the test results for both the teachers and the students, cognitive diagnostic models can provide more information in this regard.Among them, the DINA model is very straightforward and its generalization, the G-DINA model, offers a more flexible extension.However, the unrestricted parameter space of G-DINA model allows for the possibility of the lower correct rates for the students who master more attributes than those who know less.This paper considers the use of order-constrained parameter space of the G-DINA model to avoid such counter-intuitive phenomena and proposes two algorithms, the upward and downward methods, for its parameter estimation. Through simulation studies, we compare both the accuracy in parameter estimates and in classification of attribute patterns obtained from the proposed two algorithms and the existent one when the restrictive parameter space is true. Our results show that the upward method performs the best among the three and therefore it is recommended for estimation, regardless of the distributions of respondents' cognitive patterns, feature types of the test items, and sample sizes of the data.