Abstract
The goal of an exam in cognitive diagnostic assessment is to uncover whether an examinee has mastered certain attributes. Different cognitive diagnosis models (CDMs) have been developed for this purpose. The core of these CDMs is the Q-matrix, which is an item-to-attribute mapping, traditionally designed by domain experts. An expert designed Q-matrix is not without issues. For example, domain experts might neglect some attributes or have different opinions about the inclusion of some entries in the Q-matrix. It is therefore of practical importance to develop an automated method to estimate the Q-matrix. This research proposes a deterministic learning algorithm for estimating the Q-matrix. To obtain a sensible binary Q-matrix, a dichotomizing method is also devised. Results from the simulation study shows that the proposed method for estimating the Q-matrix is useful. The empirical study analyzes the ECPE data. The estimated Q-matrix is compared with the expert-designed one. All analyses in this research are carried out in R.
Highlights
As in the DINA model, αik is the mastery of attribute k for examinee i and q jk is the state of the jth item and kth attribute in the Q-matrix
Values for all guess and slip parameters are set to 0.2 for both the DINA model (s j = g j = 0.2) and reparameterized unified model (RRUM) (s jk = g jk = 0.2), and the data are created using the inverse transform sampling from two points, in which the probability is obtained from the item response function (IRF) of the DINA model and RRUM
The last 10 years have seen the development of a few cognitive diagnosis models (CDMs)-based methods for extracting the Q-matrix, whereas non-CDM based approaches have been rarely seen
Summary
Cognitive diagnostic assessment (CDA) is a framework that intends to evaluate an examinee’s mastery of a specific cognitive skill called an attribute [1]. DINA model and RRUM are non-compensatory, assuming that examinees must have mastered all the required attributes to correctly answer an item. ∏ αik , k =1 where αik is the mastery of attribute k (k = 1, · · · , K ) for examinee i and q jk is the state of the jth item and kth attribute in the Q-matrix. Where g j and s j are guess and slip parameters for item j, αi is the attribute status of examinee i. Suppose the guess and slip parameters for item 1 in Table 1 are g1 = s1 = 0.2. As in the DINA model, αik is the mastery of attribute k for examinee i and q jk is the state of the jth item and kth attribute in the Q-matrix
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