Abstract:

Cognitive diagnostic computerized adaptive testing (CD-CAT) is a popular mode of online testing of cognitive diagnostic assessment (CDA). The key to a CD-CAT system is the item selection strategies. Someof the popular strategies are developed based on Kullback-Leibler information (KL), Shannon entropy (SHE) toselect items in CD-CAT. Typically, during CD-CAT, thesefamiliar methods would use a cutoff point to transform the attribute mastery probabilities' provisional value to binary values, but at the initial stage, the cutoff point method may lead to a larger deviation. A method that can take advantage of the probabilistic information with regard to attributes may offer a better alternative. This paper proposed two item selection strategies based on the provisional value of the attribute mastery probabilities, as follows: (1) the first strategy, which is called as PPWKL (Posterior Probability Weighted Kullback-Leibler), is based on the KL information, and it can lead to maximum difference of the sum of attribute mastery probabilities, and it is weighted bythe pattern’s posterior probability as well asthe difference of the attribute mastery probabilities between the and any possible latent state; (2) the PPWKL considers the fact that not all the patterns are equally likely, but overlooks the fact that the distances between different patterns and the current estimate are not all of equal importance. Therefore, the PPWKL can be weighed by the inverse of the distance between the and any possible latent state, which is called as PHKL (Posterior Hybrid Kullback- Leibler). Then, three simulation studies were carried out, one was the fixed length of CD-CAT, and the secondwas the variant length CD-CAT, and the last wasshort length CD-CAT.Variant item selection strategiesweretaken intoconsideration in these studies, including KL, SHE, PWKL, HKL, MI, PPWKL and PHWKL. The results were compared in terms of pattern or attribute classification correct rate, itemaverage exposure ratio, item maximum exposure ratio, item minimum exposure ratio, average test length, unused item number, number of items with exposure ratioover 20%, test overlap ratio.The simulation results indicate that: (1) the comprehensive performance of PPWKL and PHKLare better than other mentioned strategies in fixed and variant lengthCD-CAT; as to PHKL and MI, each has different strengths in short length CD-CAT; (2) PHKL and PPWKL can retain a good measurement accuracy, and also improve the utilization ratio of item pool.

Key words: text CD-CAT, item selection strategies, attribute mastery probabilities, attribute mastery pattern