This paper consist of three major parts: a) describing the practical situation in which the cognitive diagnostic models is needed, b) introducing two cognitive diagnostic models (DINA, NIDA), and c) exploring monotonicity properties of these two models.
One practical data set was analyzed for the whole paper.
9 items * 417 students (2/3/4 grade);
Objects A, B, C… were showed to the students, with physical attributes Y A , Y B , Y C ….involving length, size and weight. Relationships between attributes of some pairs of adjacent objects were shown to each examinee. The examinee was asked to reason about the relationship between some pairs not shown.
Each task involved 3-5 same type of object. Some tasks consist of more than 1 item. Coding: 1—all items within the task were correctly answered, using correct deductive strategy; 0--- otherwise.
After deleting 3 items with all responses were 0, the remaining 6 items were used to fit the RASCH model. Although results indicated good fit, the model is of little use in providing diagnostic information and improving further instruction. Then DINA and NIDA model were introduced for the purpose of better modeling the items and making inference about the examinees. Details about the deterministic and probabilistic parts of the two models were also available. The monotonicity properties of two models were deeper investigated in the paper, that is, 1-s>g. In other words, more task-relevant skills an examinee possesses, the easier the task should be. However, the selected dataset not show strong support to the mononicity property of DINA and NIDA model.
The third part further study the properties of the two models using the non-parametric IRT perspective. I have not fully understand this part by now, as it seems this part was focus on relating CDM with NIRT. Main idea of this paper is to introduce two CDM models, their suitable situation in practice, statistical models, and related properties. The CDMs are especially useful when the analytic results are used to make inference for further teaching and learning.