Nonparametric Calibration of Item-by-Attribute Matrix in Cognitive Diagnosis.

A nonparametric technique based on the Hamming distance is proposed in this research by recognizing that once the attribute vector is known, or correctly estimated with high probability, one can determine the item-by-attribute vectors for new items undergoing calibration. We consider the setting where Q is known for a large item bank, and the q-vectors of additional items are estimated. The method is studied in simulation under a wide variety of conditions, and is illustrated with the Tatsuoka fraction subtraction data. A consistency theorem is developed giving conditions under which nonparametric Q calibration can be expected to work.