A Fast Algorithm for Finding Ideal Response Pattern vectors of any Test Q-Matrix

Abstract

In this paper, based on Gauss’ symbol function, a novel fast algorithm for finding the ideal item response pattern vector to correspond to a given attribute state vector of any test Q-matrix is proposed. It is simpler and faster than Tatsuoka’s Boolean description function algorithm. Furthermore, a novel discriminant validity index of any test Q-matrix is also proposed, from now on, we can find the better test Q-matrix to improve the cognitive analyses of educational tests by using this validation index.