A Classification Space: Rule Space as a Cartesian Product of the Person Parameter q in Item Response Theory, z, and Generalized zs
This chapter introduces the classification space called rule space and its coordinates, emphasizing their practical characteristics. The first coordinate is the ability measure obtained from item response theory (IRT); therefore, it is sensitive to how high each student’s score in a test is. The second coordinate is the index that measures unusualness of response patterns called person-fit statistics. In Chapter 4, determination of all the possible knowledge states from a Q matrix that is viewed as a set of hypotheses generated by domain experts was discussed. Each knowledge state consists of mastered or nonmastered attributes. The rule space enables us to interpret which knowledge states are commonly populated and, moreover, to tell the test users that different ability levels, high or low scores of students, would be located in different knowledge states.