Prediction of Solvability Dependencies between Dichotomous Test Items: A Local Order-Theoretic Measure of Association

Solvability dependencies between dichotomous test items play an important role in the psychometric theory of knowledge spaces. Knowledge space theory (KST), based on hypothesized solvability dependencies between dichotomous items, has been successfully applied for the computerized, adaptive assessment and training of knowledge. For instance, see the ALEKS system, a fully automated math tutor on the Internet: http://www.aleks.com/. A crucial problem in KST, however, is the empirical detection of such dependencies. In this paper, we present an easy-to-use association measure for the detection of solvability dependencies from multinomial response data. The approach is illustrated with simulated data using a general KST finite mixture latent variable model.