Assessment-based correct rates in learning spaces

The basic local independence model (BLIM) is the standard probabilistic model in knowledge structure theory. It assumes that the probability of a correct response to a problem is constant for all individuals that master the problem, and accordingly, for all individuals that do not master it, irrespective of the mastering of other problems. Recently published data on the problem correct rate as inferred from a response-based assessment of the mastering of the problem seem to contradict this assumption. The analysis presented in this paper, however, reveals that deviations from constancy in the observed direction are to be expected under the BLIM. They are mainly due to the inaccuracy inherent in any response-based assessment. The implications of these results for the empirical validation of the BLIM are discussed.