Robusto, E., & Stefanutti, L.
Extracting a knowledge structure from the data by a Maximum Residuals Method
A major issue in knowledge space theory (KST) is the specification of a knowledge structure for a given set Q of problems. In the literature two distinct approaches can be found: the theory-driven and the data-driven. The data-driven approach includes a number of statistical methods for deriving a knowledge structure from a large enough data set. In the present article a procedure for extracting knowledge structures from data is proposed, which is less restrictive compared to other methods. The procedure constructs a chain of knowledge structures К i of increasing size. In each step i an updating rule is applied, which is based on the residuals of the response pattern’s frequencies obtained by an application of the basic local independence model. In a simulation study, this updating rule was compared to the one at the basis of the method proposed by Schrepp (1999). The results indicate superiority of the proposed procedure in a number of different conditions. An empirical application to a data set of fraction subtraction problems shows the viability of the method.
