Modified item tree analysis of inductive reasoning data

Abstract

Recently, the coefficient k has been proposed for the selection among competing knowledge structure models for multinomial response data in Knowledge Space Theory, a modern psychometric test theory. This paper presents an application of the coefficient k to empirical data obtained from dichotomously scored inductive reasoning test items. A data set of binary scores for 366 male participants who responded to 27 test items measuring two types of inductive reasoning, ‘verbal analogy’ and ‘geometric-figural matrix completion’, is analyzed. An ‘optimal’ knowledge structure model is derived, selecting among 38 candidate competing models based on the criterion k. This is accomplished by a modified version of Item Tree Analysis, a data-analytic procedure for the derivation of knowledge structures on sets of dichotomous items. The data-analytic solution can be satisfactorily compared to theory-driven models obtained from psychological analyses of the inductive reasoning test items. Such a solution may then be utilized for the efficient computerized, adaptive assessment and training of the ability of inductive reasoning of the types of ‘verbal analogy’ and ‘geometric-figural matrix completion’.