Generalized inductive item tree analysis

Inductive item tree analysis is an established method of Boolean analysis of questionnaires. By exploratory data analysis, from a binary data matrix, the method extracts logical implications between dichotomous test items. For example, assume that we have the problems i and j of a test that can be solved or failed by subjects. With inductive item tree analysis, an implication i→j between the items i and j can be uncovered, which has the interpretation ”If a subject is able to solve item i, then this subject is also able to solve item j”. Hence, in the current form of the method, solely dichotomous items are considered. In this paper, we extend this approach to the general case of polytomous items, when more than two answer categories are possible. Thus, we introduce extensions of inductive item tree analysis that can deal with nominal polytomous (including dichotomous) and ordinal polytomous, each with item-specific, answer scales. To show their usefulness, the extensions proposed in this paper are illustrated with empirical data examples.