Item tree analysis

Item tree analysis (ITA) is a data analytical method which allows constructing a hierarchical structure on the items of a questionnaire or test from observed response patterns. Assume that we have a questionnaire with m items and that subjects can answer positive (1) or negative (0) to each of these items, i.e. the items are dichotomous. If n subjects answer the items this results in a binary data matrix D with m columns and n rows. Typical examples of this data format are test items which can be solved (1) or failed (0) by subjects. Other typical examples are questionnaires where the items are statements to which subjects can agree (1) or disagree (0). Depending on the content of the items it is possible that the response of a subject to an item j determines her or his responses to other items. It is, for example, possible that each subject who agrees to item j will also agree to item i. In this case we say that item j implies item i. The goal of an ITA is to uncover such deterministic implications from the data set D.

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