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 (short ). The goal of an ITA is to uncover such deterministic implications from the data set D.
ITA was originally developed by Van Leeuwe in 1974. The result of his algorithm, which we refer in the following as Classical ITA, is a logically consistent set of implications . Logically consistent means that if i implies j and j implies k then i implies k for each triple i, j, k of items. Thus the outcome of an ITA is a reflexive and transitive relation on the item set, i.e. a quasi-order on the items.
A different algorithm to perform an ITA was suggested in Schrepp (1999). This algorithm is called Inductive ITA.
Classical ITA and inductive ITA both construct a quasi-order on the item set by explorative data analysis. But both methods use a different algorithm to construct this quasi-order. For a given data set the resulting quasi-orders from classical and inductive ITA will usually differ.
A detailed description of the algorithms used in classical and inductive ITA can be found in Schrepp (2003) or Schrepp (2006)[1]. In a recent paper (Sargin & Ünlü, 2009) some modifications to the algorithm of inductive ITA are proposed, which improve the ability of this method to detect the correct implications from data (especially in the case of higher random response error rates).
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