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).
[1] The result of his algorithm, which we refer in the following as Classical ITA, is a logically consistent set of implications
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).
Since the basic work of Flament (1976) a number of different methods for boolean analysis have been developed.
A comparison of ITA to other methods of boolean data analysis can be found in Schrepp (2003).
There are several research papers available, which describe concrete applications of item tree analysis.
Held and Korossy (1998) analyzes implications on a set of algebra problems with classical ITA.
Item tree analysis is also used in a number of social science studies to get insight into the structure of dichotomous data.
In Bart and Krus (1973), for example, a predecessor of ITA is used to establish a hierarchical order on items that describe socially unaccepted behavior.
In Janssens (1999) a method of Boolean analysis is used to investigate the integration process of minorities into the value system of the dominant culture.
Schrepp[3] describes several applications of inductive ITA in the analysis of dependencies between items of social science questionnaires.
The ISSSP is a continuing annual program of cross-national collaboration on surveys covering important topics for social science research.