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Boolean analysis
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<p>Boolean analysis was introduced by Flament (1976). The goal of a Boolean analysis is to detect <a href="/facts/Determinism/NhvNlAbe">deterministic</a> dependencies between the items of a <a href="/facts/Questionnaire/15o4lgqm">questionnaire</a> or similar data-structures in observed response patterns. These deterministic dependencies have the form of <a href="/facts/Boolean_algebra_(logic)/VkCToAmg">logical formulas</a> connecting the items. Assume, for example, that a questionnaire contains items <i>i</i>, <i>j</i>, and <i>k</i>. Examples of such deterministic dependencies are then <i>i</i> → <i>j</i>, <i>i</i> ∧ <i>j</i> → <i>k</i>, and <i>i</i> ∨ <i>j</i> → <i>k</i>. </p><p>Since the basic work of Flament (1976) a number of different methods for Boolean analysis have been developed. See, for example, Buggenhaut and Degreef (1987), Duquenne (1987), <a href="/facts/Item_tree_analysis/4vvbVSBN">item tree analysis</a> Leeuwe (1974), Schrepp (1999), or Theuns (1998). These methods share the goal to derive deterministic dependencies between the items of a questionnaire from data, but differ in the algorithms to reach this goal. </p><p>Boolean analysis is an <a href="/facts/Exploratory_data_analysis/8hvnf7JS">explorative method</a> to detect deterministic dependencies between items. The detected dependencies must be confirmed in subsequent research. Methods of Boolean analysis do not assume that the detected dependencies describe the data completely. There may be other probabilistic dependencies as well. Thus, a Boolean analysis tries to detect interesting deterministic structures in the data, but has not the goal to uncover all structural aspects in the data set. Therefore, it makes sense to use other methods, like for example <a href="/facts/Latent_class_model/LaQ7oJDY">latent class</a> analysis, together with a Boolean analysis. </p>