Item Tree Analysis
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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 ...
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Data Analysis
Data analysis is the process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data modeling, modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively. Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and Statistical h ...
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Boolean Analysis
Boolean analysis was introduced by Flament (1976).Flament, C. (1976). "L'analyse booleenne de questionnaire", Paris: Mouton. The goal of a Boolean analysis is to detect deterministic dependencies between the items of a questionnaire or similar data-structures in observed response patterns. These deterministic dependencies have the form of logical formulas connecting the items. Assume, for example, that a questionnaire contains items ''i'', ''j'', and ''k''. Examples of such deterministic dependencies are then ''i'' → ''j'', ''i'' ∧ ''j'' → ''k'', and ''i'' ∨ ''j'' → ''k''. 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), item tree analysis Leeuwe (1974), Schrepp (1999), or Theuns (1998). These methods share the goal to derive deterministic dependencies between the items of a question ...
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