Paradoxes in multidimensional contingency tables: What does this mean for CFA?
نویسنده
چکیده
Lienert (1969, 1971a) justified his invention of Configural Frequency Analysis (CFA) by the observation that higher-order interactions may exist in threeand higher-dimensional data even if no correlations between any pairs of variables can be observed. In Lienert (1971b) Hierarchical CFA (HCFA) was proposed in order to find that subset of variables which shows the highest degree of interdependence. In HCFA, the original contingency table is collapsed in a hierarchical way until twodimensional tables result and CFA is applied to all tables in this hierarchy. Now, it has been known for more than a hundred years that collapsing contingency tables may lead to strange results which are nowadays often denoted as Simpson’s paradox (Simpson, 1951). Another paradox studied first by Lord (1967) occurs when groups are compared which may differ in their baseline values. Here, a contingency table version of this latter paradox is considered. Implications of these possible paradoxes for the interpretation of the results of CFA are discussed.
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