Correspondence analysis, association analysis, and generalized nonindependence analysis of contingency tables: Saturated and unsaturated models, and appropriate graphical displays

Abstract For the analysis of nonindependence between the row classification and column classification in an I x J contingency table, a general method is introduced (viz., generalized nonindependence analysis) that includes as special cases the usual correspondence analysis method and the two forms of association analysis (viz., unweighted and weighted association analysis). For each of these methods of analysis, both the saturated model and related unsaturated models are considered, and so are the related graphical displays. With respect to the graphical displays, we show, for example, that the usual correspondence analysis graphical display can be misleading, and that it should be replaced by a different graphical display. The advantages of using the graphical displays presented here rather than the usual correspondence analysis graphical display are discussed. AMS 1980 classification numbers: 62H17; 62H20; 62J10

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