Abstract
Nonsymmetric correspondence analysis (NSCA) aims to examine predictive relationships between rows and columns of a contingency table. The predictor categories of such tables are often accompanied by some auxiliary information. Constrained NSCA (CNSCA) incorporates such information as linear constraints on the predictor categories. However, imposing constraints also means that part of the predictive relationship is left unaccounted for by the constraints. A method of NSCA is proposed for analyzing the residual part along with the part accounted for by the constraints. The CATANOVA test may be invoked to test the significance of each part. The two tests parallel the distinction between tests of ignoring and eliminating, and help gain some insight into what is known as Simpson’s paradox in the analysis of contingency tables. Two examples are given to illustrate the distinction.
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The work reported here has been supported by a grant 10630 from the Natural Sciences and Engineering Research Council of Canada.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Takane, Y., Jung, S. Tests of ignoring and eliminating in nonsymmetric correspondence analysis. Adv Data Anal Classif 3, 315–340 (2009). https://doi.org/10.1007/s11634-009-0054-7
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DOI: https://doi.org/10.1007/s11634-009-0054-7