Abstract
In quantifying categorical data, constraints play an important role in characterizing the outcome. In the Guttman-type quantification of contingency tables and multiple-choice data (incidence data), the trivial solution due to the marginal constraints is typically removed before quantification; this removal, however, has the effect of distorting the shape of the total space. Awareness of this is important for the interpretation of the quantified outcome. The present study provides some relevant formulas for those cases that are affected by the trivial solution and those cases that are not. The characterization of the total space used by the Guttman-type quantification and pertinent discussion are presented.
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This study was supported by a grant from The Natural Sciences and Engineering Research Council of Canada to S. Nishisato.
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Nishisato, S. On quantifying different types of categorical data. Psychometrika 58, 617–629 (1993). https://doi.org/10.1007/BF02294831
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DOI: https://doi.org/10.1007/BF02294831