Adequateness and interpretability of objective functions in ordinal data analysis

Authors:
Gerhard Herden;Andreas Pallack
Affiliations:
Universitaet Duisburg-Essen (Standort Essen), Fachbereich 6 (Mathematik), Universitaetsstrasse 2, D-45117 Essen, Germany;Universitaet Duisburg-Essen (Standort Essen), Fachbereich 6 (Mathematik), Universitaetsstrasse 2, D-45117 Essen, Germany
Venue:
Journal of Multivariate Analysis
Year:
2005

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Abstract

Objective functions that are applied in ordinal data analysis must be adequate, i.e. carefully adapted to the structure of the observed data. In addition, any analysis of data that is based upon objective functions must lead to interpretable results. After a general characterization of adequate objective functions in ordinal data analysis, therefore, the particular problems of constructing adequate and interpretable dissimilarity coefficients and correlation coefficients in ordinal data analysis, stress measures (stress functions) in non-metric scaling and generalized stress measures or correlation coefficients in any theory of rank estimation will be discussed.