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A probabilistic model for nonsymmetric correspondence analysis and prediction in contingency tables

  • Roberta Siciliano
  • Ab Mooijart
  • Peter G. M. van der Heijden
Article

Summary

Nonsymmetric correspondence analysis is a model meant for the analysis of the dependence in a two-way continengy table, and is an alternative to correspondence analysis. Correspondence analysis is based on the decomposition of Pearson's Ф2-index

Nonsymmetric correspondence analysis is based on the decomposition of Goodman-Kruskal's τ-index for predicatablity.

In this paper, we approach nonsymmetric correspondence analysis as a statistical model based on a probability distribution. We provide algorithms for the maximum likelihood and the least-squares estimation with linear constraints upon model parameters.

The nonsymmetric correspondence analysis model has many properties that can be useful for prediction analysis in contingency tables. Predictability measures are introduced to identify the categories of the response variable that can be best predicted, as well as the categories of the explanatory variable having the highest predictability power. We describe the interpretation of model parameters in two examples. In the end, we discuss the relations of nonsymmetric correspondence analysis with other reduced-rank models.

Keywords

Contingency Table Correspondence Analysis American Statistical Association Latent Class Analysis Latent Class Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Società Italiana di Statistica 1993

Authors and Affiliations

  • Roberta Siciliano
    • 3
  • Ab Mooijart
    • 1
  • Peter G. M. van der Heijden
    • 2
  1. 1.Leiden UniversityThe Netherlands
  2. 2.University of UtrechtThe Netherlands
  3. 3.Dipartimento di Matematica e StatisticaUniversità di Napoli Federico IINapoliItaly

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