Studying Triadic Distance Models Under a Likelihood Function

  • Mark de Rooij
Conference paper


Triadic distance models are relatively new. Their merits and demerits are fairly unknown. In the present paper we will study triadic distance models and bring the understanding of those models to a next level. Therefore, the models are studied under a Multinomial sampling scheme and a detailed investigation of the likelihood function results in relationships with multiple correspondence analysis and three-way quasi-symmetry models.


Likelihood Function Diagonal Block Multiple Correspondence Analysis Distance Model Expected Probability 


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  1. Boik, R. J. (1996), An efficient algorithm for joint correspondence analysis,“ Psychometrika, 61, 255–269.MathSciNetMATHGoogle Scholar
  2. Carroll, J. D., and Chang, J. J. (1970), “Analysis of individual differences in multidimensional scaling via an N-way generalization of ‘Eckart-Young’ decomposition,” Psychometrika, 35, 283–319.CrossRefMATHGoogle Scholar
  3. Cox, T. F., Cox, M. A., and Branco, J. A. (1991), “Multidimensional scaling for ntuples,” British Journal of Mathematical and Statistical Psychology, 44, 195–206.CrossRefMATHGoogle Scholar
  4. Daws, J. T., (1996), “The analysis of free-sorting data: Beyond pairwise cooccurences,” Journal of Classification, 13, 57–80.CrossRefMATHGoogle Scholar
  5. De Rooij, M. (2001, submitted), “Distance models for three-way tables and three-way information: a theoretical note,”Google Scholar
  6. De Rooij, M., and Heiser, W. J. (2000), `Triadic distance models for the analysis of asymmetric three-way proximity data,“ British Journal of Mathematical and Statistical Psychology, 53, 99–119.MathSciNetCrossRefGoogle Scholar
  7. Gifi, A. (1990), Nonlinear multivariate analysis. Chichester, England: Wiley.Google Scholar
  8. Greenacre, M. J. (1984), Theory and applications of correspondence analysis. New York: Academic Press.MATHGoogle Scholar
  9. Greenacre, M. J. (1988), “Correspondence analysis of multivariate categorical data by weighted least squares,” Biometrika, 75, 457–467.MathSciNetCrossRefMATHGoogle Scholar
  10. Hayashi, C. (1972), “Two dimensional quantifications based on a measure of dissimilarity among three elements,” Annals of the Institute of Statistical A’Iathematics, 25, 251–257.CrossRefGoogle Scholar
  11. Heiser, W. J., and Bennani, M. (1997), “Triadic distance models: Axiomatization and least squares representation,” Journal of Mathematical Psychology, 41, 189-206.Google Scholar
  12. Joly, S., and Le Calvé, G. (1995), “Three-way distances,” Journal of Classification, 12, 191–205.MathSciNetCrossRefMATHGoogle Scholar
  13. Pan, G., and Harris, D. P. (1991), “A new multidimensional scaling technique based upon association of triple objects pijk and its application to the analysis of geochemical data,” Mathematical Geology, 23, 861–886.CrossRefGoogle Scholar
  14. Tateneni, K., and Browne, M. W. (2000), “A noniterative method of joint correspondence analysis,” Psychometrika, 65, 157–165.CrossRefGoogle Scholar
  15. Zielman, B., and Heiser, W. J. (1993), “The analysis of asymmetry by a slide-vector,” Psychometrika, 58, 101–114.CrossRefMATHGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Mark de Rooij
    • 1
  1. 1.Department of PsychologyLeiden UniversityThe Netherlands

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