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Studying Triadic Distance Models Under a Likelihood Function

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Summary

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.

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References

  • Boik, R. J. (1996), An efficient algorithm for joint correspondence analysis,“ Psychometrika, 61, 255–269.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Daws, J. T., (1996), “The analysis of free-sorting data: Beyond pairwise cooccurences,” Journal of Classification, 13, 57–80.

    Article  MATH  Google Scholar 

  • De Rooij, M. (2001, submitted), “Distance models for three-way tables and three-way information: a theoretical note,”

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Gifi, A. (1990), Nonlinear multivariate analysis. Chichester, England: Wiley.

    Google Scholar 

  • Greenacre, M. J. (1984), Theory and applications of correspondence analysis. New York: Academic Press.

    MATH  Google Scholar 

  • Greenacre, M. J. (1988), “Correspondence analysis of multivariate categorical data by weighted least squares,” Biometrika, 75, 457–467.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Heiser, W. J., and Bennani, M. (1997), “Triadic distance models: Axiomatization and least squares representation,” Journal of Mathematical Psychology, 41, 189-206.

    Google Scholar 

  • Joly, S., and Le Calvé, G. (1995), “Three-way distances,” Journal of Classification, 12, 191–205.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Tateneni, K., and Browne, M. W. (2000), “A noniterative method of joint correspondence analysis,” Psychometrika, 65, 157–165.

    Article  Google Scholar 

  • Zielman, B., and Heiser, W. J. (1993), “The analysis of asymmetry by a slide-vector,” Psychometrika, 58, 101–114.

    Article  MATH  Google Scholar 

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© 2002 Springer Japan

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de Rooij, M. (2002). Studying Triadic Distance Models Under a Likelihood Function. In: Nishisato, S., Baba, Y., Bozdogan, H., Kanefuji, K. (eds) Measurement and Multivariate Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65955-6_7

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  • DOI: https://doi.org/10.1007/978-4-431-65955-6_7

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65957-0

  • Online ISBN: 978-4-431-65955-6

  • eBook Packages: Springer Book Archive

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