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Properties of individual differences scaling and its interpretation

Author

Listed:
  • John C. Gower

    (The Open University)

  • Niël J. Le Roux

    (Stellenbosch University)

  • Sugnet Gardner-Lubbe

    (Stellenbosch University)

Abstract

Indscal models consider symmetric matrices $$\varvec{B}_{k}=\varvec{X}\varvec{W}_{k}\varvec{X}'$$ B k = X W k X ′ for $$k = 1, \ldots , K$$ k = 1 , … , K , where $$\varvec{X}: n \times R$$ X : n × R is a compromise matrix termed the group-average and $$\varvec{W}_{k}$$ W k is a diagonal matrix of weights given by the kth individual to the R, specified in advance, columns of $$\varvec{X}$$ X ; non-negative weights are preferred and usually $$R

Suggested Citation

  • John C. Gower & Niël J. Le Roux & Sugnet Gardner-Lubbe, 2022. "Properties of individual differences scaling and its interpretation," Statistical Papers, Springer, vol. 63(4), pages 1221-1245, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01275-8
    DOI: 10.1007/s00362-021-01275-8
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    References listed on IDEAS

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    1. Jos Berge & Henk Kiers & Wim Krijnen, 1993. "Computational solutions for the problem of negative saliences and nonsymmetry in INDSCAL," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 115-124, January.
    2. J. Carroll & Jih-Jie Chang, 1970. "Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition," Psychometrika, Springer;The Psychometric Society, vol. 35(3), pages 283-319, September.
    3. Forrest Young & Jan Leeuw & Yoshio Takane, 1976. "Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 505-529, December.
    4. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    5. Le Roux, Niël J. & Gardner-Lubbe, Sugnet & Gower, John C., 2014. "The analysis of distance of grouped data with categorical variables: Categorical canonical variate analysis," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 9-24.
    6. Jan Leeuw & Forrest Young & Yoshio Takane, 1976. "Additive structure in qualitative data: An alternating least squares method with optimal scaling features," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 471-503, December.
    7. de Leeuw, Jan & Mair, Patrick, 2009. "Multidimensional Scaling Using Majorization: SMACOF in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 31(i03).
    8. John Gower & Niel Roux & Sugnet Gardner-Lubbe, 2014. "The Canonical Analysis of Distance," Journal of Classification, Springer;The Classification Society, vol. 31(1), pages 107-128, April.
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