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Redundancy analysis for qualitative variables

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Abstract

Redundancy analysis (also called principal components analysis of instrumental variables) is a technique for two sets of variables, one set being dependent of the other. Its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables. The technique is generalized to qualitative variables; it then gives implicitly a simultaneous ‘optimal’ scaling of the dependent, qualitative variables. Examples are taken from the Dutch Life Situation Survey 1977, using Satisfaction with Life and Happiness as dependent variables. The analysis leads to one well-being scale, defined by the explanatory variables Marital status, Schooling, Income and Activity.

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References

  • Benzécri, J. P. et al. (1973).L'analyse des données (Vol. 2). Paris: Dunod.

    Google Scholar 

  • CBS (Netherlands Central Bureau of Statistics). (1978).De leefsituatie van de Nederlandse bevolking 1977 (Wellbeing of the population in the Netherlands 1977). The Hague: Staatsuitgeverij.

    Google Scholar 

  • CBS (Netherlands Central Bureau of Statistics). (1982).De leefsituatie van de Nederlandse bevolking 1977, deel 4: wonen en woongenot (Well-being of the population in the Netherlands 1977, part 4: living and living satisfaction) (by M. E. Jansen and D. Sikkel). The Hague: Staatsuitgeverij.

    Google Scholar 

  • Escoufier, Y. (1979). New results and new uses in principal components of instrumental variables. In:42nd Session of the International Statistical Institute, contributed papers, 149–152. Manilla.

  • Gifi, A. (1981).Non-linear multivariate analysis. Leyden: Department of Data Theory, Leyden University.

    Google Scholar 

  • Gleason, T. C. (1976). On redundancy in canonical analysis.Psychological Bulletin, 83, 1004–1006.

    Google Scholar 

  • Israëls, A. Z., Bethlehem, J. G., Van Driel, J., Jansen, M. E., Pannekoek, J., De Ree, S. J. M. & Sikkel, D. (1981).Multivariate methods for discrete variables. (Statistical Studies 30). The Hague: Staatsuitgeverij.

    Google Scholar 

  • Israëls, A. Z. (1981).Redundantie bij canonische correlatie-analyse (Redundancy in connection to canonical correlation analysis). Internal report, Netherlands Central Bureau of Statistics, Voorburg.

    Google Scholar 

  • Izenman, A. J. (1975). Reduced-rank regression for the multivariate linear model.Journal of Multivariate Analysis, 5, 248–264.

    Article  Google Scholar 

  • Johansson, J. K. (1981). An extension of Wollenberg's redundancy analysis.Psychometrika, 46, 93–103.

    Article  Google Scholar 

  • Keller, W. J. & Wansbeek, T. J. (1983). Multivariate methods for quantitative and qualitative data.Journal of Econometrics, 22, 91–111.

    Article  Google Scholar 

  • Leclerc, A. (1974). A study of the relationship between qualitative data. In:COMPSTAT 1974. Vienna: Physica-Verlag.

    Google Scholar 

  • Miller, J. K. (1975). In defence to the general canonical correlation index: reply to Nicewander and Wood.Psychological Bulletin, 82, 207–209.

    Google Scholar 

  • Nishisato, S. (1980).Analysis of categorical data: dual scaling and its applications. Toronto: University of Toronto Press.

    Google Scholar 

  • Rao, C. R. (1964). The use and interpretation of principal component analysis in applied research.Sankhyā A, 26, 329–358.

    Google Scholar 

  • Rao, C. R. (1973).Linear statistical inference and its applications. New York: Wiley.

    Google Scholar 

  • Robert, P. & Escoufier, Y. (1976). A unifying tool for linear multivariate statistical methods: the RV-coefficient.Applied Statistics, 25, 257–265.

    Google Scholar 

  • Sikkel, D. (1981).The relationship between canonical correlations and correspondence analysis. Internal report, Netherlands Central Bureau of Statistics, Voorburg.

    Google Scholar 

  • Stewart, D. & Love, W. (1968). A general canonical correlation index.Psychological Bulletin, 70, 160–163.

    PubMed  Google Scholar 

  • Tyler, D. E. (1982). On the optimality of the simultaneous redundancy transformations.Psychometrika, 47, 77–86.

    Article  Google Scholar 

  • Van de Geer, J. P. (1984). Linear relations amongk sets of variables.Psychometrika, 49, 79–94.

    Article  Google Scholar 

  • Van den Wollenberg, A. L. (1977). Redundancy analysis. An alternative for canonical correlation analysis.Psychometrika, 42, 207–219.

    Article  Google Scholar 

  • Young, F. W. (1981). Quantitative analysis of qualitative data.Psychometrika, 46, 357–388.

    Article  Google Scholar 

  • Young, F. W., De Leeuw, J. & Takane, Y. (1976). Regression with qualitative and quantitative variables: an alternating least squares method with optimal scaling features.Psychometrika, 41, 505–529.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistical Methods, Central Bureau of Statistics, P.O. Box 959, 2270 AZ, Voorburg, The Netherlands

    Abby Z. Israels

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  1. Abby Z. Israels
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The views expressed in this paper are those of the author and do not necessarily reflect the policies of the Netherlands Central Bureau of Statistics.

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Israels, A.Z. Redundancy analysis for qualitative variables. Psychometrika 49, 331–346 (1984). https://doi.org/10.1007/BF02306024

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  • DOI: https://doi.org/10.1007/BF02306024

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