Redundancy Analysis for Qualitative Variables | Psychometrika | Cambridge Core (original) (raw)

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.

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). In Jansen, M. E. and` Sikkel, D. (Eds.), 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), 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.Google Scholar

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.CrossRefGoogle 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, The Hague: Staatsuitgeverij.Google Scholar

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

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

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

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

Leclerc, A. (1974). A study of the relationship between qualitative data. 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.CrossRefGoogle Scholar

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

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

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

Sikkel, D. (1981). The relationship between canonical correlations and correspondence analysis, Voorburg: Netherlands Central Bureau of Statistics.Google Scholar

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

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

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

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