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A comparison of the ratio of variances in distance‐based and classical multivariate analysis

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  • Patrick J. F. Groenen
  • Jacqueline J. Meulman

Abstract

In multivariate analysis, the measure of variance accounted for plays a central role. In this paper, we show that an alternative approach, distance‐based multivariate analysis, also yields solutions that can be summarized by a ratio of variances. For classical multivariate analysis, this ratio is equal to the variance accounted for (VAF) and in distance‐based multivariate analysis it equals distance accounted for (DAF). We show that DAF in distance‐based multivariate analysis can always be made higher than VAF in classical multivariate analysis. This property is illustrated for principal components analysis, multiple correspondence analysis, multiple regression, and analysis of variance.

Suggested Citation

  • Patrick J. F. Groenen & Jacqueline J. Meulman, 2004. "A comparison of the ratio of variances in distance‐based and classical multivariate analysis," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 428-439, November.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:4:p:428-439
    DOI: 10.1111/j.1467-9574.2004.00269.x
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