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A comparison of the ratio of variances in distance‐based and classical multivariate analysis
Author(s) -
Groenen Patrick J. F.,
Meulman Jacqueline J.
Publication year - 2004
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2004.00269.x
Subject(s) - multivariate statistics , multivariate analysis , multivariate analysis of variance , mathematics , statistics , principal component analysis , variance (accounting) , measure (data warehouse) , total variation , correspondence analysis , computer science , data mining , accounting , business
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.