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  • 1
    Electronic Resource
    Electronic Resource
    Ordination in the presence of group structure, for general multivariate data (1994)
    Springer
    Journal of classification 11 (1994), S. 195-207 
    Details
    ISSN: 1432-1343
    Keywords: Canonical variate analysis ; Categorical and mixed data ; Distances ; Diversity coefficients ; Metric scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A low-dimensional representation of multivariate data is often sought when the individuals belong to a set ofa-priori groups and the objective is to highlight between-group variation relative to that within groups. If all the data are continuous then this objective can be achieved by means of canonical variate analysis, but no corresponding technique exists when the data are categorical or mixed continuous and categorical. On the other hand, if there is noa-priori grouping of the individuals, then ordination of any form of data can be achieved by use of metric scaling (principal coordinate analysis). In this paper we consider a simple extension of the latter approach to incorporate grouped data, and discuss to what extent this method can be viewed as a generalization of canonical variate analysis. Some illustrative examples are also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195679
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Between-group analysis with heterogeneous covariance matrices: The common principal component model (1990)
    Springer
    Journal of classification 7 (1990), S. 81-98 
    Details
    ISSN: 1432-1343
    Keywords: Between-group analysis ; Canonical variate analysis ; Common principal component model ; Eigenvalues and eigenvectors ; Matusita distance between populations ; Metric scaling ; Principal component analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Analysis of between-group differences using canonical variates assumes equality of population covariance matrices. Sometimes these matrices are sufficiently different for the null hypothesis of equality to be rejected, but there exist some common features which should be exploited in any analysis. The common principal component model is often suitable in such circumstances, and this model is shown to be appropriate in a practical example. Two methods for between-group analysis are proposed when this model replaces the equal dispersion matrix assumption. One method is by extension of the two-stage approach to canonical variate analysis using sequential principal component analyses as described by Campbell and Atchley (1981). The second method is by definition of a distance function between populations satisfying the common principal component model, followed by metric scaling of the resulting between-populations distance matrix. The two methods are compared with each other and with ordinary canonical variate analysis on the previously introduced data set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01889705
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    Paper (German National Licenses)
    Fulltext
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