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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)
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  • 3
    Electronic Resource
    Electronic Resource
    Ranking principal components to reflect group structure (1992)
    New York, NY : Wiley-Blackwell
    Journal of Chemometrics 6 (1992), S. 97-102 
    Details
    ISSN: 0886-9383
    Keywords: Between-group variances ; Canonical variate criterion ; Eigenvalues ; Eigenvectors ; Orthogonal projection ; Within-group variance ; Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Canonical variate analysis is the appropriate descriptive technique for multivariate data which have an a priori group structure, but problems arise with this technique when there are more variables than within-group degrees of freedom because of singularity of matrices. In such cases it is shown through illustrative examples that principal component analysis is a viable substitute provided that the principal components are ranked according to the canonical variate criterion (ratio- of between- to within-group variances) rather than the usual criterion of total variance. This ranking can also be used to select components for subsequent discriminant analysis.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cem.1180060207
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Simulation study of confidence regions for canonical variate analysis (1991)
    Springer
    Statistics and computing 1 (1991), S. 41-46 
    Details
    ISSN: 1573-1375
    Keywords: Canonical variates ; confidence regions ; inclusion rates ; Monte Carlo ; normal distribution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Canonical variate analysis often involves the construction of confidence regions round points representing group means in a 2-dimensional plot. Traditionally circles have always been constructed, but some authors have recently advocated ellipses as being more appropriate. This paper describes a Monte Carlo study investigating the effect of a range of factors on the inclusion rates of true population means within both types of region for normal data. The traditional circles do not perform too badly within a restricted range, but they are nearly always under-included. The ellipses usually have higher inclusion rates, and so are often closer to the nominal rate, but are sometimes over-included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890835
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Permutational tests for correlation matrices (1993)
    Springer
    Statistics and computing 3 (1993), S. 37-44 
    Details
    ISSN: 1573-1375
    Keywords: bootstrapping ; eigenvalues ; eigenvectors ; Monte Carlo methods ; random permutations ; significance levels
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Permutational tests are proposed for the hypotheses that two population correlation matrices have common eigenvectors, and that two population correlation matrices are equal. The only assumption made in these tests is that the distributional form is the same in the two populations; they should be useful as a prelude either to tests of mean differences in grouped standardised data or to principal component investigation of such data. The performance of the permutational tests is subjected to Monte Carlo investigation, and a comparison is made with the performance of the likelihood-ratio test for equality of covariance matrices applied to standardised data. Bootstrapping is considered as an alternative to permutation, but no particular advantages are found for it. The various tests are applied to several data sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00146952
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    Paper (German National Licenses)
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