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Canonical Analysis Applied to Multivariate Analysis of Variance

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  • Lejeune, Michel
  • Calinski, Tadeusz

Abstract

In this paper it is shown how a generalized form of canonical analysis can be useful to reveal which parametric functions of a MANOVA model, for instance treatment contrasts or combinations of observed variables, are responsible for rejection of a general linear hypothesis on these functions. For the decomposition in successive canonical terms the choice of a matrix norm is crucial. It is shown that the norm derived from the standardization of the least squares estimators of the parametric functions involved is equal to the Lawley-Hotelling statistic for testing the hypothesis under investigation. Thus, some useful interpretations based on canonical variates can be given in terms of the contributions of the various parametric functions to the overall test statistic or to statistics relevant to specific subhypotheses. Corresponding to these possibilities for interpretation, three different types of biplot are proposed. As an example, an agricultural block design experiment is thoroughly analyzed.

Suggested Citation

  • Lejeune, Michel & Calinski, Tadeusz, 2000. "Canonical Analysis Applied to Multivariate Analysis of Variance," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 100-119, January.
    • Handle: RePEc:eee:jmvana:v:72:y:2000:i:1:p:100-119
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    References listed on IDEAS

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    1. Calinski, Tadeusz & Lejeune, Michel, 1998. "Dimensionality in Manova Tested by a Closed Testing Procedure," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 181-194, May.
    2. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
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    2. Czerwińska-Kayzer, Dorota & Florek, Joanna & Kayzer, Dariusz, 2020. "Canonical Variate Analysis Applied To Determine Factors Influencing The Financial Situation Of Feed Enterprises," Roczniki (Annals), Polish Association of Agricultural Economists and Agribusiness - Stowarzyszenie Ekonomistow Rolnictwa e Agrobiznesu (SERiA), vol. 2020(2).
    3. Dorota Czerwińska-Kayzer & Joanna Florek & Ryszard Staniszewski & Dariusz Kayzer, 2021. "Application of Canonical Variate Analysis to Compare Different Groups of Food Industry Companies in Terms of Financial Liquidity and Profitability," Energies, MDPI, vol. 14(15), pages 1-16, August.

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