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Dimensionality in Manova Tested by a Closed Testing Procedure

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  • Calinski, Tadeusz
  • Lejeune, Michel
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    Abstract

    The decision on dimensionality of the space spanned by general linear functions of the parameter matrix of a MANOVA model is considered. This problem is related to the investigation, whether graphically or analytically, of significant empirical departures from the overall null hypothesis on these functions. A closed testing procedure for a sequence of relevant hypotheses is proposed. Unlike the classical procedures based on asymptotic distributions of the likelihood ratio statistics, the proposed method ensures that the Type I familywise error rate does not exceed the nominal[alpha]-level. Also, it is consistent with testing the overall null hypothesis, while relying on tests of subsequent linear hypotheses implied by the former. Examples are given to compare the proposed procedure with a classical one.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 65 (1998)
    Issue (Month): 2 (May)
    Pages: 181-194

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    Handle: RePEc:eee:jmvana:v:65:y:1998:i:2:p:181-194

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    Related research

    Keywords: canonical analysis; multivariate linear hypothesis; MANOVA model; Lawley-Hotelling trace; testing dimensionality hypotheses; closed testing procedure;

    References

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    1. Fujikoshi, Yasunori, 1974. "The likelihood ratio tests for the dimensionality of regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 4(3), pages 327-340, September.
    2. Seo, T. & Kanda, T. & Fujikoshi, Y., 1995. "The Effects of Nonnormality of Tests for Dimensionality in Canonical Correlation and MANOVA Models," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 325-337, February.
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    Cited by:
    1. 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.

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