Dimensionality in Manova Tested by a Closed Testing Procedure

Tadeusz Calinski and Michel Lejeune

Journal of Multivariate Analysis, 1998, vol. 65, issue 2, 181-194

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.

Keywords: canonical analysis; multivariate linear hypothesis; MANOVA model; Lawley-Hotelling trace; testing dimensionality hypotheses; closed testing procedure (search for similar items in EconPapers)
Date: 1998
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