50-50 multivariate analysis of variance for collinear responses
Publication details
Journal : Statistician (London. Print) , vol. 51 , p. 305–317 , 2002
International Standard Numbers
:
Printed
:
0039-0526
Electronic
:
2517-6153
Publication type : Academic article
Issue : 3
Links
:
DOI
:
doi.org/10.1111/1467-9884.0032...
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Kjetil Aune
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Summary
Classical multivariate analysis-of-variance tests perform poorly in cases with,several highly correlated responses and the tests collapse when the number of responses exceeds the number of observations. This paper presents a new method which handles this problem. The dimensionality of the data is reduced by using principal component decompositions and the final tests are still based on the classical test statistics and their distributions. The methodology is illustrated with an example from the production of sausages with responses from near infrared reflectance spectroscopy. A closely related method for testing relationships in uniresponse regression with collinear explanatory variables is also presented. The new test, which is called the 50-50 F-test, uses the first k components to calculate SSMODEL. The next of components are not involved in SSERROR and they are called buffer components.