Version 0.1-0 of a new package `ffmanova' is now available on CRAN.
The package implements 50-50 MANOVA (Langsrud, 2002) with p-value
adjustment based on rotation testing (Langsrud, 2005).
The 50-50 MANOVA method is a modified variant of classical MANOVA made
to handle several highly correlated responses. Classical MANOVA
performs poorly in such cases and it collapses when the number of
responses exceeds the number of observations. The 50-50 MANOVA method
is suggested as a general method that will handle all types of data.
Principal component analysis is an integrated part of the algorithm.
The single response special case is ordinary general linear modeling.
Type II sums of squares are used to handle unbalanced designs
(Langsrud, 2003). Furthermore, the Type II philosophy is extended to
continuous design variables. This means that the method is invariant
to scale changes. Centering of design variables is not needed. The
Type II approach ensures that common pitfalls are avoided.
A univariate F-test p-value for each response can be reported when
several responses are present. However, with a large number of
response variables, these results are questionable since we will
expect a lot of type I errors ("incorrect significance"). Therefore
the p-values need to be adjusted.
By using rotation testing it is possible to adjust the single response
p-values according to the familywise error rate criterion in an exact
and non-conservative (unlike Bonferroni) way.
It is also possible to adjust p-values according to a false discovery
rate criterion. Our method is based on rotation testing and allows
any kind of dependence among the responses (Moen et al., 2005).
Note that rotation testing is closely related to permutation testing.
One difference is that rotation testing relies on the multinormal
assumption. All the classical tests (t-test, F-test, Hotelling T^2
test, ...) can be viewed as special cases of rotation testing.
Langsrud, Ø. (2002), 50-50 Multivariate Analysis of Variance for
Collinear Responses, Journal of the Royal Statistical Society SERIES D
- The Statistician, 51, 305-317.
Langsrud, Ø. (2003), ANOVA for Unbalanced Data: Use Type II Instead of
Type III Sums of Squares, Statistics and Computing, 13, 163-167.
Langsrud, Ø. (2005), Rotation Tests, Statistics and Computing, 15, 53-60.
Moen, B., Oust, A., Langsrud, Ø., Dorrell, N., Gemma, L., Marsden,
G.L., Hinds, J., Kohler, A., Wren, B.W. and Rudi, K. (2005), An
explorative multifactor approach for investigating global survival
mechanisms of Campylobacter jejuni under environmental conditions,
Applied and Environmental Microbiology, 71, 2086-2094.
Bjørn-Helge Mevik and Øyvind Langsrud
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