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Topic: MANOVA on principal components
Replies: 10   Last Post: Jul 2, 2009 10:04 PM

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David B. Chorlian

Posts: 173
Registered: 12/7/04
Re: MANOVA on principal components
Posted: Jul 1, 2009 12:26 PM
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On Jun 30, 8:41 pm, "C. Papan" <> wrote:
> Rich Ulrich wrote:
> > On Sat, 27 Jun 2009 22:58:14 +0800, "C. Papan" <>
> > wrote:

> >> Dear all,
> >> is it appropriate to do a MANOVA on principal component scores?
> >> Thanks,
> >> Papan

> > If you are using all the components, it is a waste of time
> > and a potential source of confusion ... to do your MANOVA
> > on PC scores.  The overall tests will come out exactly the same,
> > and you will be one step removed from the underlying variables
> > when you try to make interpretations.  

> > PC is a legitimate tool for data reduction in many contexts.
> > It is especially useful if you can identify the underlying
> > constructs for the raw or rotated components.  You will
> > gain power for your MANOVA if you use only a few constructs
> > instead of using the full set of original variables, assuming
> > that you do not throw away important information in
> > the components that you discard.  

> > A small eigenvalue is *not*  a guarantee that a component
> > is meaningless, unless you are engaged in test construction
> > where you are only interested in the so-called common factors.
> > In that case, you should derive Principal factors rather than
> > Principal components.

> > Rich Ulrich
> Thanks for the comments! I have multivariate data with ~1000
> variables/subject and the first five PC's contain ca 95% of the
> variance. I want to use Manova for testing significance between means of
> groups, so in my non-expert mind I was thinking to do a MANOVA instead
> of multiple ANOVAS on each PC separately. I was, however, told that
> MANOVA on PC's does not make much sense, because the PC's are
> uncorrelated and thus I would not find correlated effects.
> Papan

You might be interested in O. Langsrud (2002) "50-50 multivariate
analysis of variance for collinear responses", _The Statistician_ 51:3
pp 305-317

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