
Re: MANOVA on principal components
Posted:
Jul 1, 2009 12:26 PM


On Jun 30, 8:41 pm, "C. Papan" <cirku...@yahoo.com> wrote: > Rich Ulrich wrote: > > On Sat, 27 Jun 2009 22:58:14 +0800, "C. Papan" <cirku...@yahoo.de> > > 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 socalled 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 nonexpert 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) "5050 multivariate analysis of variance for collinear responses", _The Statistician_ 51:3 pp 305317

