-------- Original Message --------
Subject: RE: PCA results interpretation
Date: Tue, 27 Jul 2010 11:35:31 -0400
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
Organization: Stony Brook University
To: [email protected]
Yes, that is a bit of a stretch. It assumes that PC2 and PC15 are
interesting features that you can go back and measure in a future study
rather than being in part a chance function of the particular specimens
selected for the initial study. I prefer to think of PCA as a method for
giving one a space of reduced dimensionality that captures as much of
the overall variation as possible - not as an analysis that gives axes
that are expected to particularly meaningful. If one wishes to visualize
the differences between two groups one can compare the two mean shapes.
The problem is, of course, in using a discriminant function to see the
optimal discrimination when sample sizes are too small to have reliable
estimates of the within-group covariance matrix. I suspect that is why
only two PCs were selected as characters. Difficult to get around a
lack of data. There have been prior discussion here about ways of
deciding how many PCs one could try to use in such situations.
----------------------
F. James Rohlf, Distinguished Professor
Dept. Ecology and Evolution, Stony Brook University, NY 11794-5245
-----Original Message-----
From: morphmet [mailto:[email protected]]
Sent: Monday, July 26, 2010 12:53 PM
To: morphmet
Subject: PCA results interpretation
-------- Original Message --------
Subject: PCA results interpretation
Date: Mon, 26 Jul 2010 08:49:01 -0700
From: Murat Maga <[email protected]>
To: morphmet <[email protected]>
Dear morphometricians,
I was reading a paper which compared mid-face shape in the unaffected
parents of cleft-lip kids versus the age matched controls. Results (and
their interpretation) made me think about how far PCA scores can be (or
should be) utilized. They ended up using PC2 and PC15 to define and
visualize the difference between groups. I wouldn't expect the
variation
contributed by the first group to the total variation to be too much,
they are almost normal after all. But using PC15 to define these
characteristics, could this be a bit of stretch? They only reported the
total variation accounted by these two components (14.5%). They said
none of the other PC showed evidence of group discrimination. I expect
PC15 has a minuscule contribution to this sum. So the question I have,
is it fair game to fish for PCAs as long as they provide the
discrimination you are looking between your groups. Obviously, results
don't have to be statistically significant to be biologically relevant.
And it is obviously very important to be able to detect people that
look
normal, but has higher risk of having kids with cleft.
But at what point one would say, "yes, PC15 seems to separate them, but
could this be an artifact of my samples, or some random noise"?
Another statement made by the authors:
"This finding [according to authors PC2 separates unaffected male
parents from controls and PC15 does the same for females] was confirmed
by results showing that mean PC scores on the second component differed
significantly between unaffected fathers and male controls (p=.001)".
They have a similar statement for PC15 as well. I haven't heard the
term
"mean PC scores" before? Are they talking about running an anova on the
PCs, by using groups as factors?
Thanks,
M
