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Subject: PLS and sources of covariance
Date: Tue, 5 Apr 2011 10:57:25 -0400
From: [email protected]
To: [email protected]
Hi all,
I have a question regarding PLS and the interpretation of data.
My samples are mouse embryos, the heads and faces of midgestational staged
specimens. Shape coordinates are regressed on stage (number of somites) to
remove ontogenetic variation, and yet again on centroid size to remove
allometric variation (a multiple multivariate regression is probably more
appropriate, and I will try this). The general goal of these sorts of
regressions is to remove components of shape variation not related to
differences in genotype, so different genotypes can be compared.
The residual data are "blocked" into two regions that are subject to PLS
for an analysis of shape covariance between the two blocks. The goal of
the test is to remove ontogenetic and allometric variation, perform a PLS
comparing two separate blocks of landmarks, and look for associations that
are independent of ontogentic and allometric causes of between-block
covariance.
My question is related to my recent posts. I suspect that despite
regressing on stage and size, a lingering ontogenetic component remains in
the shape data. For example, in PCA scatter plots of the regressed data,
litter mates tend to cluster together. My question is that, if ontogenetic
variation persists in data treated as above, and a PLS test detects
significant shape covariance, is it not reasonable to suspect that the
cause of the relationship is due to the stubborn presence of variation
owing to ontogenetic development? The two blocks will appear to covary in
shape because the sample contains specimens that vary in developmental
progress and at least some of that variation is still present in the data
despite attempts to regress it out. Therefore, the two blocks will show a
relationship in the PLS test because some embryos will have blocks that
are each somewhat developmentally advanced and some embryos will have
blocks that are each less developmentally advanced, and this will create a
pattern of shape covariance.
Thanks.
Eric
