-------- Original Message -------- Subject: Re: PLS and sources of covariance Date: Tue, 5 Apr 2011 14:14:02 -0400 From: Chris Klingenberg <[email protected]> Reply-To: [email protected] Organization: University of Manchester To: [email protected] Dear Eric Concerning this and previous posts: I guess the main problem is that the relation between ontogenetic stage and shape is not linear. If so, linear regression won't remove all of it. It might be possible that a suitable transformation might render it linear -- the problem is finding it... For allometry, log-transforming size often does a good job. So you might get away with using a transformation for the measure of ontogenetic stage that you use. That litter mates cluster together can either be due to such differences or to other maternal effects (physiology, nutrition, behaviour etc.; I think you said you are using mice that are genetically identical, so it's not genetic...). Regardless of the cause of it heterogeneity, it might definitely be part of the covariance among parts. To keep it constant, you could do a pooled within-litter PLS (but that reduces your degrees of freedom to the total number of embryos minus the number of litters). I hope this helps. Best wishes, Chris On 4/5/2011 6:22 PM, morphmet wrote:
-------- Original Message -------- 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
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