-------- Original Message -------- Subject: Re: Relative warp question Date: Wed, 10 Feb 2010 08:55:45 +0100 From: andrea cardini <[email protected]> To: [email protected] Dear Paul, RWs are (except in a very special case that rarely if ever occurs in biological data) just PCs of shapes. Do a PCA using the variance-covariance matrix on the GPA superimposed (aligned) coordinates and you'll get exactely the same result. This is why many of us just call it PCA of GPA superimposed data. I would not do statistical tests one PC at a time. This is because PCs are built only to maximize total sample variance but they 'don't know' anything about groups. Imagine that you're analysing triangles and you have two groups. Then you have only two PCs with non-zero eigenvalues (4 d.f. are lost in the GPA). You test differences one PC at a time and get non-significant results. You give a look at the scatterplot, however, and you see a good separation of the two groups but this separation occurs in a direction which is 45° to your PCs. The differences are not picked up by any PC on its own but you would have found them if you had done a multivariate analysis. The fact that PCs sometimes align to some extent with interesting axes of variation is accidental. You cannot exclude that there's something else interesting going on in directions which are not collinear with any of the PCs. PCs maximize TOTAL sample variance and are not optimized to fit any other model. This does not only concern tests of group differences (that should be multivariate) but any other a priori model including your "high spired vs flat and aperture size" which, as you noticed, seem to be described by several PCs. The problem with power can often, I fear, only be solved by increasing sample size. With small samples, you can still do resampling stats (e.g., pairwise permutation tests for mean shape differences etc.) but power may be low and potential issues with sampling error are still there. MorphoJ does a lot of this kind of resampling stats (see DA/CVA). TPSregr also can do pairwise tests using permutations. The IMP series has plenty of resampling stats etc. etc. Good luck. Cheers Andrea At 15:11 09/02/2010 -0500, you wrote:
-------- Original Message -------- Subject: Relative warp question Date: Mon, 1 Feb 2010 09:29:50 -0500 From: Richards Paul <[email protected]> To: <[email protected]> Hi , I am applying relative warp analysis to a population of land snails, but I am new to all the theory and methods. Im doing a preliminary analysis to see if shell colour (i.e. dark, intermediate, light) is associated with differences in shape. I have run the relative warp analysis using tpsrelw, but have a few queries about using the output and potential analysis. RW1 to 3 appear to describe the apparent shape variance I am interested in (i.e. high spired vs flat and aperture size). Do the relative warps correspond directly to the identical partial warps in the weight matrix (e.g. RW1 scores column corresponds to the first variable column in the weight matrix)? If so could I take the first variable in the weight matrix (assuming it corresponds to RW1) and perform a T test just for this variable between my dark and light colour groups? I have tried using a MANOVA approach, but because these samples werent collected specifically with this analysis in mind I am lacking enough samples in each of my colour groups to get sufficient power, but I think a T test on a per variable basis should be OK in the first instance. I would be most grateful for any advice, and apologise if I have overlooked something obvious! Thanks, Paul ---------------- Paul Richards School of Biology University of Nottingham University Park NG7 2RD +44 (0)115 8213128 [email protected] This message has been checked for viruses but the contents of an attachment may still contain software viruses which could damage your computer system: you are advised to perform your own checks. Email communications with the University of Nottingham may be monitored as permitted by UK legislation. -- For now, new message AND replies should be sent to: [email protected] /* Replies will be sent to the list. */ For more information visit http://www.morphometrics.org
Dr. Andrea Cardini Lecturer in Animal Biology Dipartimento di Biologia Animale, Universitá di Modena, via Campi 213, 41100, Modena, Italy tel: 0039 059 2055526; fax: 0039 059 2055548 Honorary Fellow Functional Morphology and Evolution Unit, Hull York Medical School University of Hull, Cottingham Road, Hull, HU6 7RX, UK University of York, Heslington, York YO10 5DD, UK E-mail address: [email protected], [email protected], [email protected] http://hyms.fme.googlepages.com/drandreacardini http://ads.ahds.ac.uk/catalogue/archive/cerco_lt_2007/overview.cfm#metadata More on publications at: http://www.cons-dev.org/marm/MARM/EMARM/framarm/framarm.html LOOK FOR BIBLIOGRAPHIA MARMOTARUM, CLICK ON THE LETTER C AND LOOK FOR "CARDINI" (p. 8-9 until March 2009) http://hyms.fme.googlepages.com/dr.sarahelton-publications LOOK FOR "CARDINI" -- For now, new message AND replies should be sent to: [email protected] /* Replies will be sent to the list. */ For more information visit http://www.morphometrics.org
