Indeed as Jim notes. The positive elements of the first latent vector of a positive definite square matrix is an "artefact". This is incorporated in the Frobenius-Perron theorem for the spectral properties of non-negative matrices. Ref. Gantmacher, F. R. Matrizenrechnung II (1966), VEB Deutscher Verlag der Wissenschaften, Berlin, pp 46-47. Fred Bookstein was as far as I am aware the first person to expose this non sequitur in the multivariate morphometric application of PCA.
Citerat fr�n [EMAIL PROTECTED]: > If the artifact of preservation is a simple bending of the entire shape > then you may wish to consider the unbending option in tpsUtil. It was > developed for some fossil fish data where several points were recorded > along the backbone to detect cases in which the specimens were > distorted > - having a backbone that was not more or less straight. The tpsUtil > program fits a quadratic to these points and then smoothly unbends the > entire shape so as to straighten the backbone. > > I think this is a much safer strategy than hoping that the first PC > measures only distortion (just as the first PC is not always a very > safe > measure of general size). > > F. James Rohlf > [EMAIL PROTECTED] > 03/17/2003 > > > -----Original Message----- > > From: [EMAIL PROTECTED] > > [mailto:[EMAIL PROTECTED] Behalf Of > > [EMAIL PROTECTED] > > Sent: Monday, March 17, 2003 11:59 AM > > To: [EMAIL PROTECTED] > > Subject: Re: question on the use of relative warp scores for > statistical > > > > > > Kristel, > > We have found precisely the same thing. RW1 often is obviously a > > fixaton effect. We informally refer to this shape axis as > "bendiness" > > and I'm sure I know precisely what it looks like even in your fish, > as > > we have seen it in so many species in my lab. > > > > Your suggested use of RW1 as a covariate seems perfectly acceptable > to > > me. The only problem is justifying that RW1 really is a fixation > > effect. I agree that enough experience seeing it makes it very > obvious > > that is what is going on, but there is no way I can think to > rigorously > > document this within the context of a given sample. (And sometimes > RW1 > > may also contain allometry and some other things mixed in with the > > fixation effect). > > > > It may be possible to justify externally that the RW1 axis is a > fixation > > effect. Once could do this experimentally, by derriving an axis > > separating two sets of images where one set is from live fish and the > > second set is from those same fish after formalin fixation. If that > > canonical (MANCOVA) axis looks very much like your RW1, then you have > a > > nice external justification. > > > > I don't think there is a statistical problem with using RW1 as a > > covariate in MANCOVA. Although RW1 is generated in the framework of > > PCA, the significance test is really not of interest. The PCA in > this > > case is just a tool to make a measurement. > > > > Please share the responses you get from your query, as this is an > > interesting problem of fairly general concern. > > > > Thom DeWitt > > > > _______________________________ > > > > Dr. Thomas J. DeWitt, Assistant Professor > > Department of Wildlife & Fisheries Sciences > > & Program in Bioenvironmental Sciences > > Texas A&M University > > 2258 TAMU > > College Station, TX 77843-2258 > > > > Tel. (979) 458-1684 (office) > > Tel. (979) 845-7522 (lab) > > Fax (979) 845-4096 > > E-mail [EMAIL PROTECTED] > > Web http://wfscnet.tamu.edu/wfscnet/facstaff/tdewitt/webpage.htm > > TAMU Map to DeWitt lab & office: > > http://www.tamu.edu/map/gifs/detail/FGHB.gif > > > > >>> <[EMAIL PROTECTED]> 03/11/03 03:24PM >>> > > analysis > > Sender: [EMAIL PROTECTED] > > Precedence: bulk > > > > Hi everybody > > > > > > > > I was wondering if anybody had some comments on the following > dilemma. > > We are currently performing a tps analysis of body shape and possible > > left-right differences in a cichlid fish, and we have come across the > > following situation. It appears that relative warp 1 depicts a > possible > > = > > artefact due to formalin fixation, which of course we would like to > > filter out. > > > > 1. We would like to know whether we can treat RW1 as you would treat > > PC1, depicting size, in a PCA, and thus immediately focus on RW2 > plotted > > against RW3. > > > > 2. Could we consider RW1 as an independent variable in a statistical > > analysis, such as a MANCOVA, in which we would treat RW1 as a > covariable > > and partial warps as variables? Would it be correct to perform this > kind > > of analysis on the relative warp scores, taking into account that > these > > scores are already the result of a statistic analysis, based on these > > partial warp scores? Can we somehow tease out the "effect" of RW1? > > > > > > Thanks in advance, > > > > > > > > Kristel Wautier > > Ghent University > > Department of Biology > > K.-L. Ledeganckstraat 35 > > 9000 Ghent > > Belgium > > > > Tel.: +32 9 264 52 31 > > Fax: +32 9 264 53 44 > > > > [EMAIL PROTECTED] > > http://allserv.rug.ac.be/~kwautier/VMDB/homepage.html > > == > > Replies will be sent to list. > > For more information see > http://life.bio.sunysb.edu/morph/morphmet.html. > > == > > Replies will be sent to list. > > For more information see > http://life.bio.sunysb.edu/morph/morphmet.html. > == > Replies will be sent to list. > For more information see > http://life.bio.sunysb.edu/morph/morphmet.html. == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
