Please allow me to clarify one comment I made regarding multivariate normality. When I was talking about the multivariate normality requirement, it was in relation to doing discriminant analysis and MANOVA, not PCA. I believe that multivariate normality is required for testing significance using these techniques. If I am wrong, then several multivariate textbooks are wrong also.
Indeed, multivariate normality is not required for PCA. PCA does not involve hypothesis testing. Having said that, several have shown using simulations that, when certain aspects of multivariate normality do not hold (e.g., when there are lots of zero values), other exploratory techniques (e.g., non-metric multidimensional scaling) perform better. I have seen some use Principal Coordinates Analysis (using distance measures other than correlation) to examine morphometric differences among taxa. Presumably, this performs better than PCA under certain circumstances. One problem I have seen is that some investigators become attached to a particular technique. When I ask them why, many respond that it is the most commonly used analysis in their particular field of study. Hopefully, we can all agree that *that* is not an adequate justification for using a particular technique. Personally, I prefer to analyze multivariate data using several different techniques (including PCA). When they provide different results, I become suspicious and am encouraged to find out why. Steve Brewer At 6:05 AM -0400 8/24/06, Highland Statistics Ltd. wrote: > > >> >>Hope this helps some. Let me know if you want information about >>SuperAnova or PC-Ord. >> >>Steve >> >> >> >> >> >>At 7:31 PM -0500 8/21/06, Chris Taylor wrote: >>>Hey Steve. What do you run those nested discriminant analyses with? >>>Hope all is well! >>> >>>Chris >>> >>>At 11:18 AM 8/21/2006, you wrote: >>>>Matthew, >>>> >>>>You may also want to do a nested discriminant analysis to determine >>>>whether the mean morphology differs among populations, while >>>>controlling for species. The nesting of populations within species >>>>should "correct for phylogeny", unless there is something I'm missing >>>>here (e.g., phylogenetic relationships among populations within >>>>species). Don't really see the need for PICs. Make sure the >>>>assumptions of multivariate normality are met. >>>> >>>>Steve >>>> >>>> >>>> >>>> >>>> >>>> > >Matthew, > >>>>At 10:30 AM -0400 8/18/06, Matthew Gifford wrote: >>>>>I am looking for advice regarding principal components analysis. My >>>>>situation is as follows: I have a >>>>>data set of morphological measurements for 6 "taxa" (4 populations >>>>>of one species and 2 >>>>>populations of another). I read somewhere that in order to do a PCA >>>>>appropriately, one needs to >>>>>have more "taxa" (i.e., rows) than measurement variables (i.e., >>>>>columns). > >This is to avoid negative eigenvalues. But if you only focus on the first >few eigenvalues, this should be no problem. > >If I use mean values for >>>>>each "taxon" then I viiolate this assumption. To circumvent this, >>>>>is it valid to do a PCA on all data >>>>>and use mean PC scores? > >No need to do this. And if you do, it doesn't solve the engative >eigenvalue problem. > > >No need for multivariate normality neither. > > > I will be using this information in >>>>>phylogenetically independent contrasts >>>>>analysis looking at ecomorphological relationships. > > >The real problem with morphometric data is that the first axes become size >and shape axes. See: > >Jolliffe IT (2002) Principal Component Analysis. Springer: New York > >and: > >Claude, J., Jolliffe, I.T., Zuur, A.F., Ieno, E.N. and Smith, G.M. >Multivariate analyses of morphometric turtle data size and shape. >Chapter 30 in Zuur, AF., Ieno, EN, Smith. GM. (Expected publication date: >March 2007). Springer > > >Kind regards, > >Alain Zuur >www.highstat.com > > > > > > > Any >>>>>thoughts/opinions are most appreciated. >>>>> > >>>>Best, >>>>> >>>>>Matthew E. Gifford >>>>>Ph.D. Candidate >>>>>Washington University, St. Louis, MO >>>>>http://www.biology.wustl.edu/larsonlab/people/Gifford/Matt's_webpage.ht >ml >>>> >>>> >>>>-- >>>>Department of Biology >>>>PO Box 1848 >>>>University of Mississippi >>>>University, Mississippi 38677-1848 >>>> >>>>Brewer web page - http://home.olemiss.edu/~jbrewer/ >>>> >>>>FAX - 662-915-5144 >>>>Phone - 662-915-1077 >>> >>>*************************************************************** >>>Christopher M. Taylor >>>Associate Professor of Biological Sciences >>>Dept. of Biological Sciences >>>Mississippi State University >>>Mississippi State, MS 39762 >>>Phone: 662-325-8591 >>>Fax: 662-325-7939 >>>Email: [EMAIL PROTECTED] >>>http://www2.msstate.edu/~ctaylor/ctaylor.htm >> >> >>-- >>Department of Biology >>PO Box 1848 >>University of Mississippi >>University, Mississippi 38677-1848 >> >>Brewer web page - http://home.olemiss.edu/~jbrewer/ >> >>FAX - 662-915-5144 >>Phone - 662-915-1077 >>========================================================================= -- Department of Biology PO Box 1848 University of Mississippi University, Mississippi 38677-1848 Brewer web page - http://home.olemiss.edu/~jbrewer/ FAX - 662-915-5144 Phone - 662-915-1077
