At 14:04 24/08/2006, Steve Brewer wrote: >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.
Steve, You are correct. Multivariate normality is only required for the hypothesis testing procedures in DA. As to multivariate textbooks...most of them give a whole series of assumptions for DA....and then go on with examples in which some of the assumptions are violated. >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. Not sure which measure of association you would use for morphometric data....but as to the choice of measures of association, and follow up methods like the Mantel test/PcOA/ANOSIM/etc....there is one case study chapter in our forthcoming book (Chapter 28: Ieno EN, Zuur AF, Bastida R, Martin, JP, Trassens M and Smith GM Multivariate analyses of South-American zoobenthic species spoilt for choice - In: Zuur, Ieno and Smith, Analysing Ecological Data. Springer). Publication date: March 2007 in which we compare two data analysis approaches applied on the same data...one is called 'the careless approach', the other 'how-it-should-be-done' approach. In the first approach, we show how you can modify settings (call it cheating) and come up with 10-15 different results (pick your p-values)...in the second approach we take a common sense approach and show how it should be done (at least according to us). But the choices you have in multivariate analysis are enormous. That's why some people get attached to methods. If you ask them why, they will say 'because my colleague uses it as well'. Anyway...I think the original question was answered. Alain >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 Dr. Alain F. Zuur Highland Statistics Ltd. 6 Laverock road UK - AB41 6FN Newburgh Tel: 0044 1358 788177 Email: [EMAIL PROTECTED] URL: www.highstat.com URL: www.brodgar.com Our statistics courses: 1. "Analysing biological and environmental data using univariate methods". 2. "Analysing biological and environmental data using multivariate methods" 3. "Analysing biological and environmental data using time series analysis" 4. "Analysing biological and environmental data using mixed modelling, GLMM and GAMM" 5. "An introduction to R" Brodgar: Software for univariate and multivariate analysis and multivariate time series analysis Brodgar complies with R GNU GPL license Statistical consultancy, courses, data analysis and software
