In addition to the sample-size cause of singularities that Dr. Rohlf mentions, you'll also get singularities from ratio-based scale adjustments because they will reduce the vcv-matrix ranks by one. To get scores on the canonical axes, you have to go through some extra steps that Darroch and Mosimann describe (but which are hard to follow, for me at least) to get canonical coefficients in terms of the original measurements, rather than on the "logshape" variables (I think I'm remembering that correctly). Dennis Slice and I both tried to figure it out a long time ago. Maybe he worked it out finally - you might ask him.
Tim Cole At 02:10 PM 5/18/2004 -0400, you wrote: >You mention that you have many more variables than specimens. As a result, >you cannot use the various alternatives that you list. Discriminant >functions, canonical variates, etc. all require that the pooled within-group >covariance matrix be based on a sample size larger than the number of >variables. If that is not true then the matrix will be singular and the >analysis will "blow up". > >Stepwise methods appear to get around this problem because they consider >fewer variables at one time. Their main limitation is in interpretation: one >cannot conclude that the variables in the "best set" are the important ones >and the other variables are unimportant. One also cannot interpret the >various probabilities produced by such methods as probabilities from usual >tests of significance. They need to be adjusted for the fact they result >from testing many combinations of variables and groups. They are just >convenient indices. > >-------------- >F. James Rohlf >State University of New York, Stony Brook, NY 11794-5245 > > > -----Original Message----- > > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On > > Behalf Of [EMAIL PROTECTED] > > Sent: Monday, May 17, 2004 10:10 AM > > To: [EMAIL PROTECTED] > > Subject: size correction & discriminant functions analyses > > > > Dear morphometrician, > > > > I have recently reviewed 3 genera of catsharks that display a great deal > > of morphological conservation within the genera, however, there is also > > prominent sexual dimorphism present (profoundly so in some species). There > > is quite a bit of shape variation between juveniles and adults, in one > > genus in particular, but I think that the shape variation is being > > obscured by the size component. > > > > I have a sizeable morphometric data set (# measures >> # taxa & specimens) > > and have used principal components analysis on the raw data to explore > > shape variation within each of the genera (not between). The first > > component was always a general component and accounted for more than 85- > > 90% of the variation in most instances, therefore the bipolar components > > only contributed relatively little to the overall shape variation > > resulting in crowded PCA plots. > > > > The main reference I have used for the analyses to date has been > > 'Pimental. 1979. Morphometrics. The multivariate analysis of biological > > data' however, it doesn't deal with size correction. Can anyone suggest a > > review that deals with size correction, or can I convert my data to ratios > > and then log transform the data? > > > > I am also looking for reviews of canonical discriminant functions analysis > > and stepwise discriminant function analysis in an attempt to quantitate > > differences between species within a genus. > > > > Thanks for your help. > > > > Brett > > > > ************************************ > > Brett Human > > Shark Researcher > > 27 Southern Ave > > West Beach SA 5024 > > Australia > > 61 8 8356 6891 > > [EMAIL PROTECTED] > > ************************************ > > > > > > > > == > > 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. Theodore M. Cole III, Ph.D. Department of Basic Medical Science School of Medicine University of Missouri - Kansas City 2411 Holmes St. Kansas City, MO 64108 USA Phone: (816) 235 -1829 FAX: (816) 235 - 6517 e-mail: [EMAIL PROTECTED] www: http://c.faculty.umkc.edu/colet == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
