A smart attempt at solving the problem can be found in Flury's Common Principal Component Analysis. Unfortunately, Professor Flury was killed in a climbing accident a few years ago (in his native Switzerland). Details of the method plus a compositional version can be found in
Richard A. Reyment and Enrico Savazzi (1999) Aspects of Multivariate Statistical Analysis in Geology. Elsevier, Amsterdam. Quoting morphmet <[EMAIL PROTECTED]>: > Hi All- > > The division involved in this particular formulation of CVA is by a > pooled covariance matrix, so there is no direct limitation in the size > of sample size within group imposed by this division. I would doubt > this form of CVA will work terribly well if there are not enough samples > within a group to make a reasonable estimate of the mean of the group. > > -Dave > > H. David Sheets, PhD > Chair,Dept of Physics, Canisius College > 2001 Main St > Buffalo NY 14208 > > >ok, but are there any requirements regarding sample size of individual > >groups? > >______________________________________ > >Paul Van Daele > >Ghent University > >Evolutionary Morphology of vertebrates > >K.L. Ledeganckstr 35 > >9000 Gent > >T + 32 9 2645233 > >F + 32 9 2645344 > > > >Dance like nobody is watching > >Kiss like you have never been loved before > >----- Original Message ----- > >From: "morphmet" <[EMAIL PROTECTED]> > >To: "morphmet" <[email protected]> > >Sent: Tuesday, February 13, 2007 10:12 PM > >Subject: RE: Advice on IMP > > > > > >> For a conventional multivariate test of significance you need to have > >> a sufficient sample size so that the degrees of freedom of the > >> covariance matrix are equal to or larger (preferably much larger) than > >> the number of variables. With 17 landmarks you will have 2*17-4 shape > >> variables so you will need more than just 15 specimens (3 groups of 5 > >> give you just 3*(5-1) = 12 degrees of freedom). > >> > >> ========================= > >> F. James Rohlf > >> Distinguished Professor, Stony Brook University > >> http://life.bio.sunysb.edu/ee/rohlf > >> > >>> -----Original Message----- > >>> From: morphmet [mailto:[EMAIL PROTECTED] > >>> Sent: Tuesday, February 13, 2007 3:17 PM > >>> To: morphmet > >>> Subject: RE: Advice on IMP > >>> > >>> Hi, > >>> > >>> I was going to post the same question regarding problem number 1 > >>> last > >>> week. I was working with a small data set (N = 5 for each of three > >>> species within one species group of a genus) with 17 landmarks on > >>> fly > >>> wings. Two of the species are sibling species, so very similar. I > >>> worked around the problem by either reducing the number of landmarks > >>> to > >>> 5 (deleting "noisy" and very similar landmarks) or by increasing the > >>> sample size. > >>> > >>> I am curious about what is causing the problem, too. > >>> > >>> Ed > >>> > >>> ************************************* > >>> Edward A. Lisowski, Ph.D. > >>> WA Department of Agriculture > >>> Plant Protection, Pest Division > >>> [EMAIL PROTECTED] > >>> 509-225-2603 (ph) 509-454-7858 (fax) > >>> > >>> > >>> > >>> > >>> > >>> -----Original Message----- > >>> From: morphmet [mailto:[EMAIL PROTECTED] > >>> Sent: Tuesday, February 13, 2007 11:36 AM > >>> To: morphmet > >>> Subject: Advice on IMP > >>> > >>> Hi everybody! > >>> I am using geometric morphometrics in a study on mandibles of mice. > >>> I > >>> have encountered problems using programs in the IMP series, and I > >>> would > >>> be very grateful if somebody more experienced with these could give > >>> me a > >>> hint on what to do here: > >>> > >>> 1)I load an output file from CoordGen and a GroupList file into > >>> CVAGen. > >>> The program displays the landmarks but does not finish the analysis, > >>> instead posting an error message: ?The within-group sum of squares > >>> and > >>> cross products matrix is singular?. I have inspected both input > >>> files > >>> several times; I cannot find any error; they do also perform well in > >>> PCAGen. What does the message tell me about my data? > >>> > >>> > >>> > >>> > >>> -- > >>> Replies will be sent to the list. > >>> For more information visit http://www.morphometrics.org > >> > >> > >> > >> > >> -- > >> Replies will be sent to the list. > >> For more information visit http://www.morphometrics.org > >> > > > > > > > >-- > >Replies will be sent to the list. > >For more information visit http://www.morphometrics.org > > > > > > -- > Replies will be sent to the list. > For more information visit http://www.morphometrics.org > -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
