Yes it does seem that putting a generalized inverse into CVAGen is the best solution, I'll try to get to it.
In the interim, what if you use a number of PC axes equal to the degrees of freedom remaining in the data (2k-4-n+1), where n is the number of groups? The percent variance remaining along the remainder of the axes should be zero (or close to it, given rounding errors in software). So this first set of variables (those with non-zero eigenvalues) would contain the same information as the whole set of PC axes, wouldn't it? It's just a simple transformation of basis set. If the above is correct, then could one just examine the variance explained along the first N PC axes, and chose N such that the remaining axes have eigenvalues essentially equal to zero, and then proceed with the CVA on those N axes, without substantial loss of variance? This is a short term solution, obviously, the ideal approach is to replace the calculation in CVAGen with a generalized inverse (and add a warning message) -Dave H. David Sheets, PhD Chair,Dept of Physics, Canisius College 2001 Main St Buffalo NY 14208 ---- Original message ---- >Date: Wed, 14 Feb 2007 15:27:29 -0500 >From: morphmet <[EMAIL PROTECTED]> >Subject: RE: Advice on IMP >To: morphmet <[email protected]> > >That approach will allow you to perform a CVA but it does have a >logical problem. CVA will work best if it can find large differences >between groups that correspond to directions that have little >variation within groups. If you use just the first few PCs based on >within-group variation then you are also eliminating potential >directions of small within-group variation in the multivariate space >that could yield the most effective separation of groups. May not be a >problem for your data but it seems a shame to eliminate the >possibility of finding such differences. > >The inclusion of semilandmarks is a different problem. For each >semilandmark there will be one more or less singular direction and >hence one within-group eigenvalue for each semilandmark that should be >close to zero. Those dimensions (PCs) should be eliminated or else one >should use a CVA program that uses a generalized inverse. The CVA >module in NTSYSpc allows one to specify a cut-off value. All >eigenvalues below that threshold (perhaps set at something like 10^-8) >will be ignored. > >========================= >F. James Rohlf >Distinguished Professor, Stony Brook University >http://life.bio.sunysb.edu/ee/rohlf > > >> -----Original Message----- >> From: morphmet [mailto:[EMAIL PROTECTED] >> Sent: Wednesday, February 14, 2007 11:49 AM >> To: morphmet >> Subject: Re: Advice on IMP >> >> Hi All- >> >> Jim Rohlf has already stated the reason for the problem here, CVA >> requires a division by a pooled covariance matrix estimated from >> your >> data. To avoid have a singularity in this matrix, you need a sample >> size larger than the degrees of freedom remaining in your variables. >> >> The ideal approach to this is to get more data, but that may be >> difficult. >> >> I have a version of CVAGen that will first perform a PCA on the >> partial >> warp scrores and uniform components, and then perform a CVA on a >> limited >> number of the PCA scores. So if you have 20 variables in the data >> and >> only 20 specimens, you might find that the first 5 or 6 PCA axes >> have >> 90% or more of the variance, so that a CVA using only 5 or 6 PCA >> axes >> might might produce reasonable results. This approach may be >> particularly useful if you are using a lot of semi-landmarks. >> >> This version of CVAGen is on the page at >> >> http://www.canisius.edu/~sheets/moremorph.html >> >> under the New Two-D Software section, called PCA_CVA. It might >> prove >> helpful. >> >> I should put a test routine for this degrees of freedom issue and >> put a >> more informative error message into the program. >> >> In the second question below, I'm not sure what is happening. I >> assume >> the two data sets have the same numbers of landmarks? >> If you can send me a copy of the files, I can have a look and chase >> this >> down. >> >> -Dave >> >> >> H. David Sheets, PhD >> Chair,Dept of Physics, Canisius College >> 2001 Main St >> Buffalo NY 14208 >> >> ---- Original message ---- >> >Date: Tue, 13 Feb 2007 14:35:55 -0500 >> >From: morphmet <[EMAIL PROTECTED]> >> >Subject: Advice on IMP >> >To: morphmet <[email protected]> >> > >> >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? >> > >> >2) I load two X1Y1CS format files into TwoGroup. The landmarks are >> >displayed and I can calculate Goodalls F. Anyway, when I click on >> ?F >> >test, Procrustes? I am getting an error message saying that ?matrix >> >dimensions must agree?. Why is this? What do I have to change? >> > >> >If anyone wishes to reply to me directly, my email address is: >> >[EMAIL PROTECTED] >> >Thank you very much and let me know if I can return you a favor. >> > >> >Louis >> > >> >_________________________________________________________________ >> >Haben Spinnen Ohren? Finden Sie es heraus ? mit dem MSN Suche >> Superquiz >> >via >> >http://www.msn-superquiz.de Jetzt mitmachen und gewinnen! >> > >> > >> > >> >-- >> >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
