-------- Original Message -------- Subject: RE: Two group CVA plot Date: Wed, 3 Sep 2008 07:44:41 -0700 (PDT) From: F. James Rohlf <[EMAIL PROTECTED]> Reply-To: <[EMAIL PROTECTED]> Organization: Stony Brook University To: <[email protected]> References: <[EMAIL PROTECTED]> With just two groups, the projections of the data onto the canonical variates axes beyond the first must be zero (within rounding error) so there will be no among-group variation to try to interpret beyond that on the first axis. Note also that the among-group covariance matrix multiplied by the inverse of the within-group covariance matrix is not symmetrical and hence the eigenvectors of this matrix will not be orthogonal. ========================= F. James Rohlf Distinguished Professor, Stony Brook University http://life.bio.sunysb.edu/ee/rohlf
-----Original Message----- From: morphmet [mailto:[EMAIL PROTECTED] Sent: Wednesday, September 03, 2008 10:11 AM To: morphmet Subject: Re: Two group CVA plot -------- Original Message -------- Subject: Re: Two group CVA plot Date: Wed, 3 Sep 2008 06:44:07 -0700 (PDT) From: <[EMAIL PROTECTED]> To: [email protected] To respond to Rebecca's question below, in CVAGen, the CVA is carried out using a Matlab function which computes the eigenvectors of the matrix resulting from dividing the between-group variance-covariance matrix by the estimated pooled within-group variance-covariance matrix. So if there is only 2 groups, there will be only one meaningful CV axis (1 eigenvector). However, the algorithms used to compute the eigenvectors does return a set of orthogonal axes from the eigenvalue decomposition. These higher ordered axes are orthogonal to the one another, and to the meaningful axes. The program is set up to allow you to plot any chosen axis against another, so that in a case with 3 meaningful axes, you could plot axes 1 and 2, and 1 and 3, etc. The default plot setting in CVAGen shows axes 1 and 2. In a case where there are only two groups, the program will plot scores along the second CVA axes, but I would not advise trying to interpret this axis, it is simply the second eigenvalue of the decomposition, orthogonal to the first. In such cases, the distribution of scores along the first axis indicates to some extent the effectiveness of the discrimination, although I would urge use of cross-validation or jackknife rates of specimen assignment as a better measure of effectiveness. The plot of scores along the axis reflects more information about the resubstitution rate of assignment, ie of specimens to which the function was fitted. Perhaps others can add comments about approaches to displaying the results of two group discrimination functions. Plotting histograms would be one option, but there may be better approaches. -Dave H. David Sheets, PhD Dept of Physics, Canisius College 2001 Main St Buffalo NY 14208 ---- Original message ---- >Date: Wed, 03 Sep 2008 09:07:20 -0400 >From: morphmet <[EMAIL PROTECTED]> >Subject: Two group CVA plot >To: morphmet <[email protected]> > > > >-------- Original Message -------- >Subject: Two group CVA plot >Date: Tue, 2 Sep 2008 07:53:07 -0700 (PDT) >From: Rebeca <[EMAIL PROTECTED]> >To: <[email protected]> > > > >Dear Morphometricians, > > > >I have been using the program CVAGen6j from the IMP series (David >Sheets) to compare the shape differences of two groups of fish samples. >The program gave me a CVA scatterplot with two axes. I would like to use >this graph because it is more appealing than a histogram, but I don't >know what is plotted on the second axis (y-axis), as I understand that >from a two group analysis you get only one canonical variate (the x-axis >in this case). Does anyone know how the plot is done? > > > >Thanks a lot, > >Rebeca > > > >Rebeca P. Rodriguez Mendoza > >e-mail: [EMAIL PROTECTED] > >CSIC > >Marine Research Institute - Fisheries > >C/ Eduardo Cabello, 6 > >Tel. 986 23 19 30 ext. 254 > >Fax: 986 29 27 62 > >36 208 Vigo, Spain > > > > >-- >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
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