Hmmm. Burnaby's method sounds very interesting. Can you point me to the original reference for it?
Kath Kathleen M. Robinette, Ph.D. Principal Research Anthropologist Air Force Research Laboratory AFRL/HEPA 2800 Q Street Wright-Patterson AFB, OH 45433-7947 (937) 255-8810 DSN 785-8810 FAX (937) 255-8752 e-mail:[EMAIL PROTECTED] -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of [EMAIL PROTECTED] Sent: Monday, February 23, 2004 10:29 AM To: [EMAIL PROTECTED] Subject: RE: Burnaby's method and discriminant analysis tolerance In Burnaby's method one does not divide by some measure of size. The method is closer to the idea of using residuals from regression to remove the effects of size (i.e., it uses subtraction not division operations). What the method does is to removes all variation parallel to a specified vector (or vectors) and thus reduces the dimensionality of the variation even though the number of variables stays the same. The formula used in Burnaby's method is quite general and has many other applications. In the Burnaby method, the variation in the columns (variables) of a data matrix are transformed to eliminate variation parallel to a specified linear combination of variables. The linear combination is usually PC1 but it can be any vector (actually it can be a set of vectors) that define directions in multivariate space in which you would like to remove all variation. The technique can also be applied to the rows (observations) of a data matrix. In this case it can be used to perform familiar operations such as computing deviations from the means or transforming a data matrix into a matrix of deviations from regression. This generality has made the equations used in the Burnaby method among my favorites! Jim -------------------- F. James Rohlf - Dept. Ecology & Evolution SUNY, Stony Brook, NY 11794-5245 > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > [EMAIL PROTECTED] > Sent: Friday, February 13, 2004 8:01 AM > To: [EMAIL PROTECTED] > Subject: Re: Burnaby's method and discriminant analysis tolerance > > > I don't really remember the details of what the Burnaby > scale-adjustment does, but I think it's somewhat similar to > Darroch and Mosimann's approach to scale adjustment (someone > correct me if I'm wrong). With D&M, the measurements are > transformed by dividing through by some reasonable measure of > size (for example, the geometric mean of all the distances). > If Burnaby and D&M are similar in what they do to the data, > you're probably having problems with discriminant analysis > because your variance-covariance matrices are singular (rank > = number of measurements > - 1) and can't be inverted. Darroch and Mosimann describe > how to get the discriminant function scores out when using > their brand of scale adjustment. > > Darroch JN and Mosimann JE (1985) Canonical and principal > components of shape. Biometrika 72: 241-252. > > I hope this helps. > > Tim Cole > > > > At 12:21 PM 2/11/2004 -0500, you wrote: > >Have anyone had problems with the tolerance in discriminant > analysis if > >the input variables for such anlaysis have previously been > transformed > >by Burnaby's method? > > > >We are studing the population structure of a fish species in > the North > >Atlantic. 17 variables (distances between landmarks) have > been measured > >for each fish , following the truss network model and in adition we > >have > measured > >some other structures as eye diameter, fin lengths, etc. We > have 4391 > >cases, distributed in seven geographical locations. In order to > >eliminate the size influence, we have used two methods, > i.e., residuals > >against standart length, and the Burnaby's method. > > > >Once we have removed the size effect, we run a discriminant > analysis to > >observe differences between areas. We have no problem if we use the > >residuals as input for the discriminant analysis. But we > cannot perform > >a discriminant analysis using as input the Burnaby's transformed > >variables, because we have problems with the tolerance of the > variables: > >the matrix is ill-conditioning. > > > >The problem doesn't seem to be in a particular variable or in a group > of > >data (data has been carefully screened for outliers). > Simply, there is > >some redundancy. However the correlations between variables are not > >particularly high. > > > >We have also study if the problem is in the data, running the > >Discriminant Analysis with different combinations of the seven > locations > >we have. But the results don't give us a clue. > > > >For example, when doing the analyses with four locations (a-d), it > >works. But as soon, as you introuduce some of the other > three (e-g), it > >fails. However, some combinations of e, f or g, with other > locations it > >works. Thus, not neccessarily the problem is in the > locations e-g, but > >when these locations are together with some other, but there is no > clear > >pattern. > > > >The same thing occurs with the variables. We have removed > the variable > >than enter at last step (when tolerance drops below the limit), but > then > >is another variable which cause problems, and if removed is > another one > >and so on. > > > >We suspect that the problem is relared with the way that > burbany method > >estimate the transformed variables. Can anyone help us? Thanks in > >advance, Lola > > > ><>< <>< <>< <>< <>< <>< <>< <><=20 > >Dolores Garabana Barro > >Institute of Fisheries Research > >Eduardo Cabello, 6 > >36208 Vigo (Spain) > >e-mail: [EMAIL PROTECTED] > > ><> ><> ><> <>< ><> ><> ><> ><> > >== > >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.htm> l. > == 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.
