Hola Lola, As Tim Cole, I don't really remember the details of the Burnaby method. But if there is any kind of ratio involved (such as dividing the measurements by a "size" variable), there is where the problem may lie. Ratios (and derived statistics) are not suitable for inferential analyses unless the original allometric relationship between the dependent and size variable goes through the origin of coordinates. The main, but not only, reason is that, with the mentioned exception, the ratio does not elliminate the influence of size. In other words, the ratio keeps being correlated to the size variable. Only this new relationship is a mathematical construct which does not have any functional or biomechanical meaning (and therefore can rend non meaningful results). The sign and value of the slope of the new relationship, for instance, will merely depend on the intercept of the original (dependent - size variables) relationship. An excellent article on the issue is:
PACKARD; G.C.; BOARDMAN, T.J. (1999): The use of percentages and size-specific indices to normalize physiological data for variation in body size: wasted time, wasted effort?. Comp. Biochem. Physiol. 122: 37-44. I think I have the pdf at hand if you wanted to take a look at it ([EMAIL PROTECTED]). But I think that your results with the residuals are rather more trustworthy. Even through it keeps being widely used in paleoanthropology, I do not use the Mossiman & James approach for these and other reasons (not sure about the geometric mean making sense when the variables are not log-normally distributed and, on the other hand, I think that there are other more efficient methods). Not sure about my view being justified though, as I read their papers long ago, and back then I dismissed the method rather by comparisson with other more handy alternatives for the particular problem that I was dealing with, than after a deep analysis of it. Would really appreciate to hear other opinions about the matter. Specially from Tim Cole, who seems to be much more familiar with the method than me. Cheers, Luis _______________________________ Luis Cabo Forensic Anthropology Laboratory, Mercyhurst Archaeological Institute, Mercyhurst College, Erie PA "...as they grow up, either turn thieves for want of work, or leave their dear native country, to fight for the Pretender in Spain, or sell themselves to the Barbadoes." (Jonathan Swift; "A Modest Proposal for preventing the postgraduate students from being a burden on their parents or country, and for making them beneficial to the publick") 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 == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
