---------------------------- Original Message ---------------------------- Subject: Re: Quantifying landmark variability From: "F. James Rohlf" <[EMAIL PROTECTED]> Date: Sat, November 5, 2005 6:30 am To: "Morphmet" <[email protected]> --------------------------------------------------------------------------
Note that the covariance matrix will be singular. 4 zero eigenvalues. This standard discriminatin methods cannot be used on the alligned data directly. You also cannot interpret the landmark displacements so directly. The apparent displacements at one landmark are also a function of all of the other landmarks. Jim Rohlf ------- Sent remotely by F. James Rohlf -----Original Message----- From: morphmet <[EMAIL PROTECTED]> Date: Fri, 04 Nov 2005 05:02:05 To:morphmet <[email protected]> Subject: RE: Quantifying landmark variability Hi Antigoni, Regarding (a): If you accept that the Procrustes algorithm is finding the true relative rotations and translations of each lizard, then the registered landmarks can be treated as if they are the true raw positions of the landmark coordinates. That is, the registered landmarks can be treated as if they had not been arbitrarily rotated and translated. Hence, Sx + Sy, the standard deviations of the landmarks in the x and y directions, will give you the amount that each landmark "moves". Interpreting Sx and Sy separately is not sensible because the x and y axes are arbitrary. Regarding (c): If are treating the registered landmarks as unrotated and untranslated data, as above, then linear discriminant analysis (also called canonical discriminant analysis) will give you a nice function highlighting the group differences in each landmark. The loadings of the function will tell you which landmark is most different across groups. A similar approach is to use logistic regression, with the group as the binary response and the registered landmark coordinates as the continuous predictor variables. Logistic regression is more robust to non-normality than linear discriminant analysis and the coefficients of the logistic regression function are interpreted similarly to linear regression coefficients (look it up). If you have more than two groups, ordinal or Poisson regression is the corresponding extension to logistic regression. Both linear discriminant analysis and logistic regression are available in most standard statistics packages. There are other methods, for example, regression trees, but their results may not be so easy to interpret. A good intro to the methods I have mentioned can be found at http://www.statsoftinc.com/textbook/stathome.html. Both the methods I describe here assume that it is valid to analysis the covariance matrix of the Procrustes-registered data. How acceptable is this? Ben Flood Ben dot Flood at ul dot ie. -----Original Message----- From: morphmet [mailto:[EMAIL PROTECTED] Sent: 03 November 2005 12:45 To: morphmet Subject: Quantifying landmark variability Good morning morphometricians I am a PhD student studying morphology of lacertid lizards in the Iberian Peninsula and for the last year I've been trying to apply GM for my investigation. Although I've passed a year trying to figure out how GM methods could be applied to my lizards, there are still some issues that I'm not very sure about, no matter how preliminary they might seem. I hope someone here might help me. I was wondering if there is some way of putting into numbers variability from landmark data. Intuitively I would say there must be because that's what they were developed to do, but I'm not sure which of the parameters calculated during the analysis would be a measure of that. In detail: a) Is there a way of putting into numbers and testing which of the landmarks in a sample present more global variablility ("move" more)? Would the variances (S, Sx, Sy) around landmarks given by the report of tpsRelw be a measure of that? b) When comparing groups within a sample, is it correct to evaluate local differences by examining partial warps independently? I know PWs are correlated and should not be separated for statistical analyses, but is there some way of quantifying and examining very local differences? c) Again when comparing groups within a sample, is there some way of evaluating which are the landmarks that contribure more to the observed differences? For example, when comparing male to female lizards I have run a canonical analysis on PWs and calculated canonical scores. Then I regressed shape variables to the canonical scores in tpsRegr to view the shape changes. When selecting to view them as vectors instead of deformation grids, I can see that some vectors are notably "longer" than others, but what is the variable that expresses the length of these vectors? I suppose it must be something related to the mean Procrustes Distance for each group (sex in my case), but I'm not completely sure about it. I'm sorry if this sounds too elemental, but passing from mathematics to the biological application of GM seems to be quite a step to take after all. I'd be very thankful for any suggestions on the above problems. Cheers Antigoni -- Antigoni Kaliontzopoulou Centro de Investigação em Biodiversidade e Recursos Genéticos (CIBIO/UP) Campus Agrário de Vairão 4485-661 Vairão PORTUGAL Herpetologia, Dep. Biologia Animal (Vertebrats) Fac. de Biologia, Univ. de Barcelona Av. Diagonal 645 08028 Barcelona SPAIN tel: +351 91 3086188 mail to: [EMAIL PROTECTED] -- Replies will be sent to the list. For more information visit http://www.morphometrics.org .
