Dear Joseph, Thanks for your detailed explanation. As it is recommended by Claude in "morphometrics with R" (2008) it's better to use the Mahalanobis distance for clustering group means, because this will be scaled by the within-group variance-covariance. In my analysis, I calculated the mean value of relative warp scores for each population and then carried out a UPGMA cluster analysis based on the Euclidian distance and results were satisfying for me and they were congruent with my other results. According to the book and other articles I ran the same analysis but based on the Mahalanobis distance in PAST software, but unfortunately whenever I ran the analysis the software error "Invalid floating point operation" appeared!! so I couldn't see the Mahalanobis's cluster!! (I couldn't realize why this error happens) Euclidian distance worked for me, but I was just curious to understand if my analyses is statistically meaningful!!
Thanks again for your answer, Elahe On Saturday, January 30, 2016 at 5:12:46 PM UTC+3:30, Joseph Kunkel wrote: > > I can not speak directly to why it is frequently used in GM cluster > analysis but I would like to mention how I look at Mahalanobis distance > based on its calculation. > > Mahalanobis distance is not a pure distance metric like Euclidian or > Manhattan distance, as you have stated it is ‘standardized’. What doe that > really mean? It sounds supeficially good. > > One way of computing it is to rotate the k-landmark data set to simplest > form treating the landmarks as factors. This way would consider all > landmarks to have a common covariance structure in XY or XYZ in three > dimensions. That is a already a streetch, since not all landmarks can be > assumed to have the same covariance structure. In addition the landmarks > have all been already centered about their centroid and rotated to > coincide, which has eliminated a dgeree of freedom of variability that can > have consequences. > > Furthermore not all species landmarks can be expected to have the same > covariance structure, which is an assumption made in the ordinary > Mahalanobis distance application to strut analysis between populations or > species. The assumption of similar data structure of course applies to the > null hypothesis where there is no difference. The typical statistical test > explodes when the null hypothesis is falsified so just when you want the > Mahalanobis distance metric to be accurate it starts misbehaving. > > After rotation to simplest axes one does an 1 df F-test between each of > the landmarks. These tests are all independent so they can be summed > together to produce a k df F-test which is Mahalonobis D squared. So > Mahalonobis D is the square root of the sum of independent F-tests, but > those F-tests are based on all sorts of assumptions about the variance of > the landmarks. I immagine on could modify calculation of D by limiting the > sum over the top 95 or 99% variance components of the principal components. > > Many times applications of analytical techniques are judged by whether > they ‘work’ or not. If a clustering method works for you, use it(?). I > am of the opinion that I use statistics to convince myself rather than the > audience. A confluence on many arguments is used to make a case. > > Joe > > -·. .· ·. .><((((º>·. .· ·. .><((((º>·. .· ·. .><((((º> .··.· >=- > =º}}}}}>< > Joseph G. Kunkel, Research Professor > UNE Biddeford ME 04005 > http://www.bio.umass.edu/biology/kunkel/ > > > On Jan 30, 2016, at 7:11 AM, Elahep <ellie....@gmail.com <javascript:>> > wrote: > > > > > > Hello all, > > > > > > > > I have seen in many GM articles people use Mahalanobis distance for > cluster analysis. What is the advantage of using Mahalanobis distance over > Euclidian distance as similarity measure in cluster analysis of shape > variables? > > > > As far as I know Mahalanobis distance is the standardized form of > Euclidean distance which standardized data with adjustments made for > correlation between variables and weights all variables equally. > > > > Why this distance measure is frequently used in GM cluster analysis?? > > > > > > > > Thanks in advance > > > > Elahe > > > > > > -- > > MORPHMET may be accessed via its webpage at http://www.morphometrics.org > > --- > > You received this message because you are subscribed to the Google > Groups "MORPHMET" group. > > To unsubscribe from this group and stop receiving emails from it, send > an email to morphmet+u...@morphometrics.org <javascript:>. > > -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.
