[Moderator: Made public as per Igor's suggestion. Followup to...well...follow.]
Thanks so much for detailed explanation. Now, the next question is: if partial warps are just "mathematical constructs", is it biologically sound to apply to them any statistical procedures for any purposes other than revealing shape distributions in the morphospace? I think such a question is actual for the relwarps as well, but these at least could be analized in respect to their correlations with particular landmarks, unlike partwarps, couldn't they? I think this consideration better be public, as it is of overall interest and importance. Thank you. Igor ----- Original Message ----- From: morphmet <[EMAIL PROTECTED]> To: Igor Ya. Pavlinov <[EMAIL PROTECTED]> Sent: Friday, January 28, 2005 5:26 PM Subject: Re: use of partial warps in DA/CVA > Would you like a private or public explanation? > > Basically, you don't use partial warps individually as characters > because they are just mathematical constructs driven by the general > arrangements of landmarks on the reference without necessary biological > relevance. Change one landmark and your probably change every principal, > hence partial, warp. You might as well analyze the x-axis of your > digitizing tablet or any other line you care to draw through the space. > They do have the nice property of being ordered by geometric scale, but > is that relevant to biology? > > Their orthogonality actually derives from this same mathematical > construction. There is no reason biological characters should be > orthogonal, this is just geometry. Relative warps, on the other hand, > still have orthogonality, which is artificial with respect to most > biological questions, but at least they represent the directions of > major variation in your sample, something of which the principal/partial > warps by themselves have not knowledge. > > Does this help? > > Best, dslice > > On Fri, 2005-01-28 at 08:54, Igor Ya. Pavlinov wrote: > > Dear dslice, I need the point to be explaned a little bit lengthy. If the > > variables (PWs, in this case) are mutually correlated is it rightful to > > treat them as orthogonal? Isn't it the cause why Rohlf suggested not to > > analyze the separate partial warps but only as a complete set thereof? > > Thank you. > > Igor > > ----- Original Message ----- > > From: morphmet <[EMAIL PROTECTED]> > > To: morphmet <[email protected]> > > Sent: Thursday, January 27, 2005 5:16 PM > > Subject: Re: use of partial warps in DA/CVA > > > > > > > Partial warps are orthogonal. For 2D or 3D data, they are pairs or > > > triplets of principal warps used to describe shape differences (partial > > > warp scores) between specimens and the reference (most appropriately the > > > sample mean). The principal warps are the eigenvectors (hence > > > orthogonal) of the bending energy matrix that is based solely on the > > > reference. > > > > > > Partial warp scores may, of course, be correlated, hence the utility of > > > relative warps analysis. > > > > > > Best, dslice > > > > > > On Thu, 2005-01-27 at 04:37, Dennis Slice wrote: > > > > ------------------------------------------- > > > > From: morphmet[SMTP:[EMAIL PROTECTED] > > > > Sent: Thursday, January 27, 2005 4:28:02 AM > > > > To: morphmet > > > > Subject: Re: use of partial warps in DA/CVA > > > > Auto forwarded by a Rule > > > > > > > > As to my knowledge, partial warps are not orthogonal, so only the > > complete > > > > set of them makes a sense to analyze. If you wish to reduce the > > morphospace > > > > dimensionality you better use relative warps. They are principal > > components > > > > of the partial warps and hence are orthogonal. You may select several > > first > > > > RWs, say 1st to 5th, which may appear enough to represent similarities > > among > > > > your objects. > > > > Cheers > > > > Igor > > > > > > > -- > > > Dennis E. Slice > > > Institute for Anthropology > > > University of Vienna > > > Vienna, Austria > > > email: [EMAIL PROTECTED] > > > > > > -- > > > 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 > -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
