Re: Statistical Reconstruction using PLS

[morphmet_moderator]

----- Forwarded message from Philipp Mitteröcker <mitte...@univie.ac.at> -----

Date: Sat, 31 Aug 2013 08:11:50 -0400
From: Philipp Mitteröcker <mitte...@univie.ac.at>
Reply-To: Philipp Mitteröcker <mitte...@univie.ac.at>
Subject: Re: Statistical Reconstruction using PLS
To: morphmet@morphometrics.org

Dear Vai,

Steps 2 and 6 are not necessary if you use an intercept in your regression model.

In order to obtain the actual maximum likelihood estimate of the missing landmarks via an EM-algorithm, you would need to iterate the described procedure:

- after the first estimate of the missing landmarks, compute a GPA of all specimens, including the reconstructed one, 

- recompute the regression using all these aligned specimens, again with the reconstructed one, 

- then predict the missing landmarks,

- and repeat these steps until convergence (until the estimate stays stable).

This also solves your concerns about the superimposition.

Best,

Philipp

Am 31.08.2013 um 04:19 schrieb morphmet_modera...@morphometrics.org:

----- Forwarded message from Vaibhav Patel <vaibhav.np2...@gmail.com> -----

Date: Thu, 29 Aug 2013 20:51:45 -0400
From: Vaibhav Patel <vaibhav.np2...@gmail.com>
Reply-To: Vaibhav Patel <vaibhav.np2...@gmail.com>
Subject: Statistical Reconstruction using PLS
To: morphmet@morphometrics.org

Dear morphmetors,

I am attempting a cranial reconstruction following the Statistical Reconstruction method described in Gunz et al. "Principles for the virtual reconstruction of hominin crania."Journal of Human Evolution 57.1 (2009): 48-62. Namely, I use the following protocol:

1. Partition the GPA aligned landmarks of each sample skull into two blocks: X corresponding to the observable landmarks on the damaged specimen, and Y corresponding to the missing landmarks. (DO NOT re-perform GPA on the separate X and Y blocks, to retain relative positions)
2. Convert the GPA aligned landmarks X and Y to procrustes residuals X0 and Y0 by subtracting off the corresponding subsets in the consensus landmark set.
3. Submit the X0 and Y0 blocks to SIMPLS (employed in Matlab's plsregress), and obtain the PLS regression coefficients beta.
4. Ordinary-Procrustes-align the damaged specimen's observable landmarks to the X-part of the consensus, then subtract off the X-part to obtain procrustes residuals. 
5. Multiply the procrustes residuals of the preceding step with beta to predict the residuals of the missing landmarks.
6. Add these predicted residuals to the Y-part of the consensus to get the coordinates of the missing landmarks in shape space.
7. Back out of shape space by using the reverse transformation of step 4 and obtain the "real space" estimates for the missing landmarks. 

Would this be one valid interpretation/implementation of the statistical technique described in Gunz et al (2009)? Specifically in step 4, I fear that using OPA to align the observable landmarks to the X-part of the consensus results in "too close" a fit.

Any advice would be tremendously useful. Thanks,
Vai

----- End forwarded message -----

___________________________________

Dr. Philipp Mitteroecker

Department of Theoretical Biology
University of Vienna
Althanstrasse 14
A-1090 Vienna, Austria

Tel: +43 1 4277 56705
Fax: +43 1 4277 9544
email: philipp.mitteroec...@univie.ac.at
homepage: http://theoretical.univie.ac.at/people/mitteroecker

----- End forwarded message -----