Re: [MORPHMET] How to project shape difference onto different PC

[Yinan Hu]

This really clarified my confusions on the PCA part. Thanks a lot for the 
reply, I really appreciate it.

Sincerely. 
Yinan

On Friday, May 18, 2018 at 4:10:21 PM UTC-4, f.james.rohlf wrote:
>
> Yes, the PC axes are “comparable”. I think the best way to think about 
> what a PCA does is to interpret it as a projection of a multidimensional 
> space down to a low dimensional space that captures as much of the overall 
> variation as possible. The first axis is somewhat special because it 
> represents the best 1-dimensional space. Past that one should think of 1 
> and 2 giving the best 2-dimensional space and 1, 2, and 3 giving the best 
> 3-dimensional space, etc. The axes themselves are not of a priori interest 
> in an application – it is the space that is of interest. A consequence is 
> that plots showing projections of points relative to PC1, PC2,etc. must be 
> plotted to the same scale (i.e., consistent with the fact that the 
> eigenvalues give the variances along each axis). If, as unfortunately often 
> the case, the axes are plotted using different scales then the space has 
> been distorted and is no longer the space that best accounts for the 
> overall variation in the data. That also distorts the impressions one gets 
> in looking at the plot as using different scales changes the relative 
> distances between points.
>
>  
>
> Within that reduced space one may find that particular axes can seem to be 
> interpretable but one should really look at the space and decide which 
> directions within the space are most interesting based on the patterns of 
> the data. That is, the data need to suggest interesting direction unless 
> one has some a priori groups one wishes to compares. Often the first PC is 
> of special interest but that is often due to allometry and the relatively 
> large impact of size variation. That is, by now, a rather boring result! 
> The individual PC axes are defined based on convenient mathematical 
> properties – not based on any biological models so each one should not be 
> considered separately as things of special interest.
>
>  
>
> The above also means that one need not just visualize variation along each 
> axis separately. One can, as in tpsRelw software, visualize any specified 
> point within the PC space or in any direction of interest within the PC 
> space.
>
>  
>
> _ _ _ _ _ _ _ _ _
>
> F. James Rohlf, Distinguished Prof. Emeritus
>
> [image: univautosig]
>
> Depts. of Anthropology and of Ecology & Evolution
>
>  
>
>  
>
> *From:* Yinan Hu  
> *Sent:* Friday, May 18, 2018 2:19 PM
> *To:* MORPHMET 
> *Subject:* Re: [MORPHMET] How to project shape difference onto different 
> PC
>
>  
>
> Dear James,
>
>  
>
> Thanks for the reply. Yes I have completed a PCA on a GM dataset with 11 
> landmarks, and you got it exactly right that I'm trying to decompose shape 
> differences onto individual PCs.  
>
>  
>
> The reason I was hesitating to do the vector projection is that I'm not 
> sure if PC scores on different PCs are directly comparable to each other. 
> For simplicity, let's say I'm only considering PC1 and PC2, which explains 
> 80% of shape variation in total (60% + 20%). Group A has a mean PC1 score 
> of 0.5, and PC2 score of 0.1; where as Group B has a mean PC1 score of 0.4 
> and PC2 score of 0.3.  Then I'm looking at a 0.1 difference along PC1 and a 
> 0.2 difference along PC2 between these two groups. 
>
>  
>
> Would this mean they differ twice as much along PC2 than PC1, such that in 
> the 80% of shape variation explained by these two PCs, 1/3 is along PC1 and 
> 2/3 is along PC2?
>
>  
>
> But considering that PC1 explains three times more variation than PC2 (60% 
> vs 20%), would this mean I should weigh the PC score difference (distance 
> along each PC)? i.e. although the absolute difference in mean PC1 score is 
> 0.1, it should be weighed three times more than the difference along PC2 so 
> in the 80% of shape variation explained by these two PCs, 3/5 is along PC1 
> and 2/5 is along PC2?
>
>  
>
>  
>
> On the other hand, I agree visualizing the shape difference along each PC 
> can be helpful, and I'm pretty sure the plotRefToTarget function from the R 
> package geomorph can achieve this.
>
>  
>
> Thanks again.
>
> Best,
>
>  
>
> Yinan
>
>  
>
>
> On Friday, May 18, 2018 at 12:53:32 PM UTC-4, K. James Soda wrote:
>
> Dear Dr. Hu,
>
> Let me begin by restating how I understand the question: You have 
> completed a PCA on a morphological data set in which there are two subsets 
> of interest. Now you would like to decompose the difference between the two 
> subsets into differences along individual PCs. Here is my two cents on the 
> issue:
>
> I would say that the literal solution to this problem would probably be 
> something along the lines of what you proposed. For simplicity, say that 
> you summarized each subset using its mean position in the PC space. This 
> would be 

[MORPHMET] Course Introduction to Geometric Morphometrics using (mostly) R, August 13-17, Canada

[soledad . esteban]

Dear colleagues,

Registration is open for the course “INTRODUCTION TO GEOMETRIC MORPHOMETRICS 
USING (MOSTLY) R”, August 13th-17th, 2018, Alberta (Canada).

Instructors: Dr Paula González (Unidad Ejecutora Estudios en Neurociencias y 
Sistemas Complejos. CONICET-HEC-UNAJ, Argentina) and Dr David Katz (University 
of Calgary, Canada).

This course is intended as an introduction to the major aspects of 2D and 3D 
landmark-based shape analysis. While we will spend some time on shape theory 
and mechanical aspects relevant statistical analyses, the goal of doing so will 
be to develop your intuition for how to—and how not to—design and interpret 
your geometric morphometrics research.
Students will learn the foundations of geometric morphometrics through lectures 
and daily exercises. The exercises are designed around a mouse skull shape 
sample from a controlled experiment with longitudinal design, though for most 
exercises, students are welcome to work with their own data instead.
Students lacking a rudimentary understanding of R will be asked to complete a 
short series of introductory exercises prior to attending the course. Most 
analyses will be done in R, although we will also use Meshlab for landmarking 
3D models, and tpsDig for 2D landmarking.

More information and registration: 
https://www.transmittingscience.org/courses/geometric-morphometrics/introduction-geometric-morphometrics-using-mostly-r

Organized by Transmitting Science and University of Calgary.

Best regards

Sole


Soledad De Esteban-Trivigno

Institut Català de Paleontologia Miquel Crusafont (ICP)

Campus de la Universitat Autònoma de Barcelona

Cerdanyola del Vallès (Barcelona). Spain

www.icp.cat

   



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