Interpreting results of PCA

[lesn...@bu.edu]

Hello,

 I am wondering if anyone may be able to provide tips for how to interpret a PCA conducted in the geomorph package, beyond stating what percentage of shape variation is accounted by the first two axes. I have plotted 14 specimens originally from 3D mesh files, and used 20 fixed landmarks and 150 surface semi landmarks in my analyses. plotTangentSpace gave me 13 components. Is there any way to draw conclusions from these components about which specific landmarks or semilandmarks may be contributing most to variation?

Thanks in advance, 

KCL

--------------------------------------------------

Katey Lesneski

PhD Candidate 

Boston University Marine Program

Department of Biology

5 Cummington Mall

Boston, MA 02215

[Mike Collyer]

Katey,

The rotation matrix (also called PC loadings) provides that.  Values with the largest absolute values contribute most to the variation.

Cheers!

Mike

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[lesn...@bu.edu]

Hi Mike,

 Thanks so much for your reply. 

  I see which components contribute most - but I am looking for a 'biological interpretation' - i.e., which of my landmarks are part of PC1 and PC2? In other words, there a way to determine which of my landmarks landmarks (of the 20 fixed and 150 semi) are part of those first 2 PC's, and of the other 11 PC's? 

Thanks,

Katey 

On Friday, April 6, 2018 at 6:15:30 PM UTC-4, Michael Collyer wrote:

Katey,

The rotation matrix (also called PC loadings) provides that.  Values with the largest absolute values contribute most to the variation.

Cheers!

Mike

On Apr 6, 2018, at 1:37 PM, lesn...@bu.edu wrote:

Hello,

 I am wondering if anyone may be able to provide tips for how to interpret a PCA conducted in the geomorph package, beyond stating what percentage of shape variation is accounted by the first two axes. I have plotted 14 specimens originally from 3D mesh files, and used 20 fixed landmarks and 150 surface semi landmarks in my analyses. plotTangentSpace gave me 13 components. Is there any way to draw conclusions from these components about which specific landmarks or semilandmarks may be contributing most to variation?

Thanks in advance, 

KCL

--------------------------------------------------

Katey Lesneski

PhD Candidate 

Boston University Marine Program

Department of Biology

5 Cummington Mall

Boston, MA 02215

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[Mike Collyer]

Katey,

I’m not sure what I am about too propose is appropriate, but you could use the loadings I mentioned to find the portion of each landmark’s contribution to the overall squared PC vector length.  For example, with 2D landmarks:

PCA <- plotTangentSpace(shapedata)

P1 <- t(matrix(PCA$rotation[,1], 2, )) # change 2 to 3 for 3D

diag(tcrossprod(P1))/sum(diag(tcrossprod(P1))) # relative portions along PC 1

P2 <- t(matrix(PCA$rotation[,2], 2, )) # change 2 to 3 for 3D

diag(tcrossprod(P2))/sum(diag(tcrossprod(P2))) # relative portions along PC 2

The largest values are those for landmarks that change the most along each PC.  Keep in mind though that landmarks are not independent.  If you have a few clustered together in your configuration, they might seem small in their contributions but their collective correlated contributions have a strong influence on PC1.  In my opinion, deformation grids via TPS are a better way to visualize which landmarks are “important”.

Mike

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[lesn...@bu.edu]

Thank you very much Michael, I will try this out!

Best,

 Katey 

[Antigoni Kaliontzopoulou]

Hi Katey,

just to add to Mike´s comment, I think what you are looking for is the last option Mike suggested. In the list returned by plotTangentSpace, you have a component called $shapes which provides the shapes corresponding to the extremes of each of the PC axes. You can use plotRefToTarget with e.g. minPC1 and maxPC1 to obtain plots that summarize shape variation across PC1 etc. Those deformation grids allow you to interpret biologically what varies the most in your shape sample.

Hope this helps,

Antigoni

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-- 
Antigoni Kaliontzopoulou 

Assistant Researcher
CIBIO/InBIO, Centro de Investigação em Biodiversidade e Recursos Genéticos
University of Porto
Campus Agrário de Vairão, 4485-661 Vairão
PORTUGAL

http://antigonik.wix.com/akaliontzopoulou
http://cibio.up.pt/people/details/akaliont

[lesn...@bu.edu]

Thanks so much for your quick reply and the suggestions have been very helpful.

 I have attached screen shots of TPS deformation grids from the plotRefToTarget function for PC1 min and PC1 max as Antigoni suggested, however, I am still struggling to determine how to interpret the grid. Any possible ideas? 

Thanks in advance,

Katey   

        PC1 min: 

PC1 max: 

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