Computation of Procrustes variance - morphol.disparity

[Dolores Messer]

Dear all,

I am struggling a bit to compute Procrustes variances. We have 3D models of 6 specimen (same species). Each model was digitized 6 times by 4 operators using 2 different systems (computer and VR), which gives us 6*6*4*2=288 sets of landmark coordinates.
For a Procrustes ANOVA, I used the crossed model specimen*system*operator.

My questions are:

1) Computing Procrustes variances for replicates
    - I am considering to compute
      MD <- morphol.disparity(coords ~ specimen*device*operator, groups = ~specimen*device*operator, data = gdf, iter = 999, print.progress = FALSE)
      to visualize the distribution of Procrustes variances for replicates for different groups.
      E.g. boxplots for both systems separately (MD$Procrustes.var[system==sys1] versus MD$Procrustes.var[system==sys2]).
      Am I correct that this gives me a distribution of the variation due to digitization for each system?
    - How would you test whether e.g. the two systems differ wrt. Procrustes variance?
      Could I compute
      MD <- morphol.disparity(coords ~ specimen*device*operator, groups = ~device, data = gdf, iter = 999, print.progress = FALSE)
      and then look at
      MD$PV.dist.Pval?
      
2) How can I compute Procrustes variances that reflect variation due to e.g. the use of a different system?
   Can I compute
   morphol.disparity(coords ~ specimen*operator, groups = ~specimen*operator, data = gdf, iter = 999, print.progress = FALSE)
   for this purpose?
   
3) Since the coordinate system is the same for all measurements on a given specimen (we were using the same 3D model), I did not use GPA for the computation of Procrustes variances. Am I doing this correctly?

Can anyone help me with this?
Thanks a lot in advance!

Best,
Dolores

[mura...@gmail.com]

Dolores,

I would suggest you think about what you want to get out of this analysis:

1. Do you more care to find out about the specifics of digitization differences in your two modes of digitization (VR vs 3D)

2. Do you more care whether these differences matter for your shape analysis?

For #1, you don't need the GPA. You actually don't need those linear shape models either. Because in each step (I assume) the digitization is happening in the same local reference frame of the individual, you can simply look at the euclidean distances of each coordinate set.  Granted this would require you to choose one as a baseline (probably the 3D as it is more common), and then you can easily look how much 'error' in your VR based method by simply calculating the distance between two sets. This would have the benefit of not getting the landmark correlated with each other due to superimposition.

For #2, you may or may not need GPA. You say the coordinate system is the same for all measurements, but consider the image below. In this case the coordinate systems are exactly the same (look at the bounding boxes), but the actual landmark position as recorded in 3D space is not (if you are curious, one is c(1.156, 88.290, -30.724) and the other is (22.542, 88.290, -20.907) .

Pretending these are two different samples measured in the same coordinate system, if you skip the GPA step in this sample, you will get very flawed results. If you do the GPA, however, the superimposition will impact the variances associated with each landmark, and you will no longer be able to calculate the true digitization error (but you can make inferences whether the difference have any impact on the shape analysis or not).

ps. this message kept stalling during sending. i apologize if anyone received multiple copies of it.

[Dolores Messer]

Thanks a lot for your answer! 

The main purpose of the analysis is to figure out whether VR is a good alternative to computer programs for digitization (so I guess mainly 1.). That's why I considered looking into the digitization 'error' of both modes, and compare this to other error sources (such as between-system or between-operator error).

Yes, you assume correctly that the digitization is happening in the same local reference frame of the individual. That's also what I meant, I do not think different individuals can be compared without applying GPA. I first looked into pairwise Procrustes distances between all combinations (e.g. between two replica to assess digitization error), but then realized that it would be better to compute variances since we have 6 replica (for each system and operator and individual). So would you not compute Procrustes variances for this purpose? (If yes, can it be done the way I tried to do it?).

Thanks a lot in advance!

Dolores

[Adams, Dean [EEOB]]

Dolores,

 

To your last point, you are entirely correct that one cannot compare variation, digitizing error, etc. across individuals without the GPA.  Bear in mind however, that upon this step, only overall digitizing error can be assessed and compared across individuals; not landmark-by-landmark variation.

Dean

 

Dr. Dean C. Adams

Director of Graduate Education, EEB Program

Professor

Department of Ecology, Evolution, and Organismal Biology

Iowa State University

https://faculty.sites.iastate.edu/dcadams/

phone: 515-294-3834

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[mura...@gmail.com]

Hi Dolores,

Then perhaps you should do both.

Based on my experience with VR, my intuition tells me digitization errors will be highly dependent on where landmarks are located (edges of the volume, vs center),  rendering artifacts, but also the skill of the operator with the controller ... So you probably want to use the euclidean distances (prior to GPA) to investigate the issue on per-landmark basis very clearly, and once you get that out of the way you can use the procrustes anova based models (after GPA) to determine overall variability between operator and modes of digitization. 

Sounds like a cool project, would love to hear what you find out.

[Dolores Messer]

Dear all,

Thanks a lot for your answers! And sorry for my very late reply.

I have been looking into euclidean distances (prior to GPA) on a per-landmark basis (euclidean distances between landmark coordinates and landmark mean), and it looks like there is no significant difference between annotation with the two systems (VR vs. computer) for five out of the six landmarks. Operators do significantly differ.

Now I am about to look into procrustes anova based models, and here I run into a question. After aligning all measurements using GPA, the landmark coordinates taken on the same specimen will be slightly moved with respect to each other, but digitization was happening in the same local reference frame of this specimen. Is this a problem?

Would it make sense to do the GPA on the mean shape of the specimens, compute the transformations (one for each specimen) to transform all individual measurements (including projection to tangent space), then do a procrustes anova? By doing so, coordinates taken on the same specimen would not be moved with respect to each other. But is this a valid approach?

Again, thanks a lot in advance!

Dolores

[Adams, Dean [EEOB]]

Dolores,

 

When one reaches the Procrustes ANOVA step of the pipeline, one is investigating patterns of shape variation (between groups in this case). At this point, the digitizing coordinate system no longer matters. Thus a GPA is perfectly fine, and in fact necessary, for proper downstream shape analyses.

Dean

 

Dr. Dean C. Adams

Director of Graduate Education, EEB Program

Professor

Department of Ecology, Evolution, and Organismal Biology

Iowa State University

https://faculty.sites.iastate.edu/dcadams/

phone: 515-294-3834

 

From: geomorph-...@googlegroups.com <geomorph-...@googlegroups.com> On Behalf Of Dolores Messer
Sent: Friday, June 25, 2021 9:41 AM
To: geomorph R package <geomorph-...@googlegroups.com>
Subject: [geomorph-r-package] Re: Computation of Procrustes variance - morphol.disparity

 

Dear all,

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[Dolores Messer]

Thanks, Dean, for your answer.

Yes, I can see that GPA is necessary to do proper analyses. But after GPA, is one not introducing some kind of error (within a specimen) as we know that all landmark configurations of one specimen were actually measured in the same local reference frame (24 configurations per measurement system and specimen)?

Thanks in advance for your help!

Dolores

[Adams, Dean [EEOB]]

Dolores,

 

No, one is not inducing error via GPA for downstream analyses  (with the exception of trying to evaluate variation at each landmark, which we discussed previously, and should not be done post-GPA). But shape analyses are fine, and in fact require GPA.

 

After GPA, shapes are aligned with respect to the overall mean, putting them in Procrustes Tangent Space. Here, differences in shape among objects are perfectly represented, as shown by the theoretical work of Kendal (1984; 1985, etc).

 

Thus, Procrustes ANOVA (which compares overall shapes across groups) does capture any differences observed in the sample.

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