Re: [MORPHMET] number of landmarks and sample size

[andrea cardini]

Dear All,
Lea's message has generated a very interesting discussion, which as 
usual has been very instructive for me.


My points were really basic ones. I am not worried about semilandmarks 
(although when I read something like "... subjects were analyzed to 
collect between 2700 and 10 400 homologous landmarks from
each rib ..." I do worry a little). My real concern is about first 
having clear ideas about why one is measuring something and only then 
deciding how to measure it. This was indirectly said by Mike's sentence 
"If I suspect curvature is important ...", which implies that only if it 
is important I try to measure it.


With faces, Jim's example, I may get a very detailed description 
(Pilipp's point) using many points. However, if all I am interested in 
is how relatively wide and long faces are, maybe I can get that 
information with just 4 points.
A much nicer example on the specificity of what one measures is Charles 
and Paul's one on bird wings in one the two papers I mentioned.


Even if I need a very detailed description and I have 1 points on 
faces, the average of my face, Jim, Mike and Philipp's faces, in a study 
on human population biology, is still just 4 people out of millions and 
cannot be an accurate estimate in that context. Good if better 
measurements (more but also specifically tailored for my aim) increase 
power, but they won't allow to get away with the need of large samples 
for robust results when I am studying small differences.
When, many years ago, in my second publication ever in geometric 
morphometrics, I wrote that the mandible of the Vancouver Island marmot 
was the most distinctive among all marmot species (despite being the 
youngest population), I was far too optimistic. It's a tiny population 
and one of the most endangered north American mammals, and all I had was 
8 specimens (mostly collected in the same years from probably just a 
couple of localities). Only years later when we managed to measure some 
50 specimens, including subfossils, from several localities and found 
the same results (including the same unusual coronoid process), I became 
more confident that those results were robust. Of course, even 50 is not 
a really big sample size when comparing closely related species, and I'd 
be happier with many more specimens. Besides, that landmark 
configuration wasn't great and probably today I would also consider 
adding some semilandmarks on curves.


Cheers

Andrea





On 31/05/17 16:42, Mike Collyer wrote:

Dear Lea,

I see others have responded to your inquiry, already.  I thought I would add an 
additional perspective.

Your question about statistical significance requires asking a follow-up 
question.  What statistical methods would you intend to use to evaluate 
“significance”?  If you are worried about the number of landmarks, your concern 
suggests you might be using parametric test statistics frequently associated 
with MANOVA, like Wilks lambda or Pilai trace.  Indeed, when using these 
statistics and converting them to approximate F values, one must have many more 
specimens than landmarks (more error degrees of freedom than shape variables, 
to be more precise), if “significance” is to be inferred from probabilities 
associated with F-distributions.  Therefore, limiting the number of landmarks 
might be a goal.

When using resampling procedures to conduct ANOVA, using fewer landmarks can 
paradoxically decrease effect sizes, as an overly simplified definition of 
shape becomes implied.  We demonstrated this in our paper: Collyer, M.L., D.J. 
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for 
phenotypes described by high-dimensional data. Heredity. 115: 357-365.  This is 
consistent with Andrea’s comment about quality over quantity with the caveat 
that limited quantity precludes quality.  In other words, too few landmarks 
translates to limited ability to discern shape differences, because the shape 
compared is basic.  In the paper, we used two separate landmark configurations: 
one with few landmarks and the other with the same landmarks plus sliding 
semilandmarks between fixed points, on different populations of fish.  We found 
that adding the semilandmarks increased the effect size for population 
differences and sexual dimorphism.  But if we constrained our analyses to 
parametric MANOVA for our small samples, we would have to use the simpler 
landmark configurations and live with the results.

I do not wish to suggest that adding more landmarks is better.  Overkill is 
certainly a concern.  I would suggest though that statistical power would be 
for me less of a concern than a proper characterization of the shape I wish to 
compare among samples.  If I suspect curvature is important but am afraid to 
use (semi)landmarks that would allow me to assess the curvature differences 
among groups, opting instead to use just the endpoints of a structure because I 
am worried about statistical power, 

RE: [MORPHMET] number of landmarks and sample size

[F. James Rohlf]

Another, though non-statistical, approach to judge whether one has an 
appropriate number of landmarks or perhaps too many is to use the tpsSuper 
software. 

One could start with many landmarks and confirm (one hopes) that the average 
unwarped image is clear implying that the landmarks have captured the variation 
of not only the landmarks but the structures around them. You can then remove 
landmarks and see whether the average looks fuzzier. If so, that reflects 
variation not well tracked by the chosen landmarks.  If there is little change 
then the landmarks you removed are not really necessary to track the variation 
in the sample. One could then continue the process. Clearly the issue is not 
just the number of landmarks but where they are located relative to the 
variation among the specimens. This process could be automated to try 
combinations of landmarks such that some measure of variation in pixels of the 
unwarped images are minimized. I seem to remember that Mardia made a suggestion 
like that many years ago.
_ _ _ _ _ _ _ _ _
F. James Rohlf, Distinguished Prof. Emeritus
Stony Brook University
Depts. of Anthropology and of Ecology & Evolution

-Original Message-
From: Murat Maga [mailto:m...@uw.edu] 
Sent: Wednesday, May 31, 2017 12:33 PM
To: Mike Collyer <mlcoll...@gmail.com>; Lea Wolter <leawolter...@gmail.com>
Cc: MORPHMET <morphmet@morphometrics.org>
Subject: RE: [MORPHMET] number of landmarks and sample size

I want to chime in on Mike's comment about density of landmarking changing the 
effect size. Nicolas Navarro and I did something similar in context of 
quantitative genetics of mandible shape and came to a similar conclusion using 
2D, 3D and 3D semi-landmarks sets on same dataset.

Navarro N, Maga AM. 2016. Does 3D Phenotyping Yield Substantial Insights in the 
Genetics of the Mouse Mandible Shape? G3: Genes, Genomes, Genetics 6:1153–1163.


-Original Message-
From: Mike Collyer [mailto:mlcoll...@gmail.com] 
Sent: Wednesday, May 31, 2017 7:43 AM
To: Lea Wolter <leawolter...@gmail.com>
Cc: MORPHMET <morphmet@morphometrics.org>
Subject: Re: [MORPHMET] number of landmarks and sample size

Dear Lea,

I see others have responded to your inquiry, already.  I thought I would add an 
additional perspective.

Your question about statistical significance requires asking a follow-up 
question.  What statistical methods would you intend to use to evaluate 
“significance”?  If you are worried about the number of landmarks, your concern 
suggests you might be using parametric test statistics frequently associated 
with MANOVA, like Wilks lambda or Pilai trace.  Indeed, when using these 
statistics and converting them to approximate F values, one must have many more 
specimens than landmarks (more error degrees of freedom than shape variables, 
to be more precise), if “significance” is to be inferred from probabilities 
associated with F-distributions.  Therefore, limiting the number of landmarks 
might be a goal.

When using resampling procedures to conduct ANOVA, using fewer landmarks can 
paradoxically decrease effect sizes, as an overly simplified definition of 
shape becomes implied.  We demonstrated this in our paper: Collyer, M.L., D.J. 
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for 
phenotypes described by high-dimensional data. Heredity. 115: 357-365.  This is 
consistent with Andrea’s comment about quality over quantity with the caveat 
that limited quantity precludes quality.  In other words, too few landmarks 
translates to limited ability to discern shape differences, because the shape 
compared is basic.  In the paper, we used two separate landmark configurations: 
one with few landmarks and the other with the same landmarks plus sliding 
semilandmarks between fixed points, on different populations of fish.  We found 
that adding the semilandmarks increased the effect size for population 
differences and sexual dimorphism.  But if we constrained our analyses to 
parametric MANOVA for our small samples, we would have to use the simpler 
landmark configurations and live with the results.

I do not wish to suggest that adding more landmarks is better.  Overkill is 
certainly a concern.  I would suggest though that statistical power would be 
for me less of a concern than a proper characterization of the shape I wish to 
compare among samples.  If I suspect curvature is important but am afraid to 
use (semi)landmarks that would allow me to assess the curvature differences 
among groups, opting instead to use just the endpoints of a structure because I 
am worried about statistical power, then I just allowed a statistical procedure 
to take me away from the biologically relevant question I sought to address.  
Andrea is correct that quality is better than quantity, but quantity can be a 
burden in either direction (too few or too many).  Additionally, statistical 
power will vary among statistical met

RE: [MORPHMET] number of landmarks and sample size

[Murat Maga]

I want to chime in on Mike's comment about density of landmarking changing the 
effect size. Nicolas Navarro and I did something similar in context of 
quantitative genetics of mandible shape and came to a similar conclusion using 
2D, 3D and 3D semi-landmarks sets on same dataset.

Navarro N, Maga AM. 2016. Does 3D Phenotyping Yield Substantial Insights in the 
Genetics of the Mouse Mandible Shape? G3: Genes, Genomes, Genetics 6:1153–1163.


-Original Message-
From: Mike Collyer [mailto:mlcoll...@gmail.com] 
Sent: Wednesday, May 31, 2017 7:43 AM
To: Lea Wolter <leawolter...@gmail.com>
Cc: MORPHMET <morphmet@morphometrics.org>
Subject: Re: [MORPHMET] number of landmarks and sample size

Dear Lea,

I see others have responded to your inquiry, already.  I thought I would add an 
additional perspective.

Your question about statistical significance requires asking a follow-up 
question.  What statistical methods would you intend to use to evaluate 
“significance”?  If you are worried about the number of landmarks, your concern 
suggests you might be using parametric test statistics frequently associated 
with MANOVA, like Wilks lambda or Pilai trace.  Indeed, when using these 
statistics and converting them to approximate F values, one must have many more 
specimens than landmarks (more error degrees of freedom than shape variables, 
to be more precise), if “significance” is to be inferred from probabilities 
associated with F-distributions.  Therefore, limiting the number of landmarks 
might be a goal.

When using resampling procedures to conduct ANOVA, using fewer landmarks can 
paradoxically decrease effect sizes, as an overly simplified definition of 
shape becomes implied.  We demonstrated this in our paper: Collyer, M.L., D.J. 
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for 
phenotypes described by high-dimensional data. Heredity. 115: 357-365.  This is 
consistent with Andrea’s comment about quality over quantity with the caveat 
that limited quantity precludes quality.  In other words, too few landmarks 
translates to limited ability to discern shape differences, because the shape 
compared is basic.  In the paper, we used two separate landmark configurations: 
one with few landmarks and the other with the same landmarks plus sliding 
semilandmarks between fixed points, on different populations of fish.  We found 
that adding the semilandmarks increased the effect size for population 
differences and sexual dimorphism.  But if we constrained our analyses to 
parametric MANOVA for our small samples, we would have to use the simpler 
landmark configurations and live with the results.

I do not wish to suggest that adding more landmarks is better.  Overkill is 
certainly a concern.  I would suggest though that statistical power would be 
for me less of a concern than a proper characterization of the shape I wish to 
compare among samples.  If I suspect curvature is important but am afraid to 
use (semi)landmarks that would allow me to assess the curvature differences 
among groups, opting instead to use just the endpoints of a structure because I 
am worried about statistical power, then I just allowed a statistical procedure 
to take me away from the biologically relevant question I sought to address.  
Andrea is correct that quality is better than quantity, but quantity can be a 
burden in either direction (too few or too many).  Additionally, statistical 
power will vary among statistical methods.  Reconsidering methods might be as 
important as reconsidering landmarks configurations.

Regards!
Mike



> On May 4, 2017, at 5:19 AM, Lea Wolter <leawolter...@gmail.com> wrote:
> 
> Hello everyone,
> 
> I am new in the field of geometric morphometrics and have a question for my 
> bachelor thesis.
> 
> I am not sure how many landmarks I should use at most in regard to the sample 
> size. I have a sample of about 22 individuals per population or maybe a bit 
> less (using sternum and epigyne of spiders) with 5 populations. 
> I have read a paper in which they use 18 landmarks with an even lower sample 
> size (3 populations with 20 individuals, 1 with 10). But I have also heard 
> that I should use twice as much individuals per population as land marks... 
> 
> Maybe there is some mathematical formula for it to know if it would be 
> statistically significant? Could you recommend some paper?
> 
> Because of the symmetry of the epigyne I am now thinking of using just one 
> half of it for setting landmarks (so I get 5 instead of 9 landmarks). For the 
> sternum I thought about 7 or 9 landmarks, so at most I would also get 18 
> landmarks like in the paper. 
> 
> I would also like to use two type specimens in the analysis, but I have just 
> this one individual per population... would it be totally nonesens in a 
> statistical point of view?
> 
> Thanks very much

Re: [MORPHMET] number of landmarks and sample size

[Mike Collyer]

Dear Lea,

I see others have responded to your inquiry, already.  I thought I would add an 
additional perspective.

Your question about statistical significance requires asking a follow-up 
question.  What statistical methods would you intend to use to evaluate 
“significance”?  If you are worried about the number of landmarks, your concern 
suggests you might be using parametric test statistics frequently associated 
with MANOVA, like Wilks lambda or Pilai trace.  Indeed, when using these 
statistics and converting them to approximate F values, one must have many more 
specimens than landmarks (more error degrees of freedom than shape variables, 
to be more precise), if “significance” is to be inferred from probabilities 
associated with F-distributions.  Therefore, limiting the number of landmarks 
might be a goal.

When using resampling procedures to conduct ANOVA, using fewer landmarks can 
paradoxically decrease effect sizes, as an overly simplified definition of 
shape becomes implied.  We demonstrated this in our paper: Collyer, M.L., D.J. 
Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for 
phenotypes described by high-dimensional data. Heredity. 115: 357-365.  This is 
consistent with Andrea’s comment about quality over quantity with the caveat 
that limited quantity precludes quality.  In other words, too few landmarks 
translates to limited ability to discern shape differences, because the shape 
compared is basic.  In the paper, we used two separate landmark configurations: 
one with few landmarks and the other with the same landmarks plus sliding 
semilandmarks between fixed points, on different populations of fish.  We found 
that adding the semilandmarks increased the effect size for population 
differences and sexual dimorphism.  But if we constrained our analyses to 
parametric MANOVA for our small samples, we would have to use the simpler 
landmark configurations and live with the results.

I do not wish to suggest that adding more landmarks is better.  Overkill is 
certainly a concern.  I would suggest though that statistical power would be 
for me less of a concern than a proper characterization of the shape I wish to 
compare among samples.  If I suspect curvature is important but am afraid to 
use (semi)landmarks that would allow me to assess the curvature differences 
among groups, opting instead to use just the endpoints of a structure because I 
am worried about statistical power, then I just allowed a statistical procedure 
to take me away from the biologically relevant question I sought to address.  
Andrea is correct that quality is better than quantity, but quantity can be a 
burden in either direction (too few or too many).  Additionally, statistical 
power will vary among statistical methods.  Reconsidering methods might be as 
important as reconsidering landmarks configurations.

Regards!
Mike



> On May 4, 2017, at 5:19 AM, Lea Wolter  wrote:
> 
> Hello everyone,
> 
> I am new in the field of geometric morphometrics and have a question for my 
> bachelor thesis.
> 
> I am not sure how many landmarks I should use at most in regard to the sample 
> size. I have a sample of about 22 individuals per population or maybe a bit 
> less (using sternum and epigyne of spiders) with 5 populations. 
> I have read a paper in which they use 18 landmarks with an even lower sample 
> size (3 populations with 20 individuals, 1 with 10). But I have also heard 
> that I should use twice as much individuals per population as land marks... 
> 
> Maybe there is some mathematical formula for it to know if it would be 
> statistically significant? Could you recommend some paper?
> 
> Because of the symmetry of the epigyne I am now thinking of using just one 
> half of it for setting landmarks (so I get 5 instead of 9 landmarks). For the 
> sternum I thought about 7 or 9 landmarks, so at most I would also get 18 
> landmarks like in the paper. 
> 
> I would also like to use two type specimens in the analysis, but I have just 
> this one individual per population... would it be totally nonesens in a 
> statistical point of view?
> 
> Thanks very much for your help!
> 
> Best regards
> Lea
> 
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