Dear Igor,
Yes, it is possible to use the package with traditional measurements. In this
case, you still need to remove strong outliers and to reduce the data to the
first principal components, but you can skip the step of the Procrustes
superimposition, which is specific to geometric morphometric data.
Also, you can't directly visualise shape patterns as grid deformation, but you
can plot the loadings of the relative eigenvectors as a bar plot. For example,
to plot the loadings of the first dimension resulting from the relative
eigenanalysis of B with respect to W, the script looks like:
# Relative eigenanalysis
relEigenBW <- relative.eigen(B, W)
# Case 1: No reduction to the first PCs was done during data preparation =>
directly plot the loadings
di <- 1 # dimension
barplot(A.BW[, di], las = 2, main = paste("Dimension", di), cex.names = 0.9)
# Case 2: A reduction to the first PCs was done during data preparation =>
pre-multiply the loadings of the relative eigenanalysis by the loadings of the
PCs obtained from the PCA performed during the data preparation
A.BW <- phen.pca$rotation %*% relEigenBW$relVectors # pre-multiply the
loadings of the relative eigenvectors
di <- 1 # dimension
barplot(A.BW[, di], las = 2, main = paste("Dimension", di), cex.names = 0.9)
Also, be careful with the effect of the allometry: depending of your research
question, it can be relevant to remove it when the effect is very strong, to be
able to detect shape variability due to other factors.
Best,
Anne
Le lundi 22 mars 2021 à 10:25:24 UTC+1, Igor Talijančić
<[email protected]> a écrit :
Greetings!
I found your package veryuseful with great applicability in numerous studies
regarding marine topics,such as investigating variability in fish populations.
I have a questionrelated to the use of package beyond the GM data. Is it
possible to usetraditional measurements as input, as in Bookstein and
Mitteroecker (2014), or the computationalcode is different?
Thanks.
Sincerely,
Igor
Dana srijeda, 31. srpnja 2019. u 12:48:32 UTC+2 korisnik
[email protected] napisao je:
Dear Patrick,
Not exactly. The between-group covariance matrix B for a set of related
populations (obtained with cov.B) corresponds to phenotypic traits, but this is
not the matrix P. Both P (for phenotype) and G (for genotype) are average
within-population covariance matrices. G is an estimate of the additive genetic
covariance matrix of the common ancestral population, but G is difficult to
estimate, so we use P instead of G as the within-group covariance matrix W
(obtained with cov.W).
To summarize correspondances between matrices:
- W <-> P <-> G <-> estimate of the additive genetic covariance matrix of the
common ancestral population
- B <-> between-group covariance matrix for a set of related populations
You can find more details about this in the section 'Stabilizing Versus
Divergent Selection of Human Craniofacial Shape' in this reference:
Bookstein FL, Mitteroecker P (2014) Comparing Covariance Matrices by Relative
Eigenanalysis, with Applications to Organismal Biology. Evolutionary Biology
41, 336–350
I hope this is helpful.
Best regards,
Anne
Le mardi 30 juillet 2019 à 14:52:18 UTC+2, lv xiao <[email protected]> a
écrit :
Dear Dr. Anne,
Thank you very much for your clear explanation. May I please ask an additional
question related to one of your recent publications entitled "Multivariate
Comparison of Variance in R".
An excerpt from the paper reads "Under idealized assumptions, the expected
amount of phenotypic change due to genetic drift is proportional to the amount
of additive genetic variation in the ancestral population. Extending this model
of neutral evolution to multiple traits leads to the expectation that the
between-group covariance matrix for a set of related populations is
proportional to the additive genetic covariance matrix of their common
ancestral population (Lande, 1979). This rational has inspired statistical
tests for natural selection by contrasting the covariance matrix of population
means with the pooled phenotypic within-population covariance matrix (as an
estimate of the ancestral genetic covariance matrix; e.g. Martin et al., 2008)".
Based on the above statement, am I right to say that the additive genetic
variace-covariance matrix (commonly denoted as G) can be estimated as the
pooled within-population covariance matrix (through the cov.W function)?
Besides, am I right to say the phenotypic variance-covariance matrix (commonly
denoted as P) can be estimated as the between-group covariance matrix (through
the cov.B function)?
Thank you again for your help.
Best regards,Patrick
On Tue, Jul 30, 2019 at 7:44 PM Anne Le Maitre <[email protected]> wrote:
Dear Patrik,
Thanks for your interest.
The difference between covW and cov.W was linked to the approach used in
calculation of pooled within-group covariance matrix: in cov.W, the average of
all the within-group covariance matrices was taken, whereas they are weighted
by the sample size in covW. For the 'iris' data, the sample sizes are equal for
all groups, so the weighting had no impact, which was not the case for the
'Tropheus' data.
Attached is a new version of the function cov.W, which will be incorporated in
the next version of the package vcvComp. I have added the argument 'weighted'.
The default is set to 'FALSE'. When set to 'TRUE', the within-group covariance
matrices are weighted by the sample sizes, as in covW. In this case, you get
the same results using cov.W and covW for 'Tropheus' and 'iris' data.
If I understand well the description of the function cov.rob used in the
internal code of covW, it computes a robust estimation of the covariance
matrix, which is a way to minimize the effect of outliers on the covariance
structure when the number of cases is above p + 1. Therefore, as long as there
is no atypical point in the dataset, using cov or cov.rob should lead exactly
to the same results. For now, the function cov.W only uses cov as internal
function, so you should check the absence of outliers before using this
function.
Best,
Anne
Le samedi 27 juillet 2019 à 04:30:45 UTC+2, lv xiao <[email protected]> a
écrit :
Pretty clear explanation. Thank you.
Regarding the pooled-within group covariance matrix, I noted that both the
cov.W function in vcvComp and the covW function in Morpho can be used.
With the iris data (used as the example of Morpho for covW), I get the same
pooled-within group covariance matrix from both functions:>
covW(iris[,1:4],iris[,5]) Sepal.Length Sepal.Width Petal.Length
Petal.WidthSepal.Length 0.26500816 0.09272109 0.16751429
0.03840136Sepal.Width 0.09272109 0.11538776 0.05524354
0.03271020Petal.Length 0.16751429 0.05524354 0.18518776
0.04266531Petal.Width 0.03840136 0.03271020 0.04266531
0.04188163attr(,"means") Sepal.Length Sepal.Width Petal.Length
Petal.Widthsetosa 5.006 3.428 1.462
0.246versicolor 5.936 2.770 4.260 1.326virginica
6.588 2.974 5.552 2.026> > cov.W(iris[,1:4],iris[,5])
[,1] [,2] [,3] [,4][1,] 0.26500816 0.09272109
0.16751429 0.03840136[2,] 0.09272109 0.11538776 0.05524354 0.03271020[3,]
0.16751429 0.05524354 0.18518776 0.04266531[4,] 0.03840136 0.03271020
0.04266531 0.04188163
However, with the data provided in vcvComp, different results were returned:
covW(pc.scores, groups = Tropheus.IK$POP.ID) PC1 PC2
PC3 PC4 PC5PC1 1.334392e-04 -9.855269e-06
-2.067332e-05 1.463312e-05 3.766745e-06PC2 -9.855269e-06 6.129627e-05
-1.022908e-05 -1.119666e-06 -9.914084e-07PC3 -2.067332e-05 -1.022908e-05
4.986701e-05 4.198867e-06 -3.080283e-07PC4 1.463312e-05 -1.119666e-06
4.198867e-06 2.655314e-05 1.573463e-06PC5 3.766745e-06 -9.914084e-07
-3.080283e-07 1.573463e-06 2.714387e-05attr(,"means")
cov.W(pc.scores, groups = Tropheus.IK$POP.ID) [,1] [,2]
[,3] [,4] [,5][1,] 1.214524e-04 -4.559118e-06
-2.098212e-05 1.082849e-05 3.301874e-06[2,] -4.559118e-06 5.601458e-05
-1.054149e-05 -2.371474e-08 -6.776709e-07[3,] -2.098212e-05 -1.054149e-05
5.201804e-05 4.779061e-06 -9.245077e-07[4,] 1.082849e-05 -2.371474e-08
4.779061e-06 2.477635e-05 1.956578e-06[5,] 3.301874e-06 -6.776709e-07
-9.245077e-07 1.956578e-06 2.741012e-05
Results remain different whether I used "classical", "mve", or "mcd". I checked
the source code of both functions and noted that covW made a decision as to
whether to use cov.rob or cov for estimation of covariance matrix depending on
whether group size is greater than 1+p (the number of traits) while cov.W used
cov regardlessly. While this might lead to different results, it is strange
then why for the iris data both functions returned the same results. Note that
for iris data, each of the three groups had group size larger than 1+p, meaning
cov.rob is used when using covW while cov is used when using cov.W. But why I
got the same results now that one function used cov.rob under the hood and the
other cov? In addition, why does the vcvComp chose to use a different approach
from Morpho in calculation of pooled-within group covariance matrix?
Best regards,Patrick
On Friday, 26 July 2019 16:02:51 UTC+8, mitterp3 wrote:
ad 1) On biological grounds, you have to decide whether you want to study
variances and covariances within each sex or within the entire population
(i.e., pooling the sexes). The same applies to population means. If the sample
is not balanced regarding sex, pooling the sexes will give the one with larger
sample size a stronger impact on the result. E.g., having more females than
males in a sample would lead to a population mean that is mostly affected by
female specimens. One way to avoid this is to calculate female and male means
(or variances) separately and then average these two sex means (or variances).
ad 2) Technically, the reason is that for one group the covariance matrix of
all variables must be inverted, which requires a strong excess of cases over
variables. This does not only apply to relPCA, but also to CVA, MANOVA, etc. In
a regression, only the covariance matrix of the independent variables is
inverted, not of the dependent variables. Hence no constraint on the dependent
variables.
There is no fixed threshold for PCs to include in further analyses such as
relPCA.
Best,
Philipp
Am Mittwoch, 17. Juli 2019 21:02:37 UTC+2 schrieb lxiao63:
Hi Dr. Mitteroecker,
Thank you for your contribution. I have two questions regarding the vcvComp
package:
1. When is it necessary to specify the sex argument in the cov.group function?
In your vignette 1, sex was sepcified because "population samples were not
balanced regarding sex". Does this mean in cases where at least one of the
groups under comparison has unequal sexes, the sex argument should be specified?
2. You mentioned in another post (https://groups.google.com/
forum/#!topic/morphmet2/ 28A1moJNmLk) that "No problem to use "redundant" or
correlated variables as dependent variables in a multivariate regression", but
why is it necessary to reduce dimensionality of the shape data before relative
PCA? In addition, is there a threshold for the proportion of total variance
the reduced data should capture so that users could determine the number of PCs
to retain?
Thanks.
On Wednesday, 17 July 2019 02:32:57 UTC+8, mitterp3 wrote:
Dear morphometrics community,
I'd like to announce our new paper "Multivariate Comparison of Variance in R",
in which we summarize and explain the methods for the analysis and comparison
of multivariate variance-covariance patterns that we developed in the last
years. We also provide functions in R. These methods are well suited for
geometric morphometric data, but - as most multivariate methods - they all
require prior variable reduction.
Hope this is helpful to some of you!
Best,
Philipp Mitteroecker
Le Maître A, Mitteroecker P (in press) Multivariate Comparison of Variance in
R. Methods in Ecology and Evolution https://doi.org/10.1111/2041- 210X.13253
Mitteroecker P (2015) Affine invariant analysis of multivariate shape
variation, with an example from human craniofacial growth. Proceedings of the
The 33rd Leeds Annual Statistical Research Workshop. Mardia KV, Gusnanto A,
Nooney C, Voss J (eds.), p. 145-149
Bookstein FL, Mitteroecker P (2014) Comparing Covariance Matrices by Relative
Eigenanalysis, with Applications to Organismal Biology. Evolutionary Biology
41, 336–350
Huttegger S, Mitteroecker P (2011) Invariance and Meaningfulness in Phenotype
spaces. Evolutionary Biology 38, 335–352
Mitteroecker P, Bookstein FL (2009) The Ontogenetic Trajectory of the
Phenotypic Covariance Matrix, with Examples from Craniofacial Shape in Rats and
Humans. Evolution 63 (3), 727-737
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