Greetings!
I found your package very useful with great applicability in numerous studies regarding marine topics, such as investigating variability in fish populations. I have a question related to the use of package beyond the GM data. Is it possible to use traditional measurements as input, as in Bookstein and Mitteroecker (2014), or the computational code 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.Width > Sepal.Length 0.26500816 0.09272109 0.16751429 0.03840136 > Sepal.Width 0.09272109 0.11538776 0.05524354 0.03271020 > Petal.Length 0.16751429 0.05524354 0.18518776 0.04266531 > Petal.Width 0.03840136 0.03271020 0.04266531 0.04188163 > attr(,"means") > Sepal.Length Sepal.Width Petal.Length Petal.Width > setosa 5.006 3.428 1.462 0.246 > versicolor 5.936 2.770 4.260 1.326 > virginica 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$POP.ID) > PC1 PC2 PC3 PC4 PC5 > PC1 1.334392e-04 -9.855269e-06 -2.067332e-05 1.463312e-05 3.766745e-06 > PC2 -9.855269e-06 6.129627e-05 -1.022908e-05 -1.119666e-06 -9.914084e-07 > PC3 -2.067332e-05 -1.022908e-05 4.986701e-05 4.198867e-06 -3.080283e-07 > PC4 1.463312e-05 -1.119666e-06 4.198867e-06 2.655314e-05 1.573463e-06 > PC5 3.766745e-06 -9.914084e-07 -3.080283e-07 1.573463e-06 2.714387e-05 > attr(,"means") > > > cov.W(pc.scores, groups = Tropheus.IK$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 > <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 <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 > > -- > > You received this message because you are subscribed to the Google Groups > "Morphmet" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/morphmet2/a662521c-d8a9-4a6f-8526-6a8a7d510d1f%40googlegroups.com > > <https://groups.google.com/d/msgid/morphmet2/a662521c-d8a9-4a6f-8526-6a8a7d510d1f%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > -- You received this message because you are subscribed to the Google Groups "Morphmet" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/b941b420-80bd-47b0-af87-88d28e9ebe39n%40googlegroups.com.
