RVcomparison: Compare Escoufier RV coefficient between two groups

In fruciano/GeometricMorphometricsMix: Miscellaneous functions useful for geometric morphometrics

Compare Escoufier RV coefficient between two groups

Description

Performs a permutation test for the difference in Escoufier RV between two groups

Usage

RVcomparison(
  Group1Block1,
  Group1Block2,
  Group2Block1,
  Group2Block2,
  perm = 999,
  center = TRUE
)

Arguments

Group1Block1, Group1Block2, Group2Block1, Group2Block2	Matrices or data frames containing the data for each group of observations (specimens) and each block of variables (observations in rows, variables in columns).
perm	number of permutations for the test
center	whether the two groups should be mean-centered prior to the test

Details

This function is one of the solutions proposed by Fruciano et al. 2013 to deal with the fact that values of Escoufier RV coefficient (Escoufier 1973), which is routinely used to quantify the levels of association between multivariate blocks of variables (landmark coordinates in the case of morphometric data, but it might be any multivariate dataset) are not comparable across groups with different number of observations/individuals (Smilde et al. 2009; Fruciano et al. 2013). The solution is a permutation test. This test was originally implemented by Adriano Franchini in the Java program RVcomparator, of which this function is an updated and improved version

Value

The function outputs a list with the following elements:

ObservedRVgrp1

Observed Escoufier RV for group 1

ObservedRVgrp2

Observed Escoufier RV for group 2

ObservedAbsoluteDifference

Absolute difference in the observed Escoufier RV between the two groups

pvalue

p value of the permutation test

Notice

The values of RV for each of the groups the function outputs are the observed ones, and can be reported but their value should not be compared. If one wants to obtain comparable values one solution (Fruciano et al 2013) is to obtain rarefied estimates, which can be done with the function RVrarefied in this package

Citation

If you use this function please cite both Fruciano et al. 2013 (for using the rarefaction procedure) and Escoufier 1973 (because the procedure is based on Escoufier RV)

References

Escoufier Y. 1973. Le Traitement des Variables Vectorielles. Biometrics 29:751-760.

Fruciano C, Franchini P, Meyer A. 2013. Resampling-Based Approaches to Study Variation in Morphological Modularity. PLoS ONE 8:e69376.

Smilde AK, Kiers HA, Bijlsma S, Rubingh CM, van Erk MJ. 2009. Matrix correlations for high-dimensional data: the modified RV-coefficient. Bioinformatics 25:401-405.

See Also

EscoufierRV

RVrarefied

Examples

if(!require(lmf)){ install.packages("lmf", repos="https://cran.mirror.garr.it/CRAN/") }
# Install package lmf if not available

set.seed(123)

S1=diag(100)
# Use uncorrelated variables for the first group

S2=diag(100)
S2[21:100,21:100]=rnorm((100-20)^2, 0.1, 0.03^2)
S2[1:20,1:20]=rnorm(20^2,0.01,0.03^2)
lower=S2[lower.tri(S2)]
S2=t(S2)
S2[lower.tri(S2)]=lower
diag(S2)=1
S2=lmf::nearPD(S2)
# Create an ad hoc covariance matrix for the second group


A=MASS::mvrnorm(50, mu=rep(0,100), Sigma=S1)
B=MASS::mvrnorm(100, mu=rep(10,100), Sigma=S2)
# Create two multivariate normal random datasets
# using the covariance matrices above
# We are going to use the first 20 variables as block 1
# and the subsequent variables as block 2

EscoufierRV(A[,1:20], A[,21:ncol(A)])
EscoufierRV(B[,1:20], B[,21:ncol(B)])
# Notice that the two observed Escoufier RV are different
# However, this difference might be due to the
# different number of observations for the two groups

RVcomparison(A[,1:20], A[,21:ncol(A)], B[,1:20], B[,21:ncol(B)])
# One of the solutions is to perform a permutation test,
# which shows us that these differences are actually significant
# (another, complementary, solution is to compute rarefied estimates
# using the function EscoufierRVrarefy)
RVrarefied(A[,1:20], A[,21:ncol(A)], samplesize=40)$Rarefied_RV
RVrarefied(B[,1:20], B[,21:ncol(B)], samplesize=40)$Rarefied_RV

fruciano/GeometricMorphometricsMix documentation built on Jan. 31, 2024, 6:24 a.m.