RVcomparison: Compare Escoufier RV coefficient between groups

In GeometricMorphometricsMix: Heterogeneous Methods for Shape and Other Multidimensional Data

Compare Escoufier RV coefficient between groups

Description

Performs permutation tests for the difference in Escoufier RV between groups. For multiple groups, performs pairwise comparisons between all pairs of groups.

Usage

RVcomparison(Block1, Block2, group, perm = 999, center = TRUE)

Arguments

Block1, Block2	Matrices or data frames containing each block of variables (observations in rows, variables in columns).
group	factor or vector indicating group membership for observations.
perm	number of permutations for the test
center	whether the 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

A data frame with one row per pairwise comparison and the following columns:

group1

Name of the first group in the comparison

group2

Name of the second group in the comparison

Observed_RV_group1

Observed Escoufier RV for the first group in the comparison

Observed_RV_group2

Observed Escoufier RV for the second group in the comparison

Absolute_difference_in_RV

Absolute difference in the observed Escoufier RV between the two groups

p_value

p value of the permutation test

For multiple groups, the data frame includes additional columns identifying the groups being compared.

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

library(MASS)
set.seed(123)

# Create sample data with different correlation structures
S1 = diag(50)  # Uncorrelated variables for group 1
S2 = diag(50)
S2[11:50, 11:50] = 0.3  # Some correlation in second block for group 2
S2 = (S2 + t(S2)) / 2  # Ensure symmetry
diag(S2) = 1

# Generate data for two groups
A = mvrnorm(30, mu = rep(0, 50), Sigma = S1)
B = mvrnorm(40, mu = rep(0, 50), Sigma = S2)

# Combine data and create group labels
combined_data1 = A[, 1:20]
combined_data2 = A[, 21:50]
combined_data1 = rbind(combined_data1, B[, 1:20])
combined_data2 = rbind(combined_data2, B[, 21:50])
groups = c(rep("GroupA", 30), rep("GroupB", 40))

# Perform RV comparison
result = RVcomparison(combined_data1, combined_data2,
                      group = groups, perm = 99)
print(result)

# Example with three groups for pairwise comparisons
C = mvrnorm(25, mu = rep(0, 50), Sigma = diag(50))
combined_data1_3grp = rbind(combined_data1, C[, 1:20])
combined_data2_3grp = rbind(combined_data2, C[, 21:50])
groups_3 = c(groups, rep("GroupC", 25))

result_3grp = RVcomparison(combined_data1_3grp, combined_data2_3grp, 
                          group = groups_3, perm = 99)
print(result_3grp)

GeometricMorphometricsMix documentation built on April 18, 2026, 1:06 a.m.