Introduction

When one is performing integration research on sets of traits in different samples, it is often necessary to determine whether those integration values are significantly different from one another. The function compare.ZVrel allows one to statistically compare effect sizes of two or more integration analyses performed using the relative eigenvalue variance.

The input for this function must be of class “rel.eig” that is, an object resulting from the function integration.Vrel. Any number of objects can be input.

compare.ZVrel()
  • \(...\): saved analyses of class rel.eig
  • \(two.tailed\): A logical value to indicate whether a two-tailed test (typical and default) should be performed.



Example of Analysis

By way of example, we present an analysis of the morphological integration among several species of plethodontid salamander These data are included with geomorph by default, as a single object. The data have been separated by species for the purposes of this example. Please see the tutorials on Data Manipulation and R Data Basic for information on how to accomplish this.

First, we subset the plethodon landmark data using the ‘species’ factor included in the plethodon dataset.

coords.gp <- coords.subset(lmks$coords, plethodon$species)



Now, we run our Vrel analyses using the map function. This allows us to run the function on each of the partitioned sets of coordinates.

Vrel.gp <- Map(function(x) integration.Vrel(x), coords.gp)

Finally, we run the comparison, and summarize the results.

out <- compare.ZVrel(Vrel.gp$Jord, Vrel.gp$Teyah)
summary(out)
## 
## Effect sizes
## 
##  Vrel.gp$Jord Vrel.gp$Teyah 
##    -0.2978931    -0.2642648 
## 
## Effect sizes for pairwise differences in rel.eig effect size
## 
##               Vrel.gp$Jord Vrel.gp$Teyah
## Vrel.gp$Jord    0.00000000    0.09804249
## Vrel.gp$Teyah   0.09804249    0.00000000
## 
## P-values
## 
##               Vrel.gp$Jord Vrel.gp$Teyah
## Vrel.gp$Jord     1.0000000     0.9218986
## Vrel.gp$Teyah    0.9218986     1.0000000

Summarizing these results returns two tables of pairwise effect sizes and p-values, as well as the effect sizes for each of the integration analyses.

This function returns an object of class “compare.rel.eig”, which is a list containing the following:

compare.ZVrel output
  • \(sample.Re.obs\): A vector of observed Vrel for each sample.
  • \(sample.Z.obs\): A vector of effect sizes for each sample.
  • \(sample.Z.var\): A vector of variances for each effect size.
  • \(pairwise.z\): A matrix of pairwise, two-sample z scores between all pairs of effect sizes.
  • \(pairwise.p\): A matrix of corresponding P-values.