two.b.pls: Two-block partial least squares analysis for shape data

Description

Function performs two-block partial least squares analysis to assess the degree of association between to blocks of Procrustes-aligned coordinates (or other variables)

Usage

two.b.pls(A1, A2, iter = 999, seed = NULL, print.progress = TRUE)

Arguments

A 3D array (p x k x n) containing GPA-aligned coordinates for the first block, or a matrix (n x variables)

A 3D array (p x k x n) containing GPA-aligned coordinates for the second block, or a matrix (n x variables)

iter

Number of iterations for significance testing

seed

An optional argument for setting the seed for random permutations of the resampling procedure. If left NULL (the default), the exact same P-values will be found for repeated runs of the analysis (with the same number of iterations). If seed = "random", a random seed will be used, and P-values will vary. One can also specify an integer for specific seed values, which might be of interest for advanced users.

print.progress

A logical value to indicate whether a progress bar should be printed to the screen. This is helpful for long-running analyses.

Value

r.pls: The correlation coefficient between scores of projected values on the first singular vectors of left (x) and right (y) blocks of landmarks (or other variables)
P.value: The empirically calculated P-value from the resampling procedure.
left.pls.vectors: The singular vectors of the left (x) block
right.pls.vectors: The singular vectors of the right (y) block
random.r: The correlation coefficients found in each random permutation of the resampling procedure.
XScores: Values of left (x) block projected onto singular vectors.
YScores: Values of right (y) block projected onto singular vectors.
svd: The singular value decomposition of the cross-covariances.
A1: Input values for the left block.
A2: Input values for the right block.
A1.matrix: Left block (matrix) found from A1.
A2.matrix: Right block (matrix) found from A2.
permutations: The number of random permutations used in the resampling procedure.
call: The match call.

Details

The function quantifies the degree of association between two blocks of shape data as defined by landmark coordinates using partial least squares (see Rohlf and Corti 2000). If geometric morphometric data are used, it is assumed that the landmarks have previously been aligned using Generalized Procrustes Analysis (GPA) [e.g., with gpagen]. If other variables are used, they must be input as a 2-Dimensional matrix (rows = specimens, columns = variables). It is also assumed that the separate inputs have specimens (observations) in the same order. The generic functions, print, summary, and plot all work with two.b.pls. The generic function, plot, produces a two-block.pls plot. This function calls plot.pls, which has two additional arguments (with defaults): label = NULL, warpgrids = TRUE. These arguments allow one to include a vector to label points and a logical statement to include warpgrids, respectively. Warpgrids can only be included for 3D arrays of Procrustes residuals. The plot is a plot of PLS scores from Block1 versus Block2 performed for the first set of PLS axes. Notes for geomorph 3.0 There is a slight change in two.b.pls plots with geomorph 3.0. Rather than use the shapes of specimens that matched minimum and maximum PLS scores, major-axis regression is used and the extreme fitted values are used to generate deformation grids. This ensures that shape deformations are exactly along the major axis of shape covariation. This axis is also shown as a best-fit line in the plot.

References

Rohlf, F.J., and M. Corti. 2000. The use of partial least-squares to study covariation in shape. Systematic Biology 49: 740-753.

Examples

Run this code

data(plethShapeFood) 
Y.gpa<-gpagen(plethShapeFood$land)    #GPA-alignment    

#2B-PLS between head shape and food use data
PLS <-two.b.pls(Y.gpa$coords,plethShapeFood$food,iter=999)
summary(PLS)
plot(PLS)

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