Function performs two-block partial least squares analysis to assess the degree of association between to blocks of Procrustes shape variables (or other variables)
two.b.pls(A1, A2, iter = 999, seed = NULL, print.progress = TRUE)A 3D array (p x k x n) containing Procrustes shape variables for the first block, or a matrix (n x variables)
A 3D array (p x k x n) containing Procrustes shape variables for the second block, or a matrix (n x variables)
Number of iterations for significance testing
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.
A logical value to indicate whether a progress bar should be printed to the screen. This is helpful for long-running analyses.
Object of class "pls" that returns a list of the following:
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). This value can only be negative if single variables are input, as it reduces to the Pearson correlation coefficient.
The empirically calculated P-value from the resampling procedure.
The singular vectors of the left (x) block
The singular vectors of the right (y) block
The correlation coefficients found in each random permutation of the resampling procedure.
Values of left (x) block projected onto singular vectors.
Values of right (y) block projected onto singular vectors.
The singular value decomposition of the cross-covariances. See svd for further details.
Input values for the left block.
Input values for the right block.
Left block (matrix) found from A1.
Right block (matrix) found from A2.
The number of random permutations used in the resampling procedure.
The match call.
The function quantifies the degree of association between two blocks of shape data as
defined by Procrustes shape variables 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. Additionally, if names for the objects are specified, these must be the same for both datasets.
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. It is imperative that one understands the arguments for plot parameters and
plotRefToTarget because arguments can be passed to both of these functions.
If one wishes to consider 3+ arrays or matrices, there are multiple options. First, one could perform multiple two.b.pls analyses and use
compare.pls to ascertain which blocks are more "integrated". Second, one could use integration.test and perform a test that
averages the amount of integration (correlations) across multiple pairwise blocks. Note that integration.test performed on two matrices or
arrays returns the same results as two.b.pls. (Thus, integration.test is more flexible and thorough.)
If one wishes to incorporate a phylogeny, phylo.integration is the function to use. This function is exactly the same as integration.test
but allows PGLS estimation of PLS vectors. Because integration.test can be used on two blocks, phylo.integration likewise allows one to
perform a phylogenetic two-block PLS analysis.
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.
Compared to previous versions of geomorph, users might notice differences in effect sizes. Previous versions used z-scores calculated with expected values of statistics from null hypotheses (sensu Collyer et al. 2015); however Adams and Collyer (2016) showed that expected values for some statistics can vary with sample size and variable number, and recommended finding the expected value, empirically, as the mean from the set of random outcomes. Geomorph 3.0.4 and subsequent versions now center z-scores on their empirically estimated expected values and where appropriate, log-transform values to assure statistics are normally distributed. This can result in negative effect sizes, when statistics are smaller than expected compared to the average random outcome. For ANOVA-based functions, the option to choose among different statistics to measure effect size is now a function argument.
Rohlf, F.J., and M. Corti. 2000. The use of partial least-squares to study covariation in shape. Systematic Biology 49: 740-753.
Collyer, M.L., D.J. Sekora, and D.C. Adams. 2015. A method for analysis of phenotypic change for phenotypes described by high-dimensional data. Heredity. 115:357-365.
Adams, D.C. and M.L. Collyer. 2016. On the comparison of the strength of morphological integration across morphometric datasets. Evolution. 70:2623-2631.
integration.test, modularity.test,
phylo.integration, and compare.pls
# NOT RUN {
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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