integration.test(A, A2 = NULL, partition.gp = NULL, iter = 999, seed = NULL, print.progress = TRUE)gpagen]. The function may be used to assess
the degree of morphological integration between two or more sets of variables.
The function estimates the degree of morphological integration using a two-block partial least squares
analysis (PLS). When used with landmark data, this analysis is referred to as singular warps analysis
(Bookstein et al. 2003). If more than two partitions are defined, the average pairwise PLS correlation is utilized as
the test statistic. The observed test value is then compared to a distribution of values obtained by randomly permuting
the individuals (rows) in one partition relative to those in the other. A significant result is found when the
observed PLS correlation is large relative to this distribution, and implies that the structures are integrated with one
another (see Bookstein et al. 2003). If only two partitions are specified, a plot of PLS scores along the first
set of PLS axes is optionally displayed, and thin-plate spline deformation grids along these axes are also shown if data were
input as a 3D array.
Input for the analysis can take one of two forms. First, one can input a single dataset (as a matrix or 3D array, along with
a vector describing which variables correspond to which partitions (for the case of a 3D array, which landmarks belong to which
partitions is specified). Alternatively, when evaluating the integration between two structures or partitions, two datasets may be provided.The generic functions, print, summary, and plot all work with modularity.test.
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.
two.b.pls, modularity.test, phylo.pls, and
phylo.integration
data(plethodon)
Y.gpa<-gpagen(plethodon$land) #GPA-alignment
#landmarks on the skull and mandible assigned to partitions
land.gps<-c("A","A","A","A","A","B","B","B","B","B","B","B")
IT <- integration.test(Y.gpa$coords, partition.gp=land.gps, iter=999)
summary(IT) # Test summary
plot(IT) # PLS plot
IT$left.pls.vectors # extracting just the left (first block) singular vectors
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