procD.pgls(f1, phy, iter = 999, seed = NULL, int.first = FALSE, RRPP = TRUE, data = NULL, print.progress = TRUE, ...)read.tree in library apegeomorph.data.frameprocD.lm for a description of the list of results generated. Additionally, procD.pgls provides
the phylogenetic correction matrix, Pcor, plus "pgls" adjusted coefficients, fitted values, and residuals.
gpagen].
Linear model fits (using the lm function)
can also be input in place of a formula. Arguments for lm can also be passed on via this function.
The user must also specify a phylogeny describing the evolutionary relationships among species (of class phylo).
Note that the specimen labels for both X and y must match the labels on the tips of the phylogeny.The function two.d.array can be used to obtain a two-dimensional data matrix from a 3D array of landmark
coordinates; however this step is no longer necessary, as procD.lm can receive 3D arrays as dependent variables. It is also
recommended that geomorph.data.frame is used to create and input a data frame. This will reduce problems caused
by conflicts between the global and function environments. In the absence of a specified data frame, procD.pgls will attempt to
coerce input data into a data frame, but success is not guaranteed.
From the phylogeny, a phylogenetic transformation matrix is obtained under a Brownian motion model, and used to
transform the X and y variables. Next, the Gower-centered distance matrix is obtained from predicted values from the
model (y~X), from which sums-of-squares, F-ratios, and R^2 are estimated for each factor in the model (see Adams, 2014).
Data are then permuted across the tips of the phylogeny, and all estimates of statistical values are obtained for the permuted data,
which are compared to the observed value to assess significance. This approach has been shown to have appropriate type I error
rates, whereas an alternative procedure for phylogenetic regression of morphometric shape data displays elevated type I error rates
(see Adams and Collyer 2015).
Two possible resampling procedures are provided. First, if RRPP=FALSE,
the rows of the matrix of shape variables
are randomized relative to the design matrix. This is analogous to a 'full' randomization. Second, if RRPP=TRUE,
a residual randomization permutation procedure is utilized (Collyer et al. 2015). Here, residual shape values from a reduced model are
obtained, and are randomized with respect to the linear model under consideration. These are then added to
predicted values from the remaining effects to obtain pseudo-values from which SS are calculated. NOTE: for
single-factor designs, the two approaches are identical. However, when evaluating factorial models it has been
shown that RRPP attains higher statistical power and thus has greater ability to identify patterns in data should
they be present (see Anderson and terBraak 2003). Effect-sizes (Z-scores) are computed as standard deviates of the sampling
distributions (of F values) generated, which might be more intuitive for P-values than F-values (see Collyer et al. 2015). In the case
that multiple factor or factor-covariate interactions are used in the model formula, one can specify whether all main effects should be
added to the model first, or interactions should precede subsequent main effects
(i.e., Y ~ a + b + c + a:b + ..., or Y ~ a + b + a:b + c + ..., respectively.)
The generic functions, print, summary, and plot all work with procD.pgls.
The generic function, plot, produces diagnostic plots for Procrustes residuals of the linear fit.
Adams, D.C., and M.L. Collyer. 2015. Permutation tests for phylogenetic comparative analyses of high-dimensional shape data: what you shuffle matters. Evolution. 69:823-829.
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.
### Example of D-PGLS for high-dimensional data
data(plethspecies)
Y.gpa<-gpagen(plethspecies$land) #GPA-alignment
gdf <- geomorph.data.frame(Y.gpa, phy = plethspecies$phy)
procD.pgls(coords ~ Csize, phy = phy, data = gdf, iter = 999, RRPP = FALSE) # randomize raw values
procD.pgls(coords ~ Csize, phy = phy, data = gdf, iter = 999, RRPP = TRUE) # randomize residuals
### Extracting objects
pleth.pgls <- procD.pgls(coords ~ Csize, phy = phy, data = gdf, iter = 999, RRPP = TRUE)
summary(pleth.pgls)
plot(pleth.pgls)
pleth.pgls$Pcor # the phylogenetic transformation (correction) matrix
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