procD.lm(f1, iter = 999, RRPP = FALSE, int.first = FALSE,
verbose = FALSE)gpagen].
The names specified for the independent (x) variables in the formula represent one or more
vectors containing continuous data or factors. It is assumed that the order of the specimens in the
shape matrix matches the order of values in the independent variables.
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 depedendent variables.
The function performs statistical assessment of the terms in the model using Procrustes distances among
specimens, rather than explained covariance matrices among variables. With this approach, the sum-of-squared
Procrustes distances are used as a measure of SS (see Goodall 1991). The observed SS are evaluated through
permutation. In morphometrics this approach is known as a Procrustes ANOVA (Goodall 1991), which is equivalent
to distance-based anova designs (Anderson 2001). 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. 2014). 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 SS sampling
distributions generated, which might be more intuitive for P-values than F-values (see Collyer et al. 2014). 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.)### MANOVA example for Goodall's F test (multivariate shape vs. factors)
data(plethodon)
Y.gpa<-gpagen(plethodon$land) #GPA-alignment
procD.lm(Y.gpa$coords ~ plethodon$species*plethodon$site,iter=99)
### Regression example
data(ratland)
rat.gpa<-gpagen(ratland) #GPA-alignment
procD.lm(rat.gpa$coords ~ rat.gpa$Csize,iter=99)
## using RRPP
procD.lm(rat.gpa$coords ~ rat.gpa$Csize,iter=49,RRPP=TRUE)Run the code above in your browser using DataLab