geomorph (version 3.0.3)

shape.predictor: Shape prediction from numeric predictors

Description

Function estimates one or more configurations based on one or more linear predictors, such as PC scores allometric relationships, or any other least squares or partial least squares regression. These configurations can be used with plotRefToTarget to generate gpaphical represntations of shape change, based on prediction criteria.

Usage

shape.predictor(A, x = NULL, Intercept = FALSE, method = c("LS", "PLS"),
  ...)

Arguments

A

An array (p x k x n) containing Procrustes residuals either from GPA or fitted values from a previous analytical procedure.

x

Linear (numeric) predictors. Can be a vector or a matrix, or a list containing vectors or matrices. Values must be numeric. If a factor is desired, one should use model.matrix to obtain a design matrix. This will impact how prediction criteria need to be provided (see below).

Intercept

Logical value to indicate whether an intercept should be used in the linear equation for predictions. Generally, this value will be FALSE for shape predictions made in ordination plots. It should be TRUE in cases where the expected shape at the point the predictor has a value of 0 is not the mean shape.

method

A choice betwen least squares (LS) or partial least squares (PLS) regression for prediction. The function defaults to LS prediction. PLS might be chosen in cases where correlation is preferred over linear regression. If PLS is chosen, a two-block PLS analysis using two.b.pls should be performed first, as only the first singular vector for pedictors will be used for defining prediction criteria (see below).

...

Any number of prediction criteria. Criteria should be presented as either a scalar (if one predictor is provided) or a vector (if more than one predictor or a prediciton matrix is provided); e.g., pred1 = c(0.1, -0.5), pred2 = c(-0.2, -0.1) (which would be the case if two predictors were provided). It is essential that the number of elements in any prediction criterion matches the number of predictors. Caution should be used when providing a design matrix to ensure that correct dummy variables are used in prediction criteria, and that either 1) an intercept is not included in the design and 2) is TRUE in the Intercept argument; or or 1) an intercept is included in the deisgn and 2) is FALSE in the Intercept argument; or 1) an intercept is not included in the design and 2) is FALSE in the Intercept argument, if no intercept is desired.

Value

A list of predicted shapes matching the number of vectors of prediction criteria provides. The predications also have names matching those of the prediction criteria.

Examples

# Examples using Plethodon data

data("plethodon")

Y.gpa <- gpagen(plethodon$land)    #GPA-alignment    
plotTangentSpace(Y.gpa$coords)

preds <- shape.predictor(Y.gpa$coords, x= NULL, Intercept = FALSE, 
pred1 = -0.1, pred2 = 0.1) # PC 1 extremes, sort of
M <- mshape(Y.gpa$coords)
plotRefToTarget(M, preds$pred1)
plotRefToTarget(M, preds[[1]]) # same result
plotRefToTarget(M, preds$pred2)

PCA <- plotTangentSpace(Y.gpa$coords)
PC <- PCA$pc.scores[,1]
preds <- shape.predictor(Y.gpa$coords, x= PC, Intercept = FALSE, 
pred1 = min(PC), pred2 = max(PC)) # PC 1 extremes, more technically
plotRefToTarget(M, preds$pred1)
plotRefToTarget(M, preds$pred2)

PC <- PCA$pc.scores[,1:2]
# user-picked spots - can be anything, but it in this case, apparent groups
preds <- shape.predictor(Y.gpa$coords, x= PC, Intercept = FALSE, 
                        pred1 = c(0.045,-0.02), pred2 = c(-0.025,0.06), pred3 = c(-0.06,-0.04)) 
plotRefToTarget(M, preds$pred1)
plotRefToTarget(M, preds$pred2)
plotRefToTarget(M, preds$pred3)

# allometry example - straight-up allometry

preds <- shape.predictor(Y.gpa$coords, x= Y.gpa$Csize, Intercept = TRUE, 
                        predmin = min(Y.gpa$Csize), predmax = max(Y.gpa$Csize)) 

plotRefToTarget(M, preds$predmin, mag=3)
plotRefToTarget(M, preds$predmax, mag=3)

# allometry example - using RegScore or PredLine via procD.allometry

gdf <- geomorph.data.frame(Y.gpa)
plethAllometry <- procD.allometry(coords~Csize, data=gdf)
plot(plethAllometry, method="RegScore")
preds <- shape.predictor(plethAllometry$Ahat, x= plethAllometry$Reg.proj, Intercept = FALSE, 
                        predmin = min(plethAllometry$Reg.proj), 
                        predmax = max(plethAllometry$Reg.proj)) 
plotRefToTarget(M, preds$predmin, mag=3)
plotRefToTarget(M, preds$predmax, mag=3)

plot(plethAllometry, method="PredLine")
preds <- shape.predictor(plethAllometry$Ahat, x= plethAllometry$pred.val, Intercept = FALSE, 
                        predmin = min(plethAllometry$pred.val), 
                        predmax = max(plethAllometry$pred.val)) 
plotRefToTarget(M, preds$predmin, mag=3)
plotRefToTarget(M, preds$predmax, mag=3)

# using factors via PCA

gdf <- geomorph.data.frame(Y.gpa, species = plethodon$species, site = plethodon$site)
pleth <- procD.lm(coords ~ species*site, data=gdf)
PCA <- prcomp(pleth$fitted)
plot(PCA$x, asp=1, pch=19)

means <- unique(round(PCA$x,3))
means # note: suggests 3 PCs useful enough

preds <- shape.predictor(arrayspecs(pleth$fitted, 12,2), x= PCA$x[,1:3],
                        Intercept = FALSE,
                        pred1 = means[1,1:3], 
                        pred2 = means[2,1:3],
                        pred3 = means[3,1:3], 
                        pred4 = means[4,1:3])                   
plotRefToTarget(M, preds$pred1, mag=2)
plotRefToTarget(M, preds$pred2, mag=2)
plotRefToTarget(M, preds$pred3, mag=2)
plotRefToTarget(M, preds$pred4, mag=2)

# Using a design matrix for factors

X <- pleth$X
X # includes intercept; remove for better functioning 
X <- X[,-1]
symJord <- c(0,1,0) # design for P. Jordani in sympatry
alloJord <- c(0,0,0) # design for P. Jordani in allopatry
preds <- shape.predictor(arrayspecs(pleth$fitted, 12,2), x = X, Intercept = TRUE, 
                        symJord=symJord, alloJord=alloJord)
plotRefToTarget(M, preds$symJord, mag=2)
plotRefToTarget(M, preds$alloJord, mag=2)

# PLS Example

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

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

preds <- shape.predictor(Y.gpa$coords, plethShapeFood$food, Intercept = FALSE,
                        method = "PLS",
                        pred1 = 2, pred2 = -4, pred3 = 2.5) # using PLS plot as a guide
M <- mshape(Y.gpa$coords)
plotRefToTarget(M, preds$pred1, mag=2)
plotRefToTarget(M, preds$pred2, mag=2)
plotRefToTarget(M, preds$pred3, mag=2)