geomorph (version 4.0.8)

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 graphical representations of shape change, based on prediction criteria.

Usage

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

Value

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

Arguments

A

A 3D array (p x k x n) containing Procrustes shape variables 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 between 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 predictors 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 prediction 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 design 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.

Author

Michael Collyer

Examples

if (FALSE) {

# Examples using Plethodon data

 data("plethodon")

 Y.gpa <- gpagen(plethodon$land)    #GPA-alignment    
 plot(gm.prcomp(Y.gpa$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 <- gm.prcomp(Y.gpa$coords)
 PC <- PCA$x[,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$x[,1:2]
# user-picked spots can be anything, but it in this case, apparent groups
 preds <- shape.predictor(Y.gpa$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$coords, x = log(Y.gpa$Csize), 
                          Intercept = TRUE, 
                          predmin = min(log(Y.gpa$Csize)), 
                          predmax = max(log(Y.gpa$Csize))) 

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

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

 gdf <- geomorph.data.frame(Y.gpa)
 plethAllometry <- procD.lm(coords ~ log(Csize), data = gdf)
 allom.plot <- plot(plethAllometry, 
 type = "regression", 
 predictor = log(gdf$Csize),
 reg.type ="RegScore") # make sure to have a predictor 

 preds <- shape.predictor(plethAllometry$GM$fitted, 
                          x = allom.plot$RegScore, Intercept = FALSE, 
                          predmin = min(allom.plot$RegScore), 
                          predmax = max(allom.plot$RegScore)) 
 plotRefToTarget(M, preds$predmin, mag = 3)
 plotRefToTarget(M, preds$predmax, mag = 3)

 allom.plot <- plot(plethAllometry, 
 type = "regression", 
 predictor = log(gdf$Csize),
 reg.type ="PredLine")
 preds <- shape.predictor(plethAllometry$GM$fitted, 
                          x = allom.plot$PredLine, Intercept = FALSE, 
                          predmin = min(allom.plot$PredLine), 
                          predmax = max(allom.plot$PredLine)) 
 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(A1 = plethShapeFood$food, A2 = Y.gpa$coords) 
 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)
}