02: Day 2 Material
General Introduction
Today we will briefly introduce some geomorph functions
for performing the analyses described yesterday. Note:
You should be able to read in your data and perform the analyses from
yesterday! Thus this tutorial augments the ‘next steps’ of a
morphometric analysis (i.e., we are beginning to flesh out the steps of
the Procrustes Paradigm for geometric morphometric analyses).
1: Generalized Procrustes Analysis (GPA) with Sliding Semilandmarks
Below is a simple 2D example containing points and curves. For 3D we could add curves and/or surfaces (see help file)
data(hummingbirds)
hummingbirds$curvepts ## before slide after
## [1,] 1 11 12
## [2,] 11 12 13
## [3,] 13 14 15
## [4,] 7 15 14
## [5,] 12 13 14
## [6,] 1 16 17
## [7,] 16 17 18
## [8,] 17 18 19
## [9,] 18 19 20
## [10,] 10 20 19
## [11,] 2 21 22
## [12,] 21 22 23
## [13,] 22 23 24
## [14,] 23 24 25
## [15,] 8 25 24gpa.BE <- gpagen(hummingbirds$land,
curves = hummingbirds$curvepts,
ProcD=FALSE,
print.progress = F)
plot(gpa.BE)
gpa.procD <- gpagen(hummingbirds$land,
curves = hummingbirds$curvepts,
ProcD=TRUE, print.progress = F)
plot(gpa.procD)
NOTE: For StereoMorph users, the notation is slightly different for specifying curves (see help file):
shapes <- StereoMorph::readShapes("Data/example.digitized")
shapesGM <- readland.shapes(shapes,
nCurvePts = c(12, 12, 12, 8, 6, 6, 6, 12, 10))
Y.gpa <- gpagen(shapesGM,
print.progress = FALSE)
plot(Y.gpa)
2: Partial Least Squares (PLS)
Here is a simple example of partial least squares:
data("plethShapeFood")
Y.gpa <- gpagen(plethShapeFood$land,
print.progress = FALSE)
food <- plethShapeFood$food
rownames(food) <- names(Y.gpa$Csize) # just to assure match
PLSfood <- two.b.pls(food, Y.gpa$coords,
print.progress = FALSE,
iter = 9999)
plot(PLSfood)
3: GLM: Regression
Here is a simple example of regression from a linear model:
fit.null <- procD.lm(coords ~ 1, data = Y.gpa,
iter = 9999)
fit.alt <- procD.lm(coords ~ log(Csize), data = Y.gpa,
turbo = FALSE, iter = 9999)
anova(fit.alt)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 10000
## Estimation method: Ordinary Least Squares
## Sums of Squares and Cross-products: Type I
## Effect sizes (Z) based on F distributions
##
## Df SS MS Rsq F Z Pr(>F)
## log(Csize) 1 0.10758 0.107583 0.23511 20.594 5.3289 1e-04 ***
## Residuals 67 0.35001 0.005224 0.76489
## Total 68 0.45759
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = coords ~ log(Csize), iter = 9999, turbo = FALSE,
## data = Y.gpa)plot(fit.alt, type = "regression",
reg.type = "RegScore",
predictor = Y.gpa$Csize)
4: Allometry
Here is a simple example of examining allometry:
data(pupfish)
plotAllSpecimens(pupfish$coords) #NOTE: already GPA-aligned
#Y.gpa <- gpagen(pupfish$coords, print.progress = FALSE) #GPA-alignment
pupfish$logSize <- log(pupfish$CS)
pupfish$Group <- interaction(pupfish$Pop, pupfish$Sex)
fit <- procD.lm(coords ~ logSize,
data = pupfish,
print.progress = FALSE)
anova(fit)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 1000
## Estimation method: Ordinary Least Squares
## Sums of Squares and Cross-products: Type I
## Effect sizes (Z) based on F distributions
##
## Df SS MS Rsq F Z Pr(>F)
## logSize 1 0.014019 0.0140193 0.24886 17.229 4.3462 0.001 ***
## Residuals 52 0.042314 0.0008137 0.75114
## Total 53 0.056333
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = coords ~ logSize, data = pupfish, print.progress = FALSE)plot(fit, type = "regression",
reg.type = "RegScore",
predictor = pupfish$logSize,
pch = 19)
#NOTE: Try also: reg.type = "PredLine"Comparing Allometric Trajectories
fit.common <- procD.lm(coords ~ logSize + Group,
data = pupfish, print.progress = FALSE)
fit.unique <- procD.lm(coords ~ logSize * Group,
data = pupfish, print.progress = FALSE)
anova(fit.unique)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 1000
## Estimation method: Ordinary Least Squares
## Sums of Squares and Cross-products: Type I
## Effect sizes (Z) based on F distributions
##
## Df SS MS Rsq F Z Pr(>F)
## logSize 1 0.014019 0.0140193 0.24886 29.2078 5.0041 0.001 ***
## Group 3 0.018230 0.0060766 0.32361 12.6601 6.4891 0.001 ***
## logSize:Group 3 0.002004 0.0006682 0.03558 1.3921 1.1451 0.136
## Residuals 46 0.022079 0.0004800 0.39194
## Total 53 0.056333
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = coords ~ logSize * Group, data = pupfish, print.progress = FALSE)par(mfcol = c(1, 2))
plot(fit.common, type = "regression",
predictor = pupfish$logSize,
reg.type = "PredLine",
pch=19,
col = pupfish$Group)
legend("topleft",
legend = unique(pupfish$Group),
pch = 21,
pt.bg = unique(pupfish$Group))
mtext("Common Slopes")
plot(fit.unique,
type = "regression",
predictor = pupfish$logSize,
reg.type = "PredLine",
pch=19,
col = pupfish$Group)
legend("topleft",
legend = unique(pupfish$Group),
pch = 21,
pt.bg = unique(pupfish$Group))
mtext("Unique Slopes")
par(mfcol = c(1, 1))Conclusion: Not much going on for this example (illustration purposes only).
5: Things to Explore on Your Own
- Remember Day 1 (read in your data, GPA, PCA, TPS)
- Perform GPA + sliders
- 3D data: Perform GPA with points, curves, surfaces, or some combination
- Perform PLS: visualize shapes along PLS
- Perform regression: visualize shapes along regression
- Generate shapes for small and large specimens in an allometry analysis
- Explore function options and output (there are many!)