heplots (version 1.0-2)

Skulls: Egyptian Skulls

Description

Measurements made on Egyptian skulls from five epochs.

Usage

data("Skulls")

source

D. J. Hand, F. Daly, A. D. Lunn, K. J. McConway and E. Ostrowski (1994). A Handbook of Small Datasets, Chapman and Hall/CRC, London.

Details

The question is whether the measurements change over time. Non-constant measurements of the skulls over time would indicate interbreeding with immigrant populations. Note that using polynomial contrasts for epoch essentially treats the time points as equally spaced.

References

Thomson, A. and Randall-Maciver, R. (1905) Ancient Races of the Thebaid, Oxford: Oxford University Press. Egyptian Skull Development, StatLib Data and Story Library, http://lib.stat.cmu.edu/DASL/Stories/EgyptianSkullDevelopment.html

Examples

data(Skulls)
# make shorter labels for epochs
Skulls$epoch <- factor(Skulls$epoch, labels=sub("c","",levels(Skulls$epoch)))
# variable labels
vlab <- c("maxBreadth", "basibHeight", "basialLength", "nasalHeight")

# fit manova model
sk.mod <- lm(cbind(mb, bh, bl, nh) ~ epoch, data=Skulls)

Manova(sk.mod)
summary(Manova(sk.mod))

# test trends over epochs
linearHypothesis(sk.mod, "epoch.L") # linear component
linearHypothesis(sk.mod, "epoch.Q") # quadratic component

# typical scatterplots are not very informative
scatterplot(mb ~ bh|epoch, data=Skulls, ellipse=TRUE, levels=0.68, smooth=FALSE, legend.coords="topright")
scatterplot(mb ~ bl|epoch, data=Skulls, ellipse=TRUE, levels=0.68, smooth=FALSE, legend.coords="topright")

# HE plots

heplot(sk.mod, hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), xlab=vlab[1], ylab=vlab[2])
pairs(sk.mod, hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), var.labels=vlab)
# 3D plot shows that nearly all of hypothesis variation is linear!
heplot3d(sk.mod, hypotheses=list(Lin="epoch.L", Quad="epoch.Q"), col=c("pink", "blue"))

# view in canonical space
if (require(candisc)) {
	sk.can <- candisc(sk.mod)
	sk.can
	heplot(sk.can)
	heplot3d(sk.can)
}