rrcov (version 1.7-2)

pottery: Archaic Greek Pottery data

Description

The Archaic Greek Pottery data set contains data on fragments of Greek pottery which were classified into two groups according to their origin: Attic or Eritrean. Six chemical variables, metallic oxide constituents, were measured: Si, Al, Fe, Ca and Ti. The main data set consists of 13 Attic objects and 14 Eritrean ones. There is a separate data set with 13 observations which can be used as a test data set. It consists of 4 observations classified as "probably Attic" and the remaining 9 as "probably Eritrean".

Usage

data(pottery)

Format

Two data frames with 27 an 13 observations on the following 7 variables.

SI

Si content

AL

Al content

FE

Fe content

MG

Mg content

CA

Ca content

TI

Ti content

origin

Origin - factor with two levels: Attic and Eritrean

Details

The Archaic Greek Pottery data set was first published by Stern and Descoeudres (1977) and later reproduced in Cooper and Weeks (1983) for illustration of linear discriminant analisys. The data set was used by Pires and Branco (2010) for illustration of their projection pursuit approach to linear discriminant analysis.

References

Cooper, R.A. and Weekes, A.J.. 1983 Data, Models, and Statistical Analysis, (Lanham, MD: Rowman & Littlefield).

Pires, A. M. and A. Branco, J. (2010) Projection-pursuit approach to robust linear discriminant analysis Journal Multivariate Analysis, Academic Press, Inc., 101, 2464--2485.

Examples

data(pottery)
x <- pottery[,c("MG", "CA")]
grp <- pottery$origin

##
## Compute robust location and covariance matrix and
## plot the tolerance ellipses
library(rrcov)
(mcd <- CovMcd(x))
col <- c(3,4)
gcol <- ifelse(grp == "Attic", col[1], col[2])
gpch <- ifelse(grp == "Attic", 16, 1)
plot(mcd, which="tolEllipsePlot", class=TRUE, col=gcol, pch=gpch)

##
## Perform classical LDA and plot the data, 0.975 tolerance ellipses
##  and LDA separation line
##
x <- pottery[,c("MG", "CA")]
grp <- pottery$origin
lda <- LdaClassic(x, grp)
lda
e1 <- getEllipse(loc=lda@center[1,], cov=lda@cov)
e2 <- getEllipse(loc=lda@center[2,], cov=lda@cov)

plot(CA~MG, data=pottery, col=gcol, pch=gpch,
    xlim=c(min(MG,e1[,1], e2[,1]), max(MG,e1[,1], e2[,1])),
    ylim=c(min(CA,e1[,2], e2[,2]), max(CA,e1[,2], e2[,2])))

ab <- lda@ldf[1,] - lda@ldf[2,]
cc <- lda@ldfconst[1] - lda@ldfconst[2]
abline(a=-cc/ab[2], b=-ab[1]/ab[2], col=2, lwd=2)

lines(e1, type="l", col=col[1])
lines(e2, type="l", col=col[2])

##
## Perform robust (MCD) LDA and plot data, classical and
##  robust separation line
##
plot(CA~MG, data=pottery, col=gcol, pch=gpch)
lda <- LdaClassic(x, grp)
ab <- lda@ldf[1,] - lda@ldf[2,]
cc <- lda@ldfconst[1] - lda@ldfconst[2]
abline(a=-cc/ab[2], b=-ab[1]/ab[2], col=2, lwd=2)
abline(a=-cc/ab[2], b=-ab[1]/ab[2], col=4, lwd=2)

rlda <- Linda(x, grp, method="mcd")
rlda
ab <- rlda@ldf[1,] - rlda@ldf[2,]
cc <- rlda@ldfconst[1] - rlda@ldfconst[2]
abline(a=-cc/ab[2], b=-ab[1]/ab[2], col=2, lwd=2)