rrcovHD (version 0.3-1)

kibler: 1985 Auto Imports Database

Description

The original data set kibler.orig consists of three types of entities: (a) the specification of an auto in terms of various characteristics, (b) its assigned insurance risk rating and (c) its normalized losses in use as compared to other cars.

The second rating corresponds to the degree to which the auto is more risky than its price indicates. Cars are initially assigned a risk factor symbol associated with its price. Then, if it is more risky (or less), this symbol is adjusted by moving it up (or down) the scale. Actuarians call this process "symboling". A value of +3 indicates that the auto is risky, -3 that it is probably pretty safe.

The third factor is the relative average loss payment per insured vehicle year. This value is normalized for all autos within a particular size classification (two-door small, station wagons, sports/speciality, etc...), and represents the average loss per car per year.

Usage

data(kibler)

Format

A data frame with 195 observations on the following 14 variables. The original data set (also available as kibler.orig) contains 205 cases and 26 variables of which 15 continuous, 1 integer and 10 nominal. The non-numeric variables and variables with many missing values were removed. Cases with missing values were removed too.

symboling

a numeric vector

wheel-base

a numeric vector

length

a numeric vector

width

a numeric vector

height

a numeric vector

curb-weight

a numeric vector

bore

a numeric vector

stroke

a numeric vector

compression-ratio

a numeric vector

horsepower

a numeric vector

peak-rpm

a numeric vector

city-mpg

a numeric vector

highway-mpg

a numeric vector

price

a numeric vector

Details

The original data set contains 205 cases and 26 variables of which 15 continuous, 1 integer and 10 nominal. The non-numeric variables and variables with many missing values were removed. Cases with missing values were removed too. Thus the data set remains with 195 cases and 14 variables.

References

Kibler, D., Aha, D.W. and Albert, M. (1989). Instance-based prediction of real-valued attributes. Computational Intelligence, Vo.l 5, 51-57.

Examples

data(kibler)
x.sd <- apply(kibler,2,sd)
xsd <- sweep(kibler, 2, x.sd, "/", check.margin = FALSE)
apply(xsd, 2, sd)

x.mad <- apply(kibler, 2, mad)
xmad <- sweep(kibler, 2, x.mad, "/", check.margin = FALSE)
apply(xmad, 2, mad)

x.qn <- apply(kibler, 2, Qn)
xqn <- sweep(kibler, 2, x.qn, "/", check.margin = FALSE)
apply(xqn, 2, Qn)


## Display the scree plot of the classical and robust PCA
screeplot(PcaClassic(xsd))
screeplot(PcaGrid(xqn))

#########################################
##
## DD-plots
##
if (FALSE) {
usr <- par(mfrow=c(2,2))
plot(SPcaGrid(xsd, lambda=0, method="sd", k=4), main="Standard PCA")    # standard
plot(SPcaGrid(xqn, lambda=0, method="Qn", k=4))                         # robust, non-sparse

plot(SPcaGrid(xqn, lambda=1,43, method="sd", k=4), main="Stdandard sparse PCA")  # sparse
plot(SPcaGrid(xqn, lambda=2.36, method="Qn", k=4), main="Robust sparse PCA")     # robust sparse
par(usr)

#########################################
##  Table 2 in Croux et al
##  - to compute EV=Explained variance and Cumulative EV we
##      need to get all 14 eigenvalues
##
rpca <- SPcaGrid(xqn, lambda=0, k=14)
srpca <- SPcaGrid(xqn, lambda=2.36, k=14)
tab <- cbind(round(getLoadings(rpca)[,1:4], 2), round(getLoadings(srpca)[,1:4], 2))

vars1 <- getEigenvalues(rpca);  vars1 <- vars1/sum(vars1)
vars2 <- getEigenvalues(srpca); vars2 <- vars2/sum(vars2)
cvars1 <- cumsum(vars1)
cvars2 <- cumsum(vars2)
ev <- round(c(vars1[1:4], vars2[1:4]),2)
cev <- round(c(cvars1[1:4], cvars2[1:4]),2)
rbind(tab, ev, cev)
}