Salinity Data

Description

This is a data set consisting of measurements of water salinity (i.e., its salt concentration) and river discharge taken in North Carolina's Pamlico Sound, recording some bi-weekly averages in March, April, and May from 1972 to 1977. This dataset was listed by Ruppert and Carroll (1980). In Carrol and Ruppert (1985) the physical background of the data is described. They indicated that observations 5 and 16 correspond to periods of very heavy discharge and showed that the discrepant observation 5 was masked by observations 3 and 16, i.e., only after deletion of these observations it was possible to identify the influential observation 5.

This data set is a prime example of the masking effect.

Usage

data(salinity)

Format

A data frame with 28 observations on the following 4 variables (in parentheses are the names used in the 1980 reference).

X1:

Lagged Salinity (‘SALLAG’)

X2:

Trend (‘TREND’)

X3:

Discharge (‘H2OFLOW’)

Y:

Salinity (‘SALINITY’)

Note

The boot package contains another version of this salinity data set, also attributed to Ruppert and Carroll (1980), but with two clear transcription errors, see the examples.

Source

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection; Wiley, p.82, table 5.

Ruppert, D. and Carroll, R.J. (1980) Trimmed least squares estimation in the linear model. JASA 75, 828–838; table 3, p.835.

Carroll, R.J. and Ruppert, D. (1985) Transformations in regression: A robust analysis. Technometrics 27, 1–12

Examples

data(salinity)
summary(lm.sali  <-        lm(Y ~ . , data = salinity))
summary(rlm.sali <- MASS::rlm(Y ~ . , data = salinity))
summary(lts.sali <-    ltsReg(Y ~ . , data = salinity))

salinity.x <- data.matrix(salinity[, 1:3])
c_sal <- covMcd(salinity.x)
plot(c_sal, "tolEllipsePlot")

## Connection with boot package's version :
if(requireNamespace("boot")) { ## 'always'
 print( head(boot.sal <- boot::salinity        ) )
 print( head(robb.sal <- salinity [, c(4, 1:3)]) ) # difference: has one digit more
 ## Otherwise the same ?
 dimnames(robb.sal) <- dimnames(boot.sal)
 ## apart from the 4th column, they are "identical":
 stopifnot( all.equal(boot.sal[, -4], robb.sal[, -4], tol = 1e-15) )

 ## But the discharge ('X3', 'dis' or 'H2OFLOW')  __differs__ in two places:
 plot(cbind(robustbase = robb.sal[,4], boot = boot.sal[,4]))
 abline(0,1, lwd=3, col=adjustcolor("red", 1/4))
 D.sal <- robb.sal[,4] - boot.sal[,4]
 stem(robb.sal[,4] - boot.sal[,4])
 which(abs(D.sal) > 0.01) ## 2 8
 ## *two* typos (=> difference ~= 1) in the version of 'boot': obs. 2 & 8 !!!
 cbind(robb = robb.sal[,4], boot = boot.sal[,4], D.sal)
}# boot