logst: Started Logarithmic Transformation

In plgraphics: User Oriented Plotting Functions

Started Logarithmic Transformation

Description

Transforms the data by a log10 transformation, modifying small and zero observations such that the transformation yields finite values.

Usage

logst(data, calib=data, threshold=NULL, mult = 1)

Arguments

data	a vector or matrix of data, which is to be transformed
calib	a vector or matrix of data used to calibrate the transformation(s), i.e., to determine the constant c needed
threshold	constant c that determines the transformation, possibly a vector with a value for each variable.
mult	a tuning constant affecting the transformation of small values, see Details

Details

Small values are determined by the threshold c. If not given by the argument threshold, then it is determined by the quartiles q_1 and q_3 of the non-zero data as those smaller than c=q_1 / (q_3/q_1)^{mult}. The rationale is that for lognormal data, this constant identifies 2 percent of the data as small. Beyond this limit, the transformation continues linear with the derivative of the log curve at this point. See code for the formula.

The function chooses log10 rather than natural logs because they can be backtransformed relatively easily in the mind.

For more details, see the vignette "logst".

Value

the transformed data. The value c needed for the transformation is returned as attr(.,"threshold").

Note

The names of the function alludes to Tudey's idea of "started logs".

Author(s)

Werner A. Stahel, ETH Zurich

Examples

dd <- c(seq(0,1,0.1),5*10^rnorm(100,0,0.2))
dd <- sort(dd)
r.dl <- logst(dd)
attr(r.dl, "threshold")
cbind(data=dd, logst=r.dl, log10=log10(dd))[1:20,]
## logst and log10 coincide for data values
##   larger than the threshold 1.55
plot(dd, r.dl, type="l")
abline(v=attr(r.dl,"threshold"),lty=2)

## precipitation data
data(d.river)
## first 25 days, precipitation data is daily,
##   thus only first record per day
dd <- d.river[d.river$date<as.Date("2010-03-01"),][seq(1,3456,144),]
plmframes(1,3)
plyx(pr~date, data=dd, innerrange=FALSE, main="raw data")
plyx(logst(pr)~date, data=dd, innerrange=FALSE, main="logst data")
abline(h=log10(attr(logst(dd$pr),"threshold")),lty=3,col="blue")
## instead of transforming the data,
##   use a logst scale on the y axis
plyx(pr~date, data=dd, innerrange=FALSE, plscale=c(NA,"logst"),
main="logst scle")

## --------------------------------------------
##  example showing the effect of fixing the threshold
data(d.blast)

##  first 3 locations
dd <- d.blast[as.numeric(d.blast$location)<=3,]
y13 <- logst(dd$tremor)
plyx(y13~as.numeric(dd$location), data=dd,
  xlim=c(0,5), ylim=c(-0.2,NA), xlab="location", ylab="lg(tremor)")

## forth location
tremor4 <- d.blast$tremor[d.blast$location=="loc4"]

## transform tremor of location 4 alone
y4raw <- logst(tremor4)
plpoints(rep(4.3,47), y4raw, col="red")
abline(h=log10(attr(y4raw, "threshold")), lty=3, col="red")
## transform tremor of location 4 using threhold from locations 1-3
y4 <- logst(tremor4, threshold=attr(y13, "threshold"))
plpoints(rep(4,47), y4, col="blue")
abline(h=log10(attr(y13, "threshold")), lty=3, col="blue")

plgraphics documentation built on Aug. 28, 2025, 9:09 a.m.