\name{loq}
\alias{loq}
\alias{loq.lm}
\alias{loq.rlm}
\alias{loq.default}
\title{Estimate a limit of quantification (LOQ)}
\usage{
loq(object, \dots, alpha = 0.05, k = 3, n = 1, w = "auto")
}
\arguments{
\item{object}{
A univariate model object of class \code{\link{lm}} or
\code{\link[MASS:rlm]{rlm}}
with model formula \code{y ~ x} or \code{y ~ x - 1},
optionally from a weighted regression.
}
\item{alpha}{
The error tolerance for the prediction of x values in the calculation.
}
\item{\dots}{
Placeholder for further arguments that might be needed by
future implementations.
}
\item{k}{
The inverse of the maximum relative error tolerated at the
desired LOQ.
}
\item{n}{
The number of replicate measurements for which the LOQ should be
specified.
}
\item{w}{
The weight that should be attributed to the LOQ. Defaults
to one for unweighted regression, and to the mean of the weights
for weighted regression. See \code{\link{massart97ex3}} for
an example how to take advantage of knowledge about the
variance function.
}
}
\value{
The estimated limit of quantification for a model used for calibration.
}
\description{
A useful operationalisation of a limit of quantification is simply the
solution of the equation
\deqn{L = k c(L)}{L = k * c(L)}
where c(L) is half of the length of the confidence interval at the limit L as
estimated by \code{\link{inverse.predict}}. By virtue of this formula, the
limit of detection is the x value, where the relative error
of the quantification with the given calibration model is 1/k.
}
\note{
IUPAC recommends to base the LOQ on the standard deviation of the
signal where x = 0. The approach taken here is to my knowledge
original to the chemCal package.
}
\examples{
data(massart97ex3)
attach(massart97ex3)
m0 <- lm(y ~ x)
loq(m0)
# Now we use a weighted regression
yx <- split(y,factor(x))
s <- round(sapply(yx,sd),digits=2)
w <- round(1/(s^2),digits=3)
weights <- w[factor(x)]
mw <- lm(y ~ x,w=weights)
loq(mw)
# In order to define the weight at the loq, we can use
# the variance function 1/y for the model
mwy <- lm(y ~ x, w = 1/y)
# Let's do this with one iteration only
loq(mwy, w = 1 / predict(mwy,list(x = loq(mwy)$x)))
# We can get better by doing replicate measurements
loq(mwy, n = 3, w = 1 / predict(mwy,list(x = loq(mwy)$x)))
}
\keyword{manip}
