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\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.loq = "auto",
var.loq = "auto", tol = "default")
}
\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. If weights are specified
in the model, either \code{w.loq} or \code{var.loq} have to
be specified.
}
\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.loq}{
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.
}
\item{var.loq}{
The approximate variance at the LOQ. The default value is
calculated from the model.
}
\item{tol}{
The default tolerance for the LOQ on the x scale is the value of the
smallest non-zero standard divided by 1000. Can be set to a
numeric value to override this.
}
}
\value{
The estimated limit of quantification for a model used for calibration.
}
\description{
The limit of quantification is the x value, where the relative error
of the quantification given the calibration model reaches a prespecified
value 1/k. Thus, it is 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
(DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by
\code{\link{inverse.predict}}, and L is obtained by iteration.
}
\note{
- IUPAC recommends to base the LOQ on the standard deviation of the signal
where x = 0.
- The calculation of a LOQ based on weighted regression is non-standard
and therefore not tested. Feedback is welcome.
}
\examples{
data(massart97ex3)
attach(massart97ex3)
m <- lm(y ~ x)
loq(m)
# We can get better by using replicate measurements
loq(m, n = 3)
}
\seealso{
Examples for \code{\link{din32645}}
}
\keyword{manip}
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