% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/loq.R
\name{loq}
\alias{loq}
\alias{loq.lm}
\alias{loq.rlm}
\alias{loq.default}
\title{Estimate a limit of quantification (LOQ)}
\usage{
loq(
  object,
  ...,
  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{\dots}{Placeholder for further arguments that might be needed by
future implementations.}

\item{alpha}{The error tolerance for the prediction of x values in the
calculation.}

\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{
\itemize{
\item IUPAC recommends to base the LOQ on the standard deviation of the
signal where x = 0.
\item The calculation of a LOQ based on weighted regression is non-standard and
therefore not tested. Feedback is welcome.
}
}
\examples{

m <- lm(y ~ x, data = massart97ex1)
loq(m)

# We can get better by using replicate measurements
loq(m, n = 3)

}
\seealso{
Examples for \code{\link{din32645}}
}