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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 = "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.
+}
+\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))))
+
+  # We can get better by doing replicate measurements
+  loq(mwy, n = 3, w = 1 / predict(mwy,list(x = loq(mwy))))
+}
+\keyword{manip}