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@@ -1,15 +1,65 @@ +#' Estimate a limit of quantification (LOQ) +#' +#' 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. +#' +#' @aliases loq loq.lm loq.rlm loq.default +#' @param 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. +#' @param alpha The error tolerance for the prediction of x values in the +#' calculation. +#' @param \dots Placeholder for further arguments that might be needed by +#' future implementations. +#' @param k The inverse of the maximum relative error tolerated at the desired +#' LOQ. +#' @param n The number of replicate measurements for which the LOQ should be +#' specified. +#' @param 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. +#' @param var.loq The approximate variance at the LOQ. The default value is +#' calculated from the model. +#' @param 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. +#' @return The estimated limit of quantification for a model used for +#' calibration. +#' @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. +#' @seealso Examples for \code{\link{din32645}} +#' @examples +#' +#' m <- lm(y ~ x, data = massart97ex1) +#' loq(m) +#' +#' # We can get better by using replicate measurements +#' loq(m, n = 3) +#' +#' @export loq <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto", var.loq = "auto", tol = "default") { UseMethod("loq") } +#' @export loq.default <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto", var.loq = "auto", tol = "default") { stop("loq is only implemented for univariate lm objects.") } +#' @export loq.lm <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto", var.loq = "auto", tol = "default") { |