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-rw-r--r--trunk/DESCRIPTION19
-rw-r--r--trunk/INDEX9
-rw-r--r--trunk/R/calfunctions.R2
-rw-r--r--trunk/R/calplot.R80
-rw-r--r--trunk/R/inverse.predict.lm.R115
-rw-r--r--trunk/R/lod.R53
-rw-r--r--trunk/R/loq.R40
-rw-r--r--trunk/TODO5
-rw-r--r--trunk/data/din32645.rdabin0 -> 453 bytes
-rw-r--r--trunk/data/massart97ex1.rdabin0 -> 193 bytes
-rw-r--r--trunk/data/massart97ex3.rdabin0 -> 296 bytes
-rw-r--r--trunk/inst/doc/Makefile33
-rw-r--r--trunk/inst/doc/Rplots.ps1970
-rw-r--r--trunk/inst/doc/chemCal-001.eps1762
-rw-r--r--trunk/inst/doc/chemCal-001.pdf1727
-rw-r--r--trunk/inst/doc/chemCal-002.eps288
-rw-r--r--trunk/inst/doc/chemCal-002.pdf275
-rw-r--r--trunk/inst/doc/chemCal.Rnw162
-rw-r--r--trunk/inst/doc/chemCal.aux18
-rw-r--r--trunk/inst/doc/chemCal.bbl0
-rw-r--r--trunk/inst/doc/chemCal.blg46
-rw-r--r--trunk/inst/doc/chemCal.log362
-rw-r--r--trunk/inst/doc/chemCal.out0
-rw-r--r--trunk/inst/doc/chemCal.pdfbin0 -> 123694 bytes
-rw-r--r--trunk/inst/doc/chemCal.tex169
-rw-r--r--trunk/man/calplot.lm.Rd62
-rw-r--r--trunk/man/chemCal-package.Rd17
-rw-r--r--trunk/man/din32645.Rd61
-rw-r--r--trunk/man/inverse.predict.Rd69
-rw-r--r--trunk/man/ipowfunc.Rd33
-rw-r--r--trunk/man/lod.Rd83
-rw-r--r--trunk/man/loq.Rd77
-rw-r--r--trunk/man/massart97ex1.Rd17
-rw-r--r--trunk/man/massart97ex3.Rd51
-rw-r--r--trunk/man/powfunc.Rd32
-rw-r--r--trunk/tests/din32645.R7
-rw-r--r--trunk/tests/din32645.Rout.save45
-rw-r--r--trunk/tests/massart97.R25
-rw-r--r--trunk/tests/massart97.Rout.save123
39 files changed, 7837 insertions, 0 deletions
diff --git a/trunk/DESCRIPTION b/trunk/DESCRIPTION
new file mode 100644
index 0000000..b2eee68
--- /dev/null
+++ b/trunk/DESCRIPTION
@@ -0,0 +1,19 @@
+Package: chemCal
+Version: 0.1-21
+Date: 2007-03-23
+Title: Calibration functions for analytical chemistry
+Author: Johannes Ranke <jranke@uni-bremen.de>
+Maintainer: Johannes Ranke <jranke@uni-bremen.de>
+Depends: R (>= 2.4.0)
+Suggests: MASS
+Description: chemCal provides simple functions for plotting linear
+ calibration functions and estimating standard errors for measurements
+ according to the Handbook of Chemometrics and Qualimetrics: Part A
+ by Massart et al. There are also functions estimating the limit
+ of detection (LOQ) and limit of quantification (LOD).
+ The functions work on model objects from - optionally weighted - linear
+ regression (lm) or robust linear regression (rlm from the MASS package).
+License: GPL version 2 or newer
+URL: http://www.r-project.org,
+ http://www.uft.uni-bremen.de/chemie/ranke/?page=chemCal,
+ http://kriemhild.uft.uni-bremen.de/viewcvs/?root=chemCal
diff --git a/trunk/INDEX b/trunk/INDEX
new file mode 100644
index 0000000..f880eb6
--- /dev/null
+++ b/trunk/INDEX
@@ -0,0 +1,9 @@
+calplot Plot calibration graphs from univariate linear
+ models
+chemCal-package Calibration functions for analytical chemistry
+din32645 Calibration data from DIN 32645
+inverse.predict Predict x from y for a linear calibration
+lod Estimate a limit of detection (LOD)
+loq Estimate a limit of quantification (LOQ)
+massart97ex3 Calibration data from Massart et al. (1997),
+ example 3
diff --git a/trunk/R/calfunctions.R b/trunk/R/calfunctions.R
new file mode 100644
index 0000000..6ce29f7
--- /dev/null
+++ b/trunk/R/calfunctions.R
@@ -0,0 +1,2 @@
+powfunc <- function(x,a,b) a * x^b
+ipowfunc <- function(y,a,b) (y/a)^1/b
diff --git a/trunk/R/calplot.R b/trunk/R/calplot.R
new file mode 100644
index 0000000..6aed9c0
--- /dev/null
+++ b/trunk/R/calplot.R
@@ -0,0 +1,80 @@
+calplot <- function(object,
+ xlim = c("auto", "auto"), ylim = c("auto", "auto"),
+ xlab = "Concentration", ylab = "Response", alpha = 0.05,
+ varfunc = NULL)
+{
+ UseMethod("calplot")
+}
+
+calplot.default <- function(object,
+ xlim = c("auto","auto"), ylim = c("auto","auto"),
+ xlab = "Concentration", ylab = "Response",
+ alpha=0.05, varfunc = NULL)
+{
+ stop("Calibration plots only implemented for univariate lm objects.")
+}
+
+calplot.lm <- function(object,
+ xlim = c("auto","auto"), ylim = c("auto","auto"),
+ xlab = "Concentration", ylab = "Response", alpha=0.05,
+ varfunc = NULL)
+{
+ if (length(object$coef) > 2)
+ stop("More than one independent variable in your model - not implemented")
+
+ if (alpha <= 0 | alpha >= 1)
+ stop("Alpha should be between 0 and 1 (exclusive)")
+
+ m <- object
+ level <- 1 - alpha
+ y <- m$model[[1]]
+ x <- m$model[[2]]
+ if (xlim[1] == "auto") xlim[1] <- 0
+ if (xlim[2] == "auto") xlim[2] <- max(x)
+ xlim <- as.numeric(xlim)
+ newdata <- list(
+ x = seq(from = xlim[[1]], to = xlim[[2]], length=250))
+ names(newdata) <- names(m$model)[[2]]
+ if (is.null(varfunc)) {
+ varfunc <- if (length(m$weights)) {
+ function(variable) mean(m$weights)
+ } else function(variable) rep(1,250)
+ }
+ pred.lim <- predict(m, newdata, interval = "prediction",
+ level=level, weights.newdata = varfunc(m))
+ conf.lim <- predict(m, newdata, interval = "confidence",
+ level=level)
+ yrange.auto <- range(c(0,pred.lim))
+ if (ylim[1] == "auto") ylim[1] <- yrange.auto[1]
+ if (ylim[2] == "auto") ylim[2] <- yrange.auto[2]
+ plot(1,
+ type = "n",
+ xlab = xlab,
+ ylab = ylab,
+ xlim = as.numeric(xlim),
+ ylim = as.numeric(ylim)
+ )
+ points(x,y, pch = 21, bg = "yellow")
+ matlines(newdata[[1]], pred.lim, lty = c(1, 4, 4),
+ col = c("black", "red", "red"))
+ if (length(object$weights) > 0) {
+ legend(min(x),
+ max(pred.lim, na.rm = TRUE),
+ legend = c("Fitted Line", "Confidence Bands"),
+ lty = c(1, 3),
+ lwd = 2,
+ col = c("black", "green4"),
+ horiz = FALSE, cex = 0.9, bg = "gray95")
+ } else {
+ matlines(newdata[[1]], conf.lim, lty = c(1, 3, 3),
+ col = c("black", "green4", "green4"))
+ legend(min(x),
+ max(pred.lim, na.rm = TRUE),
+ legend = c("Fitted Line", "Confidence Bands",
+ "Prediction Bands"),
+ lty = c(1, 3, 4),
+ lwd = 2,
+ col = c("black", "green4", "red"),
+ horiz = FALSE, cex = 0.9, bg = "gray95")
+ }
+}
diff --git a/trunk/R/inverse.predict.lm.R b/trunk/R/inverse.predict.lm.R
new file mode 100644
index 0000000..d57275c
--- /dev/null
+++ b/trunk/R/inverse.predict.lm.R
@@ -0,0 +1,115 @@
+# This is an implementation of Equation (8.28) in the Handbook of Chemometrics
+# and Qualimetrics, Part A, Massart et al (1997), page 200, validated with
+# Example 8 on the same page, extended as specified in the package vignette
+
+inverse.predict <- function(object, newdata, ...,
+ ws = "auto", alpha = 0.05, var.s = "auto")
+{
+ UseMethod("inverse.predict")
+}
+
+inverse.predict.default <- function(object, newdata, ...,
+ ws = "auto", alpha = 0.05, var.s = "auto")
+{
+ stop("Inverse prediction only implemented for univariate lm and nls objects.")
+}
+
+inverse.predict.lm <- function(object, newdata, ...,
+ ws = "auto", alpha = 0.05, var.s = "auto")
+{
+ yname = names(object$model)[[1]]
+ xname = names(object$model)[[2]]
+ if (ws == "auto") {
+ ws <- ifelse(length(object$weights) > 0, mean(object$weights), 1)
+ }
+ if (length(object$weights) > 0) {
+ wx <- split(object$weights,object$model[[xname]])
+ w <- sapply(wx,mean)
+ } else {
+ w <- rep(1,length(split(object$model[[yname]],object$model[[xname]])))
+ }
+ .inverse.predict(object = object, newdata = newdata,
+ ws = ws, alpha = alpha, var.s = var.s, w = w, xname = xname, yname = yname)
+}
+
+inverse.predict.rlm <- function(object, newdata, ...,
+ ws = "auto", alpha = 0.05, var.s = "auto")
+{
+ yname = names(object$model)[[1]]
+ xname = names(object$model)[[2]]
+ if (ws == "auto") {
+ ws <- mean(object$w)
+ }
+ wx <- split(object$weights,object$model[[xname]])
+ w <- sapply(wx,mean)
+ .inverse.predict(object = object, newdata = newdata,
+ ws = ws, alpha = alpha, var.s = var.s, w = w, xname = xname, yname = yname)
+}
+
+inverse.predict.nls <- function(object, newdata, ...,
+ ws = "auto", alpha = 0.05, var.s = "auto")
+{
+ yname = names(object$model)[[1]]
+ xname = names(object$model)[[2]]
+ if (ws == "auto") {
+ ws <- ifelse(length(object$weights) > 0, mean(object$weights), 1)
+ }
+ if (length(object$weights) > 0) {
+ wx <- split(object$weights,object$model[[xname]])
+ w <- sapply(wx,mean)
+ } else {
+ w <- rep(1,length(split(object$model[[yname]],object$model[[xname]])))
+ }
+ if (length(object$coef) > 2)
+ stop("More than one independent variable in your model - not implemented")
+}
+
+.inverse.predict <- function(object, newdata, ws, alpha, var.s, w, xname, yname)
+{
+ if (length(object$coef) > 2)
+ stop("More than one independent variable in your model - not implemented")
+
+ if (alpha <= 0 | alpha >= 1)
+ stop("Alpha should be between 0 and 1 (exclusive)")
+
+ ybars <- mean(newdata)
+ m <- length(newdata)
+
+ yx <- split(object$model[[yname]], object$model[[xname]])
+ n <- length(yx)
+ df <- n - length(object$coef)
+ x <- as.numeric(names(yx))
+ ybar <- sapply(yx,mean)
+ yhatx <- split(object$fitted.values, object$model[[xname]])
+ yhat <- sapply(yhatx, mean)
+ se <- sqrt(sum(w * (ybar - yhat)^2)/df)
+
+ if (var.s == "auto") {
+ var.s <- se^2/ws
+ }
+
+ b1 <- object$coef[[xname]]
+
+ ybarw <- sum(w * ybar)/sum(w)
+
+# This is the adapted form of equation 8.28 (see package vignette)
+ sxhats <- 1/b1 * sqrt(
+ (var.s / m) +
+ se^2 * (1/sum(w) +
+ (ybars - ybarw)^2 * sum(w) /
+ (b1^2 * (sum(w) * sum(w * x^2) - sum(w * x)^2)))
+ )
+
+ if (names(object$coef)[1] == "(Intercept)") {
+ b0 <- object$coef[["(Intercept)"]]
+ } else {
+ b0 <- 0
+ }
+
+ xs <- (ybars - b0) / b1
+ t <- qt(1-0.5*alpha, n - 2)
+ conf <- t * sxhats
+ result <- list("Prediction"=xs,"Standard Error"=sxhats,
+ "Confidence"=conf, "Confidence Limits"=c(xs - conf, xs + conf))
+ return(result)
+}
diff --git a/trunk/R/lod.R b/trunk/R/lod.R
new file mode 100644
index 0000000..f5bbb7d
--- /dev/null
+++ b/trunk/R/lod.R
@@ -0,0 +1,53 @@
+lod <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default")
+{
+ UseMethod("lod")
+}
+
+lod.default <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default")
+{
+ stop("lod is only implemented for univariate lm objects.")
+}
+
+lod.lm <- function(object, ..., alpha = 0.05, beta = 0.05, method = "default")
+{
+ if (length(object$weights) > 0) {
+ stop(paste(
+ "\nThe detemination of a lod from calibration models obtained by",
+ "weighted linear regression requires confidence intervals for",
+ "predicted y values taking into account weights for the x values",
+ "from which the predictions are to be generated.",
+ "This is not supported by the internally used predict.lm method.",
+ sep = "\n"
+ ))
+ }
+ xname <- names(object$model)[[2]]
+ yname <- names(object$model)[[1]]
+ newdata <- data.frame(0)
+ names(newdata) <- xname
+ y0 <- predict(object, newdata, interval = "prediction",
+ level = 1 - 2 * alpha)
+ yc <- y0[[1,"upr"]]
+ if (method == "din") {
+ y0.d <- predict(object, newdata, interval = "prediction",
+ level = 1 - 2 * beta)
+ deltay <- y0.d[[1, "upr"]] - y0.d[[1, "fit"]]
+ lod.y <- yc + deltay
+ lod.x <- inverse.predict(object, lod.y)$Prediction
+ } else {
+ f <- function(x) {
+ newdata <- data.frame(x)
+ names(newdata) <- xname
+ pi.y <- predict(object, newdata, interval = "prediction",
+ level = 1 - 2 * beta)
+ yd <- pi.y[[1,"lwr"]]
+ (yd - yc)^2
+ }
+ lod.x <- optimize(f,interval=c(0,max(object$model[[xname]])))$minimum
+ newdata <- data.frame(x = lod.x)
+ names(newdata) <- xname
+ lod.y <- predict(object, newdata)
+ }
+ lod <- list(lod.x, lod.y)
+ names(lod) <- c(xname, yname)
+ return(lod)
+}
diff --git a/trunk/R/loq.R b/trunk/R/loq.R
new file mode 100644
index 0000000..5776096
--- /dev/null
+++ b/trunk/R/loq.R
@@ -0,0 +1,40 @@
+loq <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
+ var.loq = "auto")
+{
+ UseMethod("loq")
+}
+
+loq.default <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
+ var.loq = "auto")
+{
+ stop("loq is only implemented for univariate lm objects.")
+}
+
+loq.lm <- function(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
+ var.loq = "auto")
+{
+ if (length(object$weights) > 0 && var.loq == "auto" && w.loq == "auto") {
+ stop(paste("If you are using a model from weighted regression,",
+ "you need to specify a reasonable approximation for the",
+ "weight (w.loq) or the variance (var.loq) at the",
+ "limit of quantification"))
+ }
+ xname <- names(object$model)[[2]]
+ yname <- names(object$model)[[1]]
+ f <- function(x) {
+ newdata <- data.frame(x = x)
+ names(newdata) <- xname
+ y <- predict(object, newdata)
+ p <- inverse.predict(object, rep(y, n), ws = w.loq,
+ var.s = var.loq, alpha = alpha)
+ (p[["Prediction"]] - k * p[["Confidence"]])^2
+ }
+ tmp <- optimize(f,interval=c(0,max(object$model[[2]])))
+ loq.x <- tmp$minimum
+ newdata <- data.frame(x = loq.x)
+ names(newdata) <- xname
+ loq.y <- predict(object, newdata)
+ loq <- list(loq.x, loq.y)
+ names(loq) <- c(xname, yname)
+ return(loq)
+}
diff --git a/trunk/TODO b/trunk/TODO
new file mode 100644
index 0000000..1fc44a7
--- /dev/null
+++ b/trunk/TODO
@@ -0,0 +1,5 @@
+- lod(): At the moment, it is not possible to calculate an lod for the
+ case of more than one replicates (m is fixed to 1). The formula
+ for the prediction of y from mean(x) in Massart et al, p. 433
+ could be used to generalize this.
+- Write methods for nonlinear calibration functions
diff --git a/trunk/data/din32645.rda b/trunk/data/din32645.rda
new file mode 100644
index 0000000..4e2913a
--- /dev/null
+++ b/trunk/data/din32645.rda
Binary files differ
diff --git a/trunk/data/massart97ex1.rda b/trunk/data/massart97ex1.rda
new file mode 100644
index 0000000..1a6fd4b
--- /dev/null
+++ b/trunk/data/massart97ex1.rda
Binary files differ
diff --git a/trunk/data/massart97ex3.rda b/trunk/data/massart97ex3.rda
new file mode 100644
index 0000000..7f60f3a
--- /dev/null
+++ b/trunk/data/massart97ex3.rda
Binary files differ
diff --git a/trunk/inst/doc/Makefile b/trunk/inst/doc/Makefile
new file mode 100644
index 0000000..8eca69e
--- /dev/null
+++ b/trunk/inst/doc/Makefile
@@ -0,0 +1,33 @@
+# Makefile for Sweave documents containing both Latex and R code
+# Author: Johannes Ranke <jranke@uni-bremen.de>
+# Last Change: 2006 Jun 23
+# based on the Makefile of Nicholas Lewin-Koh
+# in turn based on work of Rouben Rostmaian
+# SVN: $Id: Makefile.rnoweb 62 2006-05-24 08:30:59Z ranke $
+
+RNWFILES = $(wildcard *.Rnw)
+TARGETS = $(patsubst %.Rnw,%.tex,$(RNWFILE)) $(patsubst %.Rnw,%.pdf,$(RNWFILES))
+
+RERUN = "(There were undefined references|Rerun to get (cross-references|the bars) right|Table widths have changed. Rerun LaTeX.|Linenumber reference failed)"
+RERUNBIB = "No file.*\.bbl|Citation.*undefined"
+
+%.tex: %.Rnw
+ echo 'Sweave("$<")' | R --no-save --no-restore
+
+%.pdf: %.tex
+ pdflatex $<
+ egrep -c $(RERUNBIB) $*.log && (bibtex $*;pdflatex $<); true
+ egrep $(RERUN) $*.log && (pdflatex $<) ; true
+ egrep $(RERUN) $*.log && (pdflatex $<) ; true
+
+all: all-recursive $(TARGETS)
+
+clean: clean-recursive
+ rm -f *.aux *.log *.bbl *.blg *.brf *.cb *.ind *.idx *.ilg \
+ *.inx *.ps *.dvi *.toc *.out *.lot *~ *.lof *.ttt *.fff
+
+all-recursive:
+ for dir in $(wildcard *); do if [ -d $$dir ] && [ -f $$dir/Makefile ]; then cd $$dir; $(MAKE) all; cd ..; fi; done
+
+clean-recursive:
+ for dir in $(wildcard *); do if [ -d $$dir ] && [ -f $$dir/Makefile ]; then cd $$dir; $(MAKE) clean; cd ..; fi; done
diff --git a/trunk/inst/doc/Rplots.ps b/trunk/inst/doc/Rplots.ps
new file mode 100644
index 0000000..c5e68ec
--- /dev/null
+++ b/trunk/inst/doc/Rplots.ps
@@ -0,0 +1,1970 @@
+%!PS-Adobe-3.0
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diff --git a/trunk/inst/doc/chemCal.Rnw b/trunk/inst/doc/chemCal.Rnw
new file mode 100644
index 0000000..956c664
--- /dev/null
+++ b/trunk/inst/doc/chemCal.Rnw
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+\documentclass[a4paper]{article}
+%\VignetteIndexEntry{Short manual for the chemCal package}
+\usepackage{hyperref}
+
+\title{Basic calibration functions for analytical chemistry}
+\author{Johannes Ranke}
+
+\begin{document}
+\maketitle
+
+The \texttt{chemCal} package was first designed in the course of a lecture and lab
+course on "analytics of organic trace contaminants" at the University of Bremen
+from October to December 2004. In the fall 2005, an email exchange with
+Ron Wehrens led to the belief that it would be desirable to implement the
+inverse prediction method given in \cite{massart97} since it also covers the
+case of weighted regression. Studies of the IUPAC orange book and of DIN 32645
+as well as publications by Currie and the Analytical Method Committee of the
+Royal Society of Chemistry and a nice paper by Castillo and Castells provided
+further understanding of the matter.
+
+At the moment, the package consists of four functions, working on univariate
+linear models of class \texttt{lm} or \texttt{rlm}, plus to datasets for
+validation.
+
+A \href{http://bugs.r-project.org/cgi-bin/R/wishlst-fulfilled?id=8877;user=guest}{bug
+report (PR\#8877)} and the following e-mail exchange on the r-devel mailing list about
+prediction intervals from weighted regression entailed some further studies
+on this subject. However, I did not encounter any proof or explanation of the
+formula cited below yet, so I can't really confirm that Massart's method is correct.
+
+When calibrating an analytical method, the first task is to generate a suitable
+model. If we want to use the \texttt{chemCal} functions, we will have to
+restrict ourselves to univariate, possibly weighted, linear regression so far.
+
+Once such a model has been created, the calibration can be graphically
+shown by using the \texttt{calplot} function:
+
+<<echo=TRUE,fig=TRUE>>=
+library(chemCal)
+data(massart97ex3)
+m0 <- lm(y ~ x, data = massart97ex3)
+calplot(m0)
+@
+
+As we can see, the scatter increases with increasing x. This is also
+illustrated by one of the diagnostic plots for linear models
+provided by R:
+
+<<echo=TRUE,fig=TRUE>>=
+plot(m0,which=3)
+@
+
+Therefore, in Example 8 in \cite{massart97} weighted regression
+is proposed which can be reproduced by
+
+<<>>=
+attach(massart97ex3)
+yx <- split(y, x)
+ybar <- sapply(yx, mean)
+s <- round(sapply(yx, sd), digits = 2)
+w <- round(1 / (s^2), digits = 3)
+weights <- w[factor(x)]
+m <- lm(y ~ x, w = weights)
+@
+
+If we now want to predict a new x value from measured y values,
+we use the \texttt{inverse.predict} function:
+
+<<>>=
+inverse.predict(m, 15, ws=1.67)
+inverse.predict(m, 90, ws = 0.145)
+@
+
+The weight \texttt{ws} assigned to the measured y value has to be
+given by the user in the case of weighted regression, or alternatively,
+the approximate variance \texttt{var.s} at this location.
+
+\section*{Theory for \texttt{inverse.predict}}
+Equation 8.28 in \cite{massart97} gives a general equation for predicting the
+standard error $s_{\hat{x_s}}$ for an x value predicted from measurements of y
+according to the linear calibration function $ y = b_0 + b_1 \cdot x$:
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} +
+ \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+ {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} -
+ {\left( \sum{ w_i x_i } \right)}^2 \right) }}
+\end{equation}
+
+with
+
+\begin{equation}
+s_e = \sqrt{ \frac{\sum w_i (y_i - \hat{y_i})^2}{n - 2}}
+\end{equation}
+
+where $w_i$ is the weight for calibration standard $i$, $y_i$ is the mean $y$
+value (!) observed for standard $i$, $\hat{y_i}$ is the estimated value for
+standard $i$, $n$ is the number calibration standards, $w_s$ is the weight
+attributed to the sample $s$, $m$ is the number of replicate measurements of
+sample $s$, $\bar{y_s}$ is the mean response for the sample,
+$\bar{y_w} = \frac{\sum{w_i y_i}}{\sum{w_i}}$ is the weighted mean of responses
+$y_i$, and $x_i$ is the given $x$ value for standard $i$.
+
+The weight $w_s$ for the sample should be estimated or calculated in accordance
+to the weights used in the linear regression.
+
+I adjusted the above equation in order to be able to take a different
+precisions in standards and samples into account. In analogy to Equation 8.26
+from \cite{massart97} we get
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
+ {s_e}^2 \left( \frac{1}{\sum{w_i}} +
+ \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+ {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
+\end{equation}
+
+where I interpret $\frac{{s_s}^2}{w_s}$ as an estimator of the variance at location
+$\hat{x_s}$, which can be replaced by a user-specified value using the argument
+\texttt{var.s} of the function \texttt{inverse.predict}.
+
+\section*{Fitting and using a variance function}
+
+In the R package \texttt{nlme} variance functions are used for weighted
+regressions. But since the \texttt{predict.nlme} method does not calculate
+prediction intervals, this is not useful for the \texttt{calplot} function.
+
+Two approaches could be used for fitting variance functions, one based on
+residuals from an unweighted fit, and one based on just the variances
+of the different samples along the x axis. If we used the residuals for
+fitting, a bias of the model in a certain area would result in a higher
+variance, so it seems preferable to choose the second approach. Of course,
+a prerequisite is to have sufficient repetitions for each sample in any
+case.
+
+Let's take the above example and estimate a variance function
+
+<<>>=
+massart97ex3
+massart97ex3$x <- factor(massart97ex3$x)
+summary <- summaryBy(y~x, data = massart97ex3,FUN=c(mean,sd,var))
+summary$x <- as.numeric(as.vector((summary$x)))
+plot(summary$x, summary$y.var,
+ xlim=c(0,50),
+ ylim=c(0,max(summary$y.var)))
+varModel <- lm(y.var ~ I(x^2) + x, data=summary)
+varCurve <- predict(varModel, newdata=data.frame(x=0:5000/100))
+lines(0:5000/100,varCurve)
+
+
+
+
+
+\begin{thebibliography}{1}
+\bibitem{massart97}
+Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+Smeyers-Verbeke, J.
+\newblock Handbook of Chemometrics and Qualimetrics: Part A,
+\newblock Elsevier, Amsterdam, 1997
+\end{thebibliography}
+
+\end{document}
diff --git a/trunk/inst/doc/chemCal.aux b/trunk/inst/doc/chemCal.aux
new file mode 100644
index 0000000..20bfc98
--- /dev/null
+++ b/trunk/inst/doc/chemCal.aux
@@ -0,0 +1,18 @@
+\relax
+\ifx\hyper@anchor\@undefined
+\global \let \oldcontentsline\contentsline
+\gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
+\global \let \oldnewlabel\newlabel
+\gdef \newlabel#1#2{\newlabelxx{#1}#2}
+\gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
+\AtEndDocument{\let \contentsline\oldcontentsline
+\let \newlabel\oldnewlabel}
+\else
+\global \let \hyper@last\relax
+\fi
+
+\citation{massart97}
+\citation{massart97}
+\citation{massart97}
+\citation{massart97}
+\bibcite{massart97}{1}
diff --git a/trunk/inst/doc/chemCal.bbl b/trunk/inst/doc/chemCal.bbl
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+\documentclass[a4paper]{article}
+%\VignetteIndexEntry{Short manual for the chemCal package}
+\usepackage{hyperref}
+
+\title{Basic calibration functions for analytical chemistry}
+\author{Johannes Ranke}
+
+\usepackage{/usr/share/R/share/texmf/Sweave}
+\begin{document}
+\maketitle
+
+The \texttt{chemCal} package was first designed in the course of a lecture and lab
+course on "analytics of organic trace contaminants" at the University of Bremen
+from October to December 2004. In the fall 2005, an email exchange with
+Ron Wehrens led to the belief that it would be desirable to implement the
+inverse prediction method given in \cite{massart97} since it also covers the
+case of weighted regression. Studies of the IUPAC orange book and of DIN 32645
+as well as publications by Currie and the Analytical Method Committee of the
+Royal Society of Chemistry and a nice paper by Castillo and Castells provided
+further understanding of the matter.
+
+At the moment, the package consists of four functions, working on univariate
+linear models of class \texttt{lm} or \texttt{rlm}, plus to datasets for
+validation.
+
+A \href{http://bugs.r-project.org/cgi-bin/R/wishlst-fulfilled?id=8877;user=guest}{bug
+report (PR\#8877)} and the following e-mail exchange on the r-devel mailing list about
+prediction intervals from weighted regression entailed some further studies
+on this subject. However, I did not encounter any proof or explanation of the
+formula cited below yet, so I can't really confirm that Massart's method is correct.
+
+When calibrating an analytical method, the first task is to generate a suitable
+model. If we want to use the \texttt{chemCal} functions, we will have to restrict
+ourselves to univariate, possibly weighted, linear regression so far.
+
+Once such a model has been created, the calibration can be graphically
+shown by using the \texttt{calplot} function:
+
+\begin{Schunk}
+\begin{Sinput}
+> library(chemCal)
+> data(massart97ex3)
+> m0 <- lm(y ~ x, data = massart97ex3)
+> calplot(m0)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{chemCal-001}
+
+As we can see, the scatter increases with increasing x. This is also
+illustrated by one of the diagnostic plots for linear models
+provided by R:
+
+\begin{Schunk}
+\begin{Sinput}
+> plot(m0, which = 3)
+\end{Sinput}
+\end{Schunk}
+\includegraphics{chemCal-002}
+
+Therefore, in Example 8 in \cite{massart97} weighted regression
+is proposed which can be reproduced by
+
+\begin{Schunk}
+\begin{Sinput}
+> attach(massart97ex3)
+> yx <- split(y, x)
+> ybar <- sapply(yx, mean)
+> s <- round(sapply(yx, sd), digits = 2)
+> w <- round(1/(s^2), digits = 3)
+> weights <- w[factor(x)]
+> m <- lm(y ~ x, w = weights)
+\end{Sinput}
+\end{Schunk}
+
+If we now want to predict a new x value from measured y values,
+we use the \texttt{inverse.predict} function:
+
+\begin{Schunk}
+\begin{Sinput}
+> inverse.predict(m, 15, ws = 1.67)
+\end{Sinput}
+\begin{Soutput}
+$Prediction
+[1] 5.865367
+
+$`Standard Error`
+[1] 0.892611
+
+$Confidence
+[1] 2.478285
+
+$`Confidence Limits`
+[1] 3.387082 8.343652
+\end{Soutput}
+\begin{Sinput}
+> inverse.predict(m, 90, ws = 0.145)
+\end{Sinput}
+\begin{Soutput}
+$Prediction
+[1] 44.06025
+
+$`Standard Error`
+[1] 2.829162
+
+$Confidence
+[1] 7.855012
+
+$`Confidence Limits`
+[1] 36.20523 51.91526
+\end{Soutput}
+\end{Schunk}
+
+The weight \texttt{ws} assigned to the measured y value has to be
+given by the user in the case of weighted regression, or alternatively,
+the approximate variance \texttt{var.s} at this location.
+
+\section*{Theory for \texttt{inverse.predict}}
+Equation 8.28 in \cite{massart97} gives a general equation for predicting the
+standard error $s_{\hat{x_s}}$ for an x value predicted from measurements of y
+according to the linear calibration function $ y = b_0 + b_1 \cdot x$:
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{s_e}{b_1} \sqrt{\frac{1}{w_s m} + \frac{1}{\sum{w_i}} +
+ \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+ {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} -
+ {\left( \sum{ w_i x_i } \right)}^2 \right) }}
+\end{equation}
+
+with
+
+\begin{equation}
+s_e = \sqrt{ \frac{\sum w_i (y_i - \hat{y_i})^2}{n - 2}}
+\end{equation}
+
+where $w_i$ is the weight for calibration standard $i$, $y_i$ is the mean $y$
+value (!) observed for standard $i$, $\hat{y_i}$ is the estimated value for
+standard $i$, $n$ is the number calibration standards, $w_s$ is the weight
+attributed to the sample $s$, $m$ is the number of replicate measurements of
+sample $s$, $\bar{y_s}$ is the mean response for the sample,
+$\bar{y_w} = \frac{\sum{w_i y_i}}{\sum{w_i}}$ is the weighted mean of responses
+$y_i$, and $x_i$ is the given $x$ value for standard $i$.
+
+The weight $w_s$ for the sample should be estimated or calculated in accordance
+to the weights used in the linear regression.
+
+I adjusted the above equation in order to be able to take a different
+precisions in standards and samples into account. In analogy to Equation 8.26
+from \cite{massart97} we get
+
+\begin{equation}
+s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
+ {s_e}^2 \left( \frac{1}{\sum{w_i}} +
+ \frac{(\bar{y_s} - \bar{y_w})^2 \sum{w_i}}
+ {{b_1}^2 \left( \sum{w_i} \sum{w_i {x_i}^2} - {\left( \sum{ w_i x_i } \right)}^2 \right) } \right) }
+\end{equation}
+
+where I interpret $\frac{{s_s}^2}{w_s}$ as an estimator of the variance at location
+$\hat{x_s}$, which can be replaced by a user-specified value using the argument
+\texttt{var.s} of the function \texttt{inverse.predict}.
+
+\begin{thebibliography}{1}
+\bibitem{massart97}
+Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+Smeyers-Verbeke, J.
+\newblock Handbook of Chemometrics and Qualimetrics: Part A,
+\newblock Elsevier, Amsterdam, 1997
+\end{thebibliography}
+
+\end{document}
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index 0000000..6f6d584
--- /dev/null
+++ b/trunk/man/calplot.lm.Rd
@@ -0,0 +1,62 @@
+\name{calplot}
+\alias{calplot}
+\alias{calplot.default}
+\alias{calplot.lm}
+\title{Plot calibration graphs from univariate linear models}
+\description{
+ Produce graphics of calibration data, the fitted model as well
+ as confidence, and, for unweighted regression, prediction bands.
+}
+\usage{
+ calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
+ xlab = "Concentration", ylab = "Response", alpha=0.05, varfunc = NULL)
+}
+\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}.
+ }
+ \item{xlim}{
+ The limits of the plot on the x axis.
+ }
+ \item{ylim}{
+ The limits of the plot on the y axis.
+ }
+ \item{xlab}{
+ The label of the x axis.
+ }
+ \item{ylab}{
+ The label of the y axis.
+ }
+ \item{alpha}{
+ The error tolerance level for the confidence and prediction bands.
+ }
+ \item{varfunc}{
+ The variance function for generating the weights in the model.
+ Currently, this argument is ignored (see note below).
+ }
+}
+\value{
+ A plot of the calibration data, of your fitted model as well as lines showing
+ the confidence limits. Prediction limits are only shown for models from
+ unweighted regression.
+}
+\note{
+ Prediction bands for models from weighted linear regression require weights
+ for the data, for which responses should be predicted. Prediction intervals
+ using weights e.g. from a variance function are currently not supported by
+ the internally used function \code{\link{predict.lm}}, therefore,
+ \code{calplot} does not draw prediction bands for such models.
+}
+\examples{
+data(massart97ex3)
+m <- lm(y ~ x, data = massart97ex3)
+calplot(m)
+}
+\author{
+ Johannes Ranke
+ \email{jranke@uni-bremen.de}
+ \url{http://www.uft.uni-bremen.de/chemie/ranke}
+}
+\keyword{regression}
diff --git a/trunk/man/chemCal-package.Rd b/trunk/man/chemCal-package.Rd
new file mode 100644
index 0000000..4456150
--- /dev/null
+++ b/trunk/man/chemCal-package.Rd
@@ -0,0 +1,17 @@
+\name{chemCal-package}
+\alias{chemCal-package}
+\docType{package}
+\title{
+ Calibration functions for analytical chemistry
+}
+\description{
+ See \url{../DESCRIPTION}
+}
+\details{
+ There is a package vignette located in \url{../doc/chemCal.pdf}.
+}
+\author{
+ Author and Maintainer: Johannes Ranke <jranke@uni-bremen.de>
+}
+\keyword{manip}
+}
diff --git a/trunk/man/din32645.Rd b/trunk/man/din32645.Rd
new file mode 100644
index 0000000..cacbf07
--- /dev/null
+++ b/trunk/man/din32645.Rd
@@ -0,0 +1,61 @@
+\name{din32645}
+\docType{data}
+\alias{din32645}
+\title{Calibration data from DIN 32645}
+\description{
+ Sample dataset to test the package.
+}
+\usage{data(din32645)}
+\format{
+ A dataframe containing 10 rows of x and y values.
+}
+\examples{
+data(din32645)
+m <- lm(y ~ x, data = din32645)
+calplot(m)
+
+## Prediction of x with confidence interval
+(prediction <- inverse.predict(m, 3500, alpha = 0.01))
+
+# This should give 0.07434 according to test data from Dintest, which
+# was collected from Procontrol 3.1 (isomehr GmbH) in this case
+round(prediction$Confidence,5)
+
+## Critical value:
+(crit <- lod(m, alpha = 0.01, beta = 0.5))
+
+# According to DIN 32645, we should get 0.07 for the critical value
+# (decision limit, "Nachweisgrenze")
+round(crit$x, 2)
+# and according to Dintest test data, we should get 0.0698 from
+round(crit$x, 4)
+
+## Limit of detection (smallest detectable value given alpha and beta)
+# In German, the smallest detectable value is the "Erfassungsgrenze", and we
+# should get 0.14 according to DIN, which we achieve by using the method
+# described in it:
+lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
+round(lod.din$x, 2)
+
+## Limit of quantification
+# This accords to the test data coming with the test data from Dintest again,
+# except for the last digits of the value cited for Procontrol 3.1 (0.2121)
+(loq <- loq(m, alpha = 0.01))
+round(loq$x,4)
+
+# A similar value is obtained using the approximation
+# LQ = 3.04 * LC (Currie 1999, p. 120)
+3.04 * lod(m,alpha = 0.01, beta = 0.5)$x
+}
+\references{
+ DIN 32645 (equivalent to ISO 11843), Beuth Verlag, Berlin, 1994
+
+ Dintest. Plugin for MS Excel for evaluations of calibration data. Written
+ by Georg Schmitt, University of Heidelberg.
+ \url{http://www.rzuser.uni-heidelberg.de/~df6/download/dintest.htm}
+
+ Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
+ detection and quantification capabilities (IUPAC Recommendations 1995).
+ Analytica Chimica Acta 391, 105 - 126.
+}
+\keyword{datasets}
diff --git a/trunk/man/inverse.predict.Rd b/trunk/man/inverse.predict.Rd
new file mode 100644
index 0000000..347d670
--- /dev/null
+++ b/trunk/man/inverse.predict.Rd
@@ -0,0 +1,69 @@
+\name{inverse.predict}
+\alias{inverse.predict}
+\alias{inverse.predict.lm}
+\alias{inverse.predict.rlm}
+\alias{inverse.predict.default}
+\title{Predict x from y for a linear calibration}
+\usage{inverse.predict(object, newdata, \dots,
+ ws, alpha=0.05, var.s = "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}.
+ }
+ \item{newdata}{
+ A vector of observed y values for one sample.
+ }
+ \item{\dots}{
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ }
+ \item{ws}{
+ The weight attributed to the sample. This argument is obligatory
+ if \code{object} has weights.
+ }
+ \item{alpha}{
+ The error tolerance level for the confidence interval to be reported.
+ }
+ \item{var.s}{
+ The estimated variance of the sample measurements. The default is to take
+ the residual standard error from the calibration and to adjust it
+ using \code{ws}, if applicable. This means that \code{var.s}
+ overrides \code{ws}.
+ }
+}
+\value{
+ A list containing the predicted x value, its standard error and a
+ confidence interval.
+}
+\description{
+ This function predicts x values using a univariate linear model that has been
+ generated for the purpose of calibrating a measurement method. Prediction
+ intervals are given at the specified confidence level.
+ The calculation method was taken from Massart et al. (1997). In particular,
+ Equations 8.26 and 8.28 were combined in order to yield a general treatment
+ of inverse prediction for univariate linear models, taking into account
+ weights that have been used to create the linear model, and at the same
+ time providing the possibility to specify a precision in sample measurements
+ differing from the precision in standard samples used for the calibration.
+ This is elaborated in the package vignette.
+}
+\note{
+ The function was validated with examples 7 and 8 from Massart et al. (1997).
+}
+\references{
+ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+ Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
+ p. 200
+}
+\examples{
+# This is example 7 from Chapter 8 in Massart et al. (1997)
+data(massart97ex1)
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15) # 6.1 +- 4.9
+inverse.predict(m, 90) # 43.9 +- 4.9
+inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+}
+\keyword{manip}
diff --git a/trunk/man/ipowfunc.Rd b/trunk/man/ipowfunc.Rd
new file mode 100644
index 0000000..e09e590
--- /dev/null
+++ b/trunk/man/ipowfunc.Rd
@@ -0,0 +1,33 @@
+\name{ipowfunc}
+\alias{ipowfunc}
+\title{Power function}
+\description{
+ Inverse of the arithmetic power function \code{\link{powfunc}} used for
+ modelling univariate nonlinear calibration data. }
+\usage{
+ ipowfunc(x,a,b)
+}
+\arguments{
+ \item{x}{
+ Independent variable}
+ \item{a}{
+ Coefficient}
+ \item{b}{
+ Exponent}
+}
+\value{
+ The result of evaluating the function
+ \deqn{f(x) = \frac{y}{a}^\frac{1}{b}}{f(x) = y/a^1/b}
+ which is the inverse of the function defined by \code{\link{powfunc}}
+}
+\author{
+ Johannes Ranke
+ \email{jranke@uni-bremen.de}
+ \url{http://www.uft.uni-bremen.de/chemie/ranke}
+}
+\seealso{
+ The original function \code{\link{powfunc}}.
+}
+\keyword{models}
+\keyword{regression}
+\keyword{nonlinear}
diff --git a/trunk/man/lod.Rd b/trunk/man/lod.Rd
new file mode 100644
index 0000000..e468e1d
--- /dev/null
+++ b/trunk/man/lod.Rd
@@ -0,0 +1,83 @@
+\name{lod}
+\alias{lod}
+\alias{lod.lm}
+\alias{lod.rlm}
+\alias{lod.default}
+\title{Estimate a limit of detection (LOD)}
+\usage{
+ lod(object, \dots, alpha = 0.05, beta = 0.05, method = "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.
+ }
+ \item{\dots}{
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ }
+ \item{alpha}{
+ The error tolerance for the decision limit (critical value).
+ }
+ \item{beta}{
+ The error tolerance beta for the detection limit.
+ }
+ \item{method}{
+ The default method uses a prediction interval at the LOD
+ for the estimation of the LOD, which obviously requires
+ iteration. This is described for example in Massart, p. 432 ff.
+ The \dQuote{din} method uses the prediction interval at
+ x = 0 as an approximation.
+ }
+}
+\value{
+ A list containig the corresponding x and y values of the estimated limit of
+ detection of a model used for calibration.
+}
+\description{
+ The decision limit (German: Nachweisgrenze) is defined as the signal or
+ analyte concentration that is significantly different from the blank signal
+ with a first order error alpha (one-sided significance test).
+ The detection limit, or more precise, the minimum detectable value
+ (German: Erfassungsgrenze), is then defined as the signal or analyte
+ concentration where the probability that the signal is not detected although
+ the analyte is present (type II or false negative error), is beta (also a
+ one-sided significance test).
+}
+\note{
+ - The default values for alpha and beta are the ones recommended by IUPAC.
+ - The estimation of the LOD in terms of the analyte amount/concentration
+ xD from the LOD in the signal domain SD is done by simply inverting the
+ calibration function (i.e. assuming a known calibration function).
+ - The calculation of a LOD from weighted calibration models requires
+ a weights argument for the internally used \code{\link{predict.lm}}
+ function, which is currently not supported in R.
+}
+\references{
+ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+ Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
+ Chapter 13.7.8
+
+ J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and
+ Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules.
+ Web edition.
+
+ Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including
+ detection and quantification capabilities (IUPAC Recommendations 1995).
+ Analytica Chimica Acta 391, 105 - 126.
+}
+\examples{
+data(din32645)
+m <- lm(y ~ x, data = din32645)
+lod(m)
+
+# The critical value (decision limit, German Nachweisgrenze) can be obtained
+# by using beta = 0.5:
+lod(m, alpha = 0.01, beta = 0.5)
+}
+\seealso{
+ Examples for \code{\link{din32645}}
+}
+\keyword{manip}
diff --git a/trunk/man/loq.Rd b/trunk/man/loq.Rd
new file mode 100644
index 0000000..7541e77
--- /dev/null
+++ b/trunk/man/loq.Rd
@@ -0,0 +1,77 @@
+\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")
+}
+\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.
+ }
+}
+\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}
diff --git a/trunk/man/massart97ex1.Rd b/trunk/man/massart97ex1.Rd
new file mode 100644
index 0000000..44e1b85
--- /dev/null
+++ b/trunk/man/massart97ex1.Rd
@@ -0,0 +1,17 @@
+\name{massart97ex1}
+\docType{data}
+\alias{massart97ex1}
+\title{Calibration data from Massart et al. (1997), example 1}
+\description{
+ Sample dataset from p. 175 to test the package.
+}
+\usage{data(massart97ex1)}
+\format{
+ A dataframe containing 6 observations of x and y data.
+}
+\source{
+ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+ Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
+ Chapter 8.
+}
+\keyword{datasets}
diff --git a/trunk/man/massart97ex3.Rd b/trunk/man/massart97ex3.Rd
new file mode 100644
index 0000000..efdcf02
--- /dev/null
+++ b/trunk/man/massart97ex3.Rd
@@ -0,0 +1,51 @@
+\name{massart97ex3}
+\docType{data}
+\alias{massart97ex3}
+\title{Calibration data from Massart et al. (1997), example 3}
+\description{
+ Sample dataset from p. 188 to test the package.
+}
+\usage{data(massart97ex3)}
+\format{
+ A dataframe containing 6 levels of x values with 5
+ observations of y for each level.
+}
+\examples{
+data(massart97ex3)
+attach(massart97ex3)
+yx <- split(y, x)
+ybar <- sapply(yx, mean)
+s <- round(sapply(yx, sd), digits = 2)
+w <- round(1 / (s^2), digits = 3)
+weights <- w[factor(x)]
+m <- lm(y ~ x, w = weights)
+calplot(m)
+
+# The following concords with the book p. 200
+inverse.predict(m, 15, ws = 1.67) # 5.9 +- 2.5
+inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
+
+# The LOD is only calculated for models from unweighted regression
+# with this version of chemCal
+m0 <- lm(y ~ x)
+lod(m0)
+
+# Limit of quantification from unweighted regression
+loq(m0)
+
+# For calculating the limit of quantification from a model from weighted
+# regression, we need to supply weights, internally used for inverse.predict
+# If we are not using a variance function, we can use the weight from
+# the above example as a first approximation (x = 15 is close to our
+# loq approx 14 from above).
+loq(m, w.loq = 1.67)
+# The weight for the loq should therefore be derived at x = 7.3 instead
+# of 15, but the graphical procedure of Massart (p. 201) to derive the
+# variances on which the weights are based is quite inaccurate anyway.
+}
+\source{
+ Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J.,
+ Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A,
+ Chapter 8.
+}
+\keyword{datasets}
diff --git a/trunk/man/powfunc.Rd b/trunk/man/powfunc.Rd
new file mode 100644
index 0000000..73fe3b0
--- /dev/null
+++ b/trunk/man/powfunc.Rd
@@ -0,0 +1,32 @@
+\name{powfunc}
+\alias{powfunc}
+\title{Power function}
+\description{
+ Arithmetic power function for modelling univariate nonlinear calibration data.
+}
+\usage{
+ powfunc(x,a,b)
+}
+\arguments{
+ \item{x}{
+ Independent variable}
+ \item{a}{
+ Coefficient}
+ \item{b}{
+ Exponent}
+}
+\value{
+ The result of evaluating the function
+ \deqn{f(x) = a x^b}{f(x) = a * x^b}
+}
+\author{
+ Johannes Ranke
+ \email{jranke@uni-bremen.de}
+ \url{http://www.uft.uni-bremen.de/chemie/ranke}
+}
+\seealso{
+ The inverse of this function \code{\link{ipowfunc}}.
+}
+\keyword{models}
+\keyword{regression}
+\keyword{nonlinear}
diff --git a/trunk/tests/din32645.R b/trunk/tests/din32645.R
new file mode 100644
index 0000000..e5ffed7
--- /dev/null
+++ b/trunk/tests/din32645.R
@@ -0,0 +1,7 @@
+require(chemCal)
+data(din32645)
+m <- lm(y ~ x, data = din32645)
+inverse.predict(m, 3500, alpha = 0.01)
+lod <- lod(m, alpha = 0.01, beta = 0.5)
+lod(m, alpha = 0.01, beta = 0.01)
+loq <- loq(m, alpha = 0.01)
diff --git a/trunk/tests/din32645.Rout.save b/trunk/tests/din32645.Rout.save
new file mode 100644
index 0000000..c5ed5a7
--- /dev/null
+++ b/trunk/tests/din32645.Rout.save
@@ -0,0 +1,45 @@
+
+R : Copyright 2006, The R Foundation for Statistical Computing
+Version 2.3.1 (2006-06-01)
+ISBN 3-900051-07-0
+
+R is free software and comes with ABSOLUTELY NO WARRANTY.
+You are welcome to redistribute it under certain conditions.
+Type 'license()' or 'licence()' for distribution details.
+
+R is a collaborative project with many contributors.
+Type 'contributors()' for more information and
+'citation()' on how to cite R or R packages in publications.
+
+Type 'demo()' for some demos, 'help()' for on-line help, or
+'help.start()' for an HTML browser interface to help.
+Type 'q()' to quit R.
+
+> require(chemCal)
+Loading required package: chemCal
+[1] TRUE
+> data(din32645)
+> m <- lm(y ~ x, data = din32645)
+> inverse.predict(m, 3500, alpha = 0.01)
+$Prediction
+[1] 0.1054792
+
+$`Standard Error`
+[1] 0.02215619
+
+$Confidence
+[1] 0.07434261
+
+$`Confidence Limits`
+[1] 0.03113656 0.17982178
+
+> lod <- lod(m, alpha = 0.01, beta = 0.5)
+> lod(m, alpha = 0.01, beta = 0.01)
+$x
+[1] 0.132904
+
+$y
+[1] 3764.977
+
+> loq <- loq(m, alpha = 0.01)
+>
diff --git a/trunk/tests/massart97.R b/trunk/tests/massart97.R
new file mode 100644
index 0000000..00f837f
--- /dev/null
+++ b/trunk/tests/massart97.R
@@ -0,0 +1,25 @@
+require(chemCal)
+data(massart97ex1)
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15) # 6.1 +- 4.9
+inverse.predict(m, 90) # 43.9 +- 4.9
+inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+
+data(massart97ex3)
+attach(massart97ex3)
+yx <- split(y, x)
+ybar <- sapply(yx, mean)
+s <- round(sapply(yx, sd), digits = 2)
+w <- round(1 / (s^2), digits = 3)
+weights <- w[factor(x)]
+m <- lm(y ~ x, w = weights)
+#calplot(m)
+
+inverse.predict(m, 15, ws = 1.67) # 5.9 +- 2.5
+inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
+
+m0 <- lm(y ~ x)
+lod(m0)
+
+loq(m0)
+loq(m, w.loq = 1.67)
diff --git a/trunk/tests/massart97.Rout.save b/trunk/tests/massart97.Rout.save
new file mode 100644
index 0000000..cb113d0
--- /dev/null
+++ b/trunk/tests/massart97.Rout.save
@@ -0,0 +1,123 @@
+
+R : Copyright 2006, The R Foundation for Statistical Computing
+Version 2.3.1 (2006-06-01)
+ISBN 3-900051-07-0
+
+R is free software and comes with ABSOLUTELY NO WARRANTY.
+You are welcome to redistribute it under certain conditions.
+Type 'license()' or 'licence()' for distribution details.
+
+R is a collaborative project with many contributors.
+Type 'contributors()' for more information and
+'citation()' on how to cite R or R packages in publications.
+
+Type 'demo()' for some demos, 'help()' for on-line help, or
+'help.start()' for an HTML browser interface to help.
+Type 'q()' to quit R.
+
+> require(chemCal)
+Loading required package: chemCal
+[1] TRUE
+> data(massart97ex1)
+> m <- lm(y ~ x, data = massart97ex1)
+> inverse.predict(m, 15) # 6.1 +- 4.9
+$Prediction
+[1] 6.09381
+
+$`Standard Error`
+[1] 1.767278
+
+$Confidence
+[1] 4.906751
+
+$`Confidence Limits`
+[1] 1.187059 11.000561
+
+> inverse.predict(m, 90) # 43.9 +- 4.9
+$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.767747
+
+$Confidence
+[1] 4.908053
+
+$`Confidence Limits`
+[1] 39.03178 48.84788
+
+> inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
+$Prediction
+[1] 43.93983
+
+$`Standard Error`
+[1] 1.141204
+
+$Confidence
+[1] 3.168489
+
+$`Confidence Limits`
+[1] 40.77134 47.10832
+
+>
+> data(massart97ex3)
+> attach(massart97ex3)
+> yx <- split(y, x)
+> ybar <- sapply(yx, mean)
+> s <- round(sapply(yx, sd), digits = 2)
+> w <- round(1 / (s^2), digits = 3)
+> weights <- w[factor(x)]
+> m <- lm(y ~ x, w = weights)
+> #calplot(m)
+>
+> inverse.predict(m, 15, ws = 1.67) # 5.9 +- 2.5
+$Prediction
+[1] 5.865367
+
+$`Standard Error`
+[1] 0.892611
+
+$Confidence
+[1] 2.478285
+
+$`Confidence Limits`
+[1] 3.387082 8.343652
+
+> inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
+$Prediction
+[1] 44.06025
+
+$`Standard Error`
+[1] 2.829162
+
+$Confidence
+[1] 7.855012
+
+$`Confidence Limits`
+[1] 36.20523 51.91526
+
+>
+> m0 <- lm(y ~ x)
+> lod(m0)
+$x
+[1] 5.406637
+
+$y
+[1] 13.63822
+
+>
+> loq(m0)
+$x
+[1] 13.97767
+
+$y
+[1] 30.62355
+
+> loq(m, w.loq = 1.67)
+$x
+[1] 7.346231
+
+$y
+[1] 17.90784
+
+>

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