1 files changed, 31 insertions, 16 deletions
diff --git a/inst/doc/chemCal.tex b/inst/doc/chemCal.tex
index e26172f..0469848 100644
--- a/inst/doc/chemCal.tex
+++ b/inst/doc/chemCal.tex
@@ -9,15 +9,29 @@
 \begin{document}
 \maketitle
 
-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
-\footnote{
-For the weighted case, the function \texttt{predict.lm} would have to be 
-adapted (Bug report PR\#8877), in order to allow for weights for the x values
-used to predict the y values. This affects the functions \texttt{calplot}
-and \texttt{lod}.
-}, linear regression so far.
+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:
@@ -26,8 +40,7 @@ shown by using the \texttt{calplot} function:
 \begin{Sinput}
 > library(chemCal)
 > data(massart97ex3)
-> attach(massart97ex3)
-> m0 <- lm(y ~ x)
+> m0 <- lm(y ~ x, data = massart97ex3)
 > calplot(m0)
 \end{Sinput}
 \end{Schunk}
@@ -49,6 +62,7 @@ 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)
@@ -58,9 +72,6 @@ is proposed which can be reproduced by
 \end{Sinput}
 \end{Schunk}
 
-Unfortunately, \texttt{calplot} does not work on weighted linear models,
-as noted in the footnote above.
-
 If we now want to predict a new x value from measured y values,
 we use the \texttt{inverse.predict} function:
 
@@ -100,8 +111,8 @@ $`Confidence Limits`
 \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. By default, 
-the mean of the weights used in the linear regression is used.
+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
@@ -143,6 +154,10 @@ s_{\hat{x_s}} = \frac{1}{b_1} \sqrt{\frac{{s_s}^2}{w_s m} +
             {{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.,