Some cosmetic changes, and the vignette created during package building.

git-svn-id: http://kriemhild.uft.uni-bremen.de/svn/chemCal@17 5fad18fb-23f0-0310-ab10-e59a3bee62b4

8 files changed, 5906 insertions, 5795 deletions

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diff --git a/inst/doc/chemCal.pdf b/inst/doc/chemCal.pdf
index 027e053..799fe9b 100644
--- a/inst/doc/chemCal.pdf
+++ b/inst/doc/chemCal.pdf
diff --git a/inst/doc/chemCal.tex b/inst/doc/chemCal.tex
index 0469848..32c5143 100644
--- a/inst/doc/chemCal.tex
+++ b/inst/doc/chemCal.tex
@@ -1,169 +1,169 @@
-\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] 0.7288138
-
-$Confidence
-[1] 2.023511
-
-$`Confidence Limits`
-[1] 3.841856 7.888878
-\end{Soutput}
-\begin{Sinput}
-> inverse.predict(m, 90, ws = 0.145)
-\end{Sinput}
-\begin{Soutput}
-$Prediction
-[1] 44.06025
-
-$`Standard Error`
-[1] 2.310001
-
-$Confidence
-[1] 6.41359
-
-$`Confidence Limits`
-[1] 37.64666 50.47384
-\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}
+\documentclass[a4paper]{article}

+%\VignetteIndexEntry{Short manual for the chemCal package}

+\usepackage{hyperref}

+

+\title{Basic calibration functions for analytical chemistry}

+\author{Johannes Ranke}

+

+\usepackage{d:/Programme/R/R-2.3.1/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}