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Diffstat (limited to 'trunk')
| -rw-r--r-- | trunk/chemCal/DESCRIPTION | 4 | ||||
| -rw-r--r-- | trunk/chemCal/inst/doc/chemCal-001.pdf | 1727 | ||||
| -rw-r--r-- | trunk/chemCal/inst/doc/chemCal-002.pdf | 275 | ||||
| -rw-r--r-- | trunk/chemCal/inst/doc/chemCal.log | 362 | ||||
| -rw-r--r-- | trunk/chemCal/inst/doc/chemCal.pdf | bin | 123694 -> 0 bytes | |||
| -rw-r--r-- | trunk/chemCal/inst/doc/chemCal.tex | 169 | ||||
| -rw-r--r-- | trunk/chemCal/man/chemCal-package.Rd | 1 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/Makefile (renamed from trunk/chemCal/inst/doc/Makefile) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/Rplots.pdf | bin | 0 -> 28827 bytes | |||
| -rw-r--r-- | trunk/chemCal/vignettes/Rplots.ps (renamed from trunk/chemCal/inst/doc/Rplots.ps) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal-001.eps (renamed from trunk/chemCal/inst/doc/chemCal-001.eps) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal-001.pdf | bin | 0 -> 12038 bytes | |||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal-002.eps (renamed from trunk/chemCal/inst/doc/chemCal-002.eps) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal-002.pdf | bin | 0 -> 5031 bytes | |||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.Rnw (renamed from trunk/chemCal/inst/doc/chemCal.Rnw) | 7 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.aux (renamed from trunk/chemCal/inst/doc/chemCal.aux) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.bbl (renamed from trunk/chemCal/inst/doc/chemCal.bbl) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.blg (renamed from trunk/chemCal/inst/doc/chemCal.blg) | 2 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.log | 399 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.out (renamed from trunk/chemCal/inst/doc/chemCal.out) | 0 | ||||
| -rw-r--r-- | trunk/chemCal/vignettes/chemCal.pdf | bin | 0 -> 185068 bytes |
21 files changed, 405 insertions, 2541 deletions
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-%\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} diff --git a/trunk/chemCal/man/chemCal-package.Rd b/trunk/chemCal/man/chemCal-package.Rd index 4456150..fb09cb1 100644 --- a/trunk/chemCal/man/chemCal-package.Rd +++ b/trunk/chemCal/man/chemCal-package.Rd @@ -14,4 +14,3 @@ Author and Maintainer: Johannes Ranke <jranke@uni-bremen.de> } \keyword{manip} -} diff --git a/trunk/chemCal/inst/doc/Makefile b/trunk/chemCal/vignettes/Makefile index 8eca69e..8eca69e 100644 --- a/trunk/chemCal/inst/doc/Makefile +++ b/trunk/chemCal/vignettes/Makefile diff --git a/trunk/chemCal/vignettes/Rplots.pdf b/trunk/chemCal/vignettes/Rplots.pdf Binary files differnew file mode 100644 index 0000000..4029222 --- /dev/null +++ b/trunk/chemCal/vignettes/Rplots.pdf diff --git a/trunk/chemCal/inst/doc/Rplots.ps b/trunk/chemCal/vignettes/Rplots.ps index c5e68ec..c5e68ec 100644 --- a/trunk/chemCal/inst/doc/Rplots.ps +++ b/trunk/chemCal/vignettes/Rplots.ps diff --git a/trunk/chemCal/inst/doc/chemCal-001.eps b/trunk/chemCal/vignettes/chemCal-001.eps index acc5f4b..acc5f4b 100644 --- a/trunk/chemCal/inst/doc/chemCal-001.eps +++ b/trunk/chemCal/vignettes/chemCal-001.eps diff --git a/trunk/chemCal/vignettes/chemCal-001.pdf b/trunk/chemCal/vignettes/chemCal-001.pdf Binary files differnew file mode 100644 index 0000000..a8c2629 --- /dev/null +++ b/trunk/chemCal/vignettes/chemCal-001.pdf diff --git a/trunk/chemCal/inst/doc/chemCal-002.eps b/trunk/chemCal/vignettes/chemCal-002.eps index c0ee749..c0ee749 100644 --- a/trunk/chemCal/inst/doc/chemCal-002.eps +++ b/trunk/chemCal/vignettes/chemCal-002.eps diff --git a/trunk/chemCal/vignettes/chemCal-002.pdf b/trunk/chemCal/vignettes/chemCal-002.pdf Binary files differnew file mode 100644 index 0000000..86bf0ac --- /dev/null +++ b/trunk/chemCal/vignettes/chemCal-002.pdf diff --git a/trunk/chemCal/inst/doc/chemCal.Rnw b/trunk/chemCal/vignettes/chemCal.Rnw index 956c664..3c46540 100644 --- a/trunk/chemCal/inst/doc/chemCal.Rnw +++ b/trunk/chemCal/vignettes/chemCal.Rnw @@ -22,7 +22,7 @@ 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 +A \href{http://bugs.r-project.org/bugzilla3/show_bug.cgi?id=8877}{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 @@ -136,6 +136,7 @@ case. Let's take the above example and estimate a variance function <<>>= +library(doBy) massart97ex3 massart97ex3$x <- factor(massart97ex3$x) summary <- summaryBy(y~x, data = massart97ex3,FUN=c(mean,sd,var)) @@ -146,9 +147,7 @@ plot(summary$x, summary$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} diff --git a/trunk/chemCal/inst/doc/chemCal.aux b/trunk/chemCal/vignettes/chemCal.aux index 20bfc98..20bfc98 100644 --- a/trunk/chemCal/inst/doc/chemCal.aux +++ b/trunk/chemCal/vignettes/chemCal.aux diff --git a/trunk/chemCal/inst/doc/chemCal.bbl b/trunk/chemCal/vignettes/chemCal.bbl index e69de29..e69de29 100644 --- a/trunk/chemCal/inst/doc/chemCal.bbl +++ b/trunk/chemCal/vignettes/chemCal.bbl diff --git a/trunk/chemCal/inst/doc/chemCal.blg b/trunk/chemCal/vignettes/chemCal.blg index 72f5a0e..2904a63 100644 --- a/trunk/chemCal/inst/doc/chemCal.blg +++ 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