diff options
Diffstat (limited to 'inst/doc')
| -rw-r--r-- | inst/doc/Makefile | 2 | ||||
| -rw-r--r-- | inst/doc/chemCal-001.pdf | 4 | ||||
| -rw-r--r-- | inst/doc/chemCal-002.pdf | 4 | ||||
| -rw-r--r-- | inst/doc/chemCal.Rnw | 59 | ||||
| -rw-r--r-- | inst/doc/chemCal.aux | 1 | ||||
| -rw-r--r-- | inst/doc/chemCal.log | 69 | ||||
| -rw-r--r-- | inst/doc/chemCal.pdf | bin | 133895 -> 123681 bytes | |||
| -rw-r--r-- | inst/doc/chemCal.tex | 47 |
8 files changed, 107 insertions, 79 deletions
diff --git a/inst/doc/Makefile b/inst/doc/Makefile index 9c5cd3a..8eca69e 100644 --- a/inst/doc/Makefile +++ b/inst/doc/Makefile @@ -1,6 +1,6 @@ # Makefile for Sweave documents containing both Latex and R code # Author: Johannes Ranke <jranke@uni-bremen.de> -# Last Change: 2006 Mai 24 +# 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 $ diff --git a/inst/doc/chemCal-001.pdf b/inst/doc/chemCal-001.pdf index 9ca7c06..9e77bb2 100644 --- a/inst/doc/chemCal-001.pdf +++ b/inst/doc/chemCal-001.pdf @@ -2,8 +2,8 @@ %ρ\r 1 0 obj << -/CreationDate (D:20060524104614) -/ModDate (D:20060524104614) +/CreationDate (D:20060623173000) +/ModDate (D:20060623173000) /Title (R Graphics Output) /Producer (R 2.3.1) /Creator (R) diff --git a/inst/doc/chemCal-002.pdf b/inst/doc/chemCal-002.pdf index 262f50a..44ab8b6 100644 --- a/inst/doc/chemCal-002.pdf +++ b/inst/doc/chemCal-002.pdf @@ -2,8 +2,8 @@ %ρ\r 1 0 obj << -/CreationDate (D:20060524104614) -/ModDate (D:20060524104614) +/CreationDate (D:20060623173002) +/ModDate (D:20060623173002) /Title (R Graphics Output) /Producer (R 2.3.1) /Creator (R) diff --git a/inst/doc/chemCal.Rnw b/inst/doc/chemCal.Rnw index afa5ad7..8cdc97c 100644 --- a/inst/doc/chemCal.Rnw +++ b/inst/doc/chemCal.Rnw @@ -8,15 +8,29 @@ \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: @@ -24,8 +38,7 @@ shown by using the \texttt{calplot} function: <<echo=TRUE,fig=TRUE>>= library(chemCal) data(massart97ex3) -attach(massart97ex3) -m0 <- lm(y ~ x) +m0 <- lm(y ~ x, data = massart97ex3) calplot(m0) @ @@ -41,28 +54,26 @@ Therefore, in Example 8 in \cite{massart97} weighted regression is proposed which can be reproduced by <<>>= -yx <- split(y,x) -ybar <- sapply(yx,mean) -s <- round(sapply(yx,sd),digits=2) -w <- round(1/(s^2),digits=3) +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) +m <- lm(y ~ x, w = weights) @ -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: <<>>= -inverse.predict(m,15,ws=1.67) +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. 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 @@ -104,6 +115,10 @@ 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., diff --git a/inst/doc/chemCal.aux b/inst/doc/chemCal.aux index 0eb51cc..20bfc98 100644 --- a/inst/doc/chemCal.aux +++ b/inst/doc/chemCal.aux @@ -14,4 +14,5 @@ \citation{massart97} \citation{massart97} \citation{massart97} +\citation{massart97} \bibcite{massart97}{1} diff --git a/inst/doc/chemCal.log b/inst/doc/chemCal.log index 237b975..fc0ba0f 100644 --- a/inst/doc/chemCal.log +++ b/inst/doc/chemCal.log @@ -1,4 +1,4 @@ -This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2006.4.8) 24 MAY 2006 10:46 +This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2006.5.30) 23 JUN 2006 17:30 entering extended mode **chemCal.tex (./chemCal.tex @@ -297,65 +297,62 @@ LaTeX Font Info: External font `cmex10' loaded for size (Font) <8> on input line 11. LaTeX Font Info: External font `cmex10' loaded for size (Font) <6> on input line 11. -LaTeX Font Info: Try loading font information for T1+aett on input line 13. +LaTeX Font Info: Try loading font information for T1+aett on input line 12. (/usr/share/texmf-tetex/tex/latex/ae/t1aett.fd File: t1aett.fd 1997/11/16 Font definitions for T1/aett. ) -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <7> on input line 15. -LaTeX Font Info: External font `cmex10' loaded for size -(Font) <5> on input line 15. - <chemCal-001.pdf, id=7, 433.62pt x 433.62pt> File: chemCal-001.pdf Graphic file (type pdf) <use chemCal-001.pdf> [1 -{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map} <./chemCal-001.pdf>] -<chemCal-002.pdf, id=47, 433.62pt x 433.62pt> +{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] +<chemCal-002.pdf, id=31, 433.62pt x 433.62pt> File: chemCal-002.pdf Graphic file (type pdf) - <use chemCal-002.pdf> -LaTeX Font Info: Try loading font information for TS1+aett on input line 75. + <use chemCal-002.pdf> [2 <./chemCal-001.pdf>] +LaTeX Font Info: Try loading font information for TS1+aett on input line 86. -LaTeX Font Info: No file TS1aett.fd. on input line 75. +LaTeX Font Info: No file TS1aett.fd. on input line 86. LaTeX Font Warning: Font shape `TS1/aett/m/n' undefined (Font) using `TS1/cmr/m/n' instead -(Font) for symbol `textasciigrave' on input line 75. +(Font) for symbol `textasciigrave' on input line 86. -[2 <./chemCal-002.pdf>] +[3 <./chemCal-002.pdf>] LaTeX Font Warning: Font shape `T1/aett/bx/n' undefined -(Font) using `T1/aett/m/n' instead on input line 106. +(Font) using `T1/aett/m/n' instead on input line 117. -[3] [4] (./chemCal.aux) +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <7> on input line 119. +LaTeX Font Info: External font `cmex10' loaded for size +(Font) <5> on input line 119. +[4] [5] (./chemCal.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) Here is how much of TeX's memory you used: - 3772 strings out of 94500 - 51588 string characters out of 1175772 + 3756 strings out of 94499 + 51475 string characters out of 1175813 97245 words of memory out of 1000000 - 6857 multiletter control sequences out of 10000+50000 - 29608 words of font info for 66 fonts, out of 500000 for 2000 + 6853 multiletter control sequences out of 10000+50000 + 22302 words of font info for 54 fonts, out of 500000 for 2000 580 hyphenation exceptions out of 8191 - 35i,8n,21p,255b,279s stack positions out of 1500i,500n,5000p,200000b,5000s + 35i,7n,21p,255b,283s stack positions out of 1500i,500n,5000p,200000b,5000s PDF statistics: - 95 PDF objects out of 300000 + 93 PDF objects out of 300000 12 named destinations out of 131072 27 words of extra memory for PDF output out of 65536 -</usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmex10.pfb></usr/share/texmf-t -etex/fonts/type1/bluesky/cm/cmsy10.pfb></usr/share/texmf-tetex/fonts/type1/blue -sky/cm/cmmi5.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmmi7.pfb></usr -/share/texmf-tetex/fonts/type1/bluesky/cm/cmmi10.pfb></usr/share/texmf-tetex/fo -nts/type1/bluesky/cm/cmtt12.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/ -cmbx12.pfb> </var/cache/fonts/pk/ljfour/jknappen/tc/tcrm1000.600pk></usr/share/ -texmf-tetex/fonts/type1/bluesky/cm/cmtt8.pfb></usr/share/texmf-tetex/fonts/type -1/bluesky/cm/cmr8.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmr6.pfb>< -/usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmsltt10.pfb></usr/share/texmf-te -tex/fonts/type1/bluesky/cm/cmr7.pfb></usr/share/texmf-tetex/fonts/type1/bluesky -/cm/cmtt10.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmr10.pfb></usr/s -hare/texmf-tetex/fonts/type1/bluesky/cm/cmr12.pfb></usr/share/texmf-tetex/fonts -/type1/bluesky/cm/cmr17.pfb> -Output written on chemCal.pdf (4 pages, 133895 bytes). +</usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmr5.pfb></usr/share/texmf-tet +ex/fonts/type1/bluesky/cm/cmex10.pfb></usr/share/texmf-tetex/fonts/type1/bluesk +y/cm/cmsy10.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmmi5.pfb></usr/ +share/texmf-tetex/fonts/type1/bluesky/cm/cmmi7.pfb></usr/share/texmf-tetex/font +s/type1/bluesky/cm/cmr7.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmmi +10.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmtt12.pfb></usr/share/te +xmf-tetex/fonts/type1/bluesky/cm/cmbx12.pfb> </var/cache/fonts/pk/ljfour/jknapp +en/tc/tcrm1000.600pk></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmsltt10.pf +b></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmtt10.pfb></usr/share/texmf-t +etex/fonts/type1/bluesky/cm/cmr10.pfb></usr/share/texmf-tetex/fonts/type1/blues +ky/cm/cmr12.pfb></usr/share/texmf-tetex/fonts/type1/bluesky/cm/cmr17.pfb> +Output written on chemCal.pdf (5 pages, 123681 bytes). diff --git a/inst/doc/chemCal.pdf b/inst/doc/chemCal.pdf Binary files differindex 45a50eb..027e053 100644 --- a/inst/doc/chemCal.pdf +++ b/inst/doc/chemCal.pdf 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., |