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authorranke <ranke@5fad18fb-23f0-0310-ab10-e59a3bee62b4>2006-05-23 15:24:58 +0000
committerranke <ranke@5fad18fb-23f0-0310-ab10-e59a3bee62b4>2006-05-23 15:24:58 +0000
commit3b3d6dfc88c4b8b6475147a3afb5258a5fc82fa5 (patch)
tree4aeecbfa8cde4ccde4ab8145e74095e6df73f1d8 /inst
parentf381f9a6a8a47b89ec25cd627833a7248da7932b (diff)
First version published on my website.
git-svn-id: http://kriemhild.uft.uni-bremen.de/svn/chemCal@14 5fad18fb-23f0-0310-ab10-e59a3bee62b4
Diffstat (limited to 'inst')
-rw-r--r--inst/doc/Rplots.ps2499
-rw-r--r--inst/doc/chemCal-001.eps2126
-rw-r--r--inst/doc/chemCal-001.pdf3118
-rw-r--r--inst/doc/chemCal-002.eps288
-rw-r--r--inst/doc/chemCal-002.pdf275
-rw-r--r--inst/doc/chemCal.Rnw70
-rw-r--r--inst/doc/chemCal.aux1
-rw-r--r--inst/doc/chemCal.log131
-rw-r--r--inst/doc/chemCal.pdfbin107447 -> 133965 bytes
-rw-r--r--inst/doc/chemCal.tex89
10 files changed, 4709 insertions, 3888 deletions
diff --git a/inst/doc/Rplots.ps b/inst/doc/Rplots.ps
index 654b7c3..c5e68ec 100644
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diff --git a/inst/doc/chemCal.Rnw b/inst/doc/chemCal.Rnw
index 77888b4..afa5ad7 100644
--- a/inst/doc/chemCal.Rnw
+++ b/inst/doc/chemCal.Rnw
@@ -1,9 +1,5 @@
\documentclass[a4paper]{article}
%\VignetteIndexEntry{Short manual for the chemCal package}
-\newcommand{\chemCal}{{\tt chemCal}}
-\newcommand{\calplot}{{\tt calplot}}
-\newcommand{\calpredict}{{\tt calpredict}}
-\newcommand{\R}{{\tt R}}
\usepackage{hyperref}
\title{Basic calibration functions for analytical chemistry}
@@ -12,24 +8,15 @@
\begin{document}
\maketitle
-The \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 could be heavily improved if the
-inverse prediction method given in \cite{massart97} would be implemented,
-since it also covers the case of weighted regression.
-
-At the moment, the package consists of three functions, working
-on univariate linear models of class \texttt{lm} or \texttt{rlm}.
-
When calibrating an analytical method, the first task is to generate
-a suitable model. If we want to use the \chemCal{} functions, we
-will have to restrict ourselves to univariate, possibly weighted, linear
-regression so far.
-
-For the weighted case, the function \code{predict.lm} had to be
-rewritten, in order to allow for weights for the x values used to
-predict the y values.
+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.
Once such a model has been created, the calibration can be graphically
shown by using the \texttt{calplot} function:
@@ -38,26 +25,46 @@ shown by using the \texttt{calplot} function:
library(chemCal)
data(massart97ex3)
attach(massart97ex3)
-m <- lm(y ~ x, w = rep(0.01,length(x)))
-calplot(m)
+m0 <- lm(y ~ x)
+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
+
+<<>>=
+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)
@
-This is a reproduction of Example 8 in \cite{massart97}. We can
-see the influence of the weighted regression on the confidence
-and prediction bands of the calibration.
+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, 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.
-\section*{Theory}
+\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$:
@@ -65,7 +72,8 @@ 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) }}
+ {{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
@@ -85,9 +93,9 @@ $y_i$, 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
+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} +
diff --git a/inst/doc/chemCal.aux b/inst/doc/chemCal.aux
index 20bfc98..0eb51cc 100644
--- a/inst/doc/chemCal.aux
+++ b/inst/doc/chemCal.aux
@@ -14,5 +14,4 @@
\citation{massart97}
\citation{massart97}
\citation{massart97}
-\citation{massart97}
\bibcite{massart97}{1}
diff --git a/inst/doc/chemCal.log b/inst/doc/chemCal.log
index 86ecc8e..26ebd4a 100644
--- a/inst/doc/chemCal.log
+++ b/inst/doc/chemCal.log
@@ -1,4 +1,4 @@
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+This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) (format=pdflatex 2006.4.8) 23 MAY 2006 16:51
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File: ts1cmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions
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Package: nameref 2003/12/03 v2.21 Cross-referencing by name of section
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diff --git a/inst/doc/chemCal.pdf b/inst/doc/chemCal.pdf
index 5c6b1ea..bee18f0 100644
--- a/inst/doc/chemCal.pdf
+++ b/inst/doc/chemCal.pdf
Binary files differ
diff --git a/inst/doc/chemCal.tex b/inst/doc/chemCal.tex
index a9e8495..8887496 100644
--- a/inst/doc/chemCal.tex
+++ b/inst/doc/chemCal.tex
@@ -1,9 +1,5 @@
\documentclass[a4paper]{article}
%\VignetteIndexEntry{Short manual for the chemCal package}
-\newcommand{\chemCal}{{\tt chemCal}}
-\newcommand{\calplot}{{\tt calplot}}
-\newcommand{\calpredict}{{\tt calpredict}}
-\newcommand{\R}{{\tt R}}
\usepackage{hyperref}
\title{Basic calibration functions for analytical chemistry}
@@ -13,20 +9,15 @@
\begin{document}
\maketitle
-The \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 could be heavily improved if the
-inverse prediction method given in \cite{massart97} would be implemented,
-since it also covers the case of weighted regression.
-
-At the moment, the package only consists of two functions, working
-on univariate linear models of class \texttt{lm} or \texttt{rlm}.
-
When calibrating an analytical method, the first task is to generate
-a suitable model. If we want to use the \chemCal{} functions, we
-will have to restrict ourselves to univariate, possibly weighted, linear
-regression so far.
+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.
Once such a model has been created, the calibration can be graphically
shown by using the \texttt{calplot} function:
@@ -36,20 +27,39 @@ shown by using the \texttt{calplot} function:
> library(chemCal)
> data(massart97ex3)
> attach(massart97ex3)
-> yx <- split(y, factor(x))
+> m0 <- lm(y ~ x)
+> 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}
+> 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)
\end{Sinput}
\end{Schunk}
-\includegraphics{chemCal-001}
-This is a reproduction of Example 8 in \cite{massart97}. We can
-see the influence of the weighted regression on the confidence
-and prediction bands of the calibration.
+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:
@@ -63,13 +73,29 @@ $Prediction
[1] 5.865367
$`Standard Error`
-[1] 0.7288138
+[1] 0.892611
+
+$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] 2.023511
+[1] 7.855012
$`Confidence Limits`
-[1] 3.841856 7.888878
+[1] 36.20523 51.91526
\end{Soutput}
\end{Schunk}
@@ -77,7 +103,7 @@ 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.
-\section*{Theory}
+\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$:
@@ -85,7 +111,8 @@ 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) }}
+ {{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
@@ -105,9 +132,9 @@ $y_i$, 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
+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} +

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