From 73e650114af77582238abf5273e63005e0b2287e Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Mon, 6 Mar 2017 17:00:48 +0100 Subject: Static documentation now built by pkgdown::build_site() --- docs/articles/chemCal.Rnw | 130 + docs/articles/index.html | 98 + docs/authors.html | 100 + docs/calplot.lm-2.png | Bin 21681 -> 0 bytes docs/calplot.lm.html | 169 -- docs/chemCal-package.html | 99 - docs/css/bootstrap-responsive.css | 815 ----- docs/css/bootstrap-responsive.min.css | 9 - docs/css/bootstrap.css | 4983 ------------------------------- docs/css/bootstrap.min.css | 9 - docs/css/highlight.css | 28 - docs/css/staticdocs.css | 25 - docs/din32645-2.png | Bin 19858 -> 0 bytes docs/din32645.html | 188 -- docs/img/glyphicons-halflings-white.png | Bin 8777 -> 0 bytes docs/img/glyphicons-halflings.png | Bin 13826 -> 0 bytes docs/index.html | 146 +- docs/inverse.predict.html | 204 -- docs/jquery.sticky-kit.min.js | 9 + docs/js/bootstrap.js | 1825 ----------- docs/js/bootstrap.min.js | 6 - docs/link.svg | 12 + docs/lod.html | 199 -- docs/loq.html | 191 -- docs/massart97ex1.html | 102 - docs/massart97ex3-5.png | Bin 16419 -> 0 bytes docs/massart97ex3.html | 194 -- docs/pkgdown.css | 113 + docs/pkgdown.js | 8 + docs/reference.html | 118 - docs/reference/calplot-2.png | Bin 0 -> 21681 bytes docs/reference/calplot.lm.html | 177 ++ docs/reference/chemCal-package.html | 115 + docs/reference/din32645-2.png | Bin 0 -> 19858 bytes docs/reference/din32645.html | 175 ++ docs/reference/index.html | 146 + docs/reference/inverse.predict.html | 211 ++ docs/reference/lod.html | 210 ++ docs/reference/loq.html | 205 ++ docs/reference/massart97ex1.html | 118 + docs/reference/massart97ex3-5.png | Bin 0 -> 16419 bytes docs/reference/massart97ex3.html | 188 ++ docs/vignettes/chemCal.pdf | Bin 165858 -> 0 bytes 43 files changed, 2093 insertions(+), 9232 deletions(-) create mode 100644 docs/articles/chemCal.Rnw create mode 100644 docs/articles/index.html create mode 100644 docs/authors.html delete mode 100644 docs/calplot.lm-2.png delete mode 100644 docs/calplot.lm.html delete mode 100644 docs/chemCal-package.html delete mode 100644 docs/css/bootstrap-responsive.css delete mode 100644 docs/css/bootstrap-responsive.min.css delete mode 100644 docs/css/bootstrap.css delete mode 100644 docs/css/bootstrap.min.css delete mode 100644 docs/css/highlight.css delete mode 100644 docs/css/staticdocs.css delete mode 100644 docs/din32645-2.png delete mode 100644 docs/din32645.html delete mode 100644 docs/img/glyphicons-halflings-white.png delete mode 100644 docs/img/glyphicons-halflings.png delete mode 100644 docs/inverse.predict.html create mode 100644 docs/jquery.sticky-kit.min.js delete mode 100644 docs/js/bootstrap.js delete mode 100644 docs/js/bootstrap.min.js create mode 100644 docs/link.svg delete mode 100644 docs/lod.html delete mode 100644 docs/loq.html delete mode 100644 docs/massart97ex1.html delete mode 100644 docs/massart97ex3-5.png delete mode 100644 docs/massart97ex3.html create mode 100644 docs/pkgdown.css create mode 100644 docs/pkgdown.js delete mode 100644 docs/reference.html create mode 100644 docs/reference/calplot-2.png create mode 100644 docs/reference/calplot.lm.html create mode 100644 docs/reference/chemCal-package.html create mode 100644 docs/reference/din32645-2.png create mode 100644 docs/reference/din32645.html create mode 100644 docs/reference/index.html create mode 100644 docs/reference/inverse.predict.html create mode 100644 docs/reference/lod.html create mode 100644 docs/reference/loq.html create mode 100644 docs/reference/massart97ex1.html create mode 100644 docs/reference/massart97ex3-5.png create mode 100644 docs/reference/massart97ex3.html delete mode 100644 docs/vignettes/chemCal.pdf (limited to 'docs') diff --git a/docs/articles/chemCal.Rnw b/docs/articles/chemCal.Rnw new file mode 100644 index 0000000..30e0331 --- /dev/null +++ b/docs/articles/chemCal.Rnw @@ -0,0 +1,130 @@ +\documentclass[a4paper]{article} +%\VignetteIndexEntry{Short manual for the chemCal package} +\usepackage{hyperref} + +\title{Basic calibration functions for analytical chemistry} +\author{Johannes Ranke} + +\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/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 +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: + +<>= +library(chemCal) +data(massart97ex3) +m0 <- lm(y ~ x, data = massart97ex3) +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: + +<>= +plot(m0,which=3) +@ + +Therefore, in Example 8 in \cite{massart97} weighted regression +is proposed which can be reproduced by + +<<>>= +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) +@ + +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, 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/docs/articles/index.html b/docs/articles/index.html new file mode 100644 index 0000000..5c6fdad --- /dev/null +++ b/docs/articles/index.html @@ -0,0 +1,98 @@ + + + + + + + + +Articles • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
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Vignette reference version 0.1-37.9000

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All vignettes

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Developed by Johannes Ranke.

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Site built with pkgdown.

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+ + + diff --git a/docs/authors.html b/docs/authors.html new file mode 100644 index 0000000..546e902 --- /dev/null +++ b/docs/authors.html @@ -0,0 +1,100 @@ + + + + + + + + +Authors • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
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Authors

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    Johannes Ranke. Author, maintainer, copyright holder. +

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Developed by Johannes Ranke.

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Site built with pkgdown.

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+ + + diff --git a/docs/calplot.lm-2.png b/docs/calplot.lm-2.png deleted file mode 100644 index 7e40a4b..0000000 Binary files a/docs/calplot.lm-2.png and /dev/null differ diff --git a/docs/calplot.lm.html b/docs/calplot.lm.html deleted file mode 100644 index 07cacd8..0000000 --- a/docs/calplot.lm.html +++ /dev/null @@ -1,169 +0,0 @@ - - - - -calplot. chemCal 0.1-37 - - - - - - - - - - - - - - - -
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Plot calibration graphs from univariate linear models

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Usage

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calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
-    xlab = "Concentration", ylab = "Response", alpha=0.05, varfunc = NULL)
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Arguments

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object
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- A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1. -
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xlim
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ylim
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xlab
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- The label of the x axis. -
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ylab
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- The label of the y axis. -
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alpha
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- The error tolerance level for the confidence and prediction bands. Note that this - includes both tails of the Gaussian distribution, unlike the alpha and beta parameters - used in lod (see note below). -
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varfunc
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- The variance function for generating the weights in the model. - Currently, this argument is ignored (see note below). -
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Description

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Produce graphics of calibration data, the fitted model as well - as confidence, and, for unweighted regression, prediction bands.

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Value

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- A plot of the calibration data, of your fitted model as well as lines showing - the confidence limits. Prediction limits are only shown for models from - unweighted regression. -

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Note

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Prediction bands for models from weighted linear regression require weights - for the data, for which responses should be predicted. Prediction intervals - using weights e.g. from a variance function are currently not supported by - the internally used function predict.lm, therefore, - calplot does not draw prediction bands for such models.

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It is possible to compare the calplot prediction bands with the - lod values if the lod() alpha and beta parameters are - half the value of the calplot() alpha parameter.

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Examples

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data(massart97ex3)
-m <- lm(y ~ x, data = massart97ex3)
-calplot(m)

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Author

- - Johannes Ranke - jranke@uni-bremen.de - http://www.uft.uni-bremen.de/chemie/ranke - - -
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- - \ No newline at end of file diff --git a/docs/chemCal-package.html b/docs/chemCal-package.html deleted file mode 100644 index 56a636c..0000000 --- a/docs/chemCal-package.html +++ /dev/null @@ -1,99 +0,0 @@ - - - - -chemCal-package. chemCal 0.1-37 - - - - - - - - - - - - - - - -
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- Calibration functions for analytical chemistry -

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Description

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See ../DESCRIPTION

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Details

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There is a package vignette located in ../doc/chemCal.pdf.

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Author

- - Author and Maintainer: Johannes Ranke <jranke@uni-bremen.de> - - -
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- - \ No newline at end of file diff --git a/docs/css/bootstrap-responsive.css b/docs/css/bootstrap-responsive.css deleted file mode 100644 index 06e55c0..0000000 --- a/docs/css/bootstrap-responsive.css +++ /dev/null @@ -1,815 +0,0 @@ -/*! - * Bootstrap Responsive v2.0.4 - * - * Copyright 2012 Twitter, Inc - * Licensed under the Apache License v2.0 - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Designed and built with all the love in the world @twitter by @mdo and @fat. - */ - -.clearfix { - *zoom: 1; -} - -.clearfix:before, -.clearfix:after { - display: table; - content: ""; -} - -.clearfix:after { - clear: both; -} - -.hide-text { - font: 0/0 a; - color: transparent; - text-shadow: none; - background-color: transparent; - border: 0; -} - -.input-block-level { - display: block; - width: 100%; - min-height: 28px; - -webkit-box-sizing: border-box; - -moz-box-sizing: border-box; - -ms-box-sizing: border-box; - box-sizing: border-box; -} - -.hidden { - display: none; - visibility: 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-moz-border-radius: 0; - border-radius: 0; -} - -.btn-group > .btn:first-child { - margin-left: 0; - -webkit-border-bottom-left-radius: 4px; - border-bottom-left-radius: 4px; - -webkit-border-top-left-radius: 4px; - border-top-left-radius: 4px; - -moz-border-radius-bottomleft: 4px; - -moz-border-radius-topleft: 4px; -} - -.btn-group > .btn:last-child, -.btn-group > .dropdown-toggle { - -webkit-border-top-right-radius: 4px; - border-top-right-radius: 4px; - -webkit-border-bottom-right-radius: 4px; - border-bottom-right-radius: 4px; - -moz-border-radius-topright: 4px; - -moz-border-radius-bottomright: 4px; -} - -.btn-group > .btn.large:first-child { - margin-left: 0; - -webkit-border-bottom-left-radius: 6px; - border-bottom-left-radius: 6px; - -webkit-border-top-left-radius: 6px; - border-top-left-radius: 6px; - -moz-border-radius-bottomleft: 6px; - -moz-border-radius-topleft: 6px; -} - -.btn-group > .btn.large:last-child, -.btn-group > .large.dropdown-toggle { - 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#e5e5e5}.carousel{position:relative;margin-bottom:18px;line-height:1}.carousel-inner{position:relative;width:100%;overflow:hidden}.carousel .item{position:relative;display:none;-webkit-transition:.6s ease-in-out left;-moz-transition:.6s ease-in-out left;-ms-transition:.6s ease-in-out left;-o-transition:.6s ease-in-out left;transition:.6s ease-in-out left}.carousel .item>img{display:block;line-height:1}.carousel .active,.carousel .next,.carousel .prev{display:block}.carousel .active{left:0}.carousel .next,.carousel .prev{position:absolute;top:0;width:100%}.carousel .next{left:100%}.carousel .prev{left:-100%}.carousel .next.left,.carousel .prev.right{left:0}.carousel .active.left{left:-100%}.carousel .active.right{left:100%}.carousel-control{position:absolute;top:40%;left:15px;width:40px;height:40px;margin-top:-20px;font-size:60px;font-weight:100;line-height:30px;color:#fff;text-align:center;background:#222;border:3px solid #fff;-webkit-border-radius:23px;-moz-border-radius:23px;border-radius:23px;opacity:.5;filter:alpha(opacity=50)}.carousel-control.right{right:15px;left:auto}.carousel-control:hover{color:#fff;text-decoration:none;opacity:.9;filter:alpha(opacity=90)}.carousel-caption{position:absolute;right:0;bottom:0;left:0;padding:10px 15px 5px;background:#333;background:rgba(0,0,0,0.75)}.carousel-caption h4,.carousel-caption p{color:#fff}.hero-unit{padding:60px;margin-bottom:30px;background-color:#eee;-webkit-border-radius:6px;-moz-border-radius:6px;border-radius:6px}.hero-unit h1{margin-bottom:0;font-size:60px;line-height:1;letter-spacing:-1px;color:inherit}.hero-unit p{font-size:18px;font-weight:200;line-height:27px;color:inherit}.pull-right{float:right}.pull-left{float:left}.hide{display:none}.show{display:block}.invisible{visibility:hidden} diff --git a/docs/css/highlight.css b/docs/css/highlight.css deleted file mode 100644 index cd3ead6..0000000 --- a/docs/css/highlight.css +++ /dev/null @@ -1,28 +0,0 @@ -/* Syntax highlighting ---------------------------------------------------- */ - -pre .input { - border-left: 3px solid #ccc; - padding-left: 0.5em; -} -pre .output { - background-color: #eee; -} - -.number {color:rgb(21,20,181);} -.functioncall {color:#264D66 ;} -.string {color:#375D81 ;} -.keyword {font-weight:bolder ;color:black;} -.argument {color:#264D66 ;} -.comment {color: #4C886B;} -.formalargs {color: #264D66;} -.eqformalargs {color:#264D66;} -.slot {font-style:italic;} -.symbol {color:black ;} -.prompt {color:black ;} - -pre img { - background-color: #fff; - border: 1px solid #ccc; - display: block; - margin: 0.5em auto 0.5em auto; -} diff --git a/docs/css/staticdocs.css b/docs/css/staticdocs.css deleted file mode 100644 index 15d7408..0000000 --- a/docs/css/staticdocs.css +++ /dev/null @@ -1,25 +0,0 @@ -h2 {padding-top: 20px} - -.icon img { - float: right; - border: 1px solid #ccc; -} -.index .internal {display: none;} -ul.index li {margin-bottom: 0.5em; clear: both;} - -footer { - margin-top: 45px; - padding: 35px 0 36px; - border-top: 1px solid #e5e5e5; -} -footer p { - margin-bottom: 0; - color: #555; -} - -.sidebar h2 { - font-size: 1.1em; - padding-top: 0.5em; -} - -.sidebar li {margin-bottom: 0.5em;} diff --git a/docs/din32645-2.png b/docs/din32645-2.png deleted file mode 100644 index 1d1e8ab..0000000 Binary files a/docs/din32645-2.png and /dev/null differ diff --git a/docs/din32645.html b/docs/din32645.html deleted file mode 100644 index 8266a10..0000000 --- a/docs/din32645.html +++ /dev/null @@ -1,188 +0,0 @@ - - - - -din32645. chemCal 0.1-37 - - - - - - - - - - - - - - - -
-
-
- chemCal 0.1-37 -
- -
-
-
-
- - -
-
- -
- -

Calibration data from DIN 32645

- -
-
-

Usage

- 
data(din32645)
- -
-

Description

- -

Sample dataset to test the package.

- -
- -
-

Format

- -

A dataframe containing 10 rows of x and y values.

- -
- -
-

References

- -

DIN 32645 (equivalent to ISO 11843), Beuth Verlag, Berlin, 1994

- -

Dintest. Plugin for MS Excel for evaluations of calibration data. Written - by Georg Schmitt, University of Heidelberg. Formerly available from - the Website of the University of Heidelberg.

- -

Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including - detection and quantification capabilities (IUPAC Recommendations 1995). - Analytica Chimica Acta 391, 105 - 126.

- -
- -

Examples

- 
data(din32645)
-m <- lm(y ~ x, data = din32645)
-calplot(m)

-

-

-## Prediction of x with confidence interval
-(prediction <- inverse.predict(m, 3500, alpha = 0.01))

-
$Prediction
-[1] 0.1054792
-
-$`Standard Error`
-[1] 0.02215619
-
-$Confidence
-[1] 0.07434261
-
-$`Confidence Limits`
-[1] 0.03113656 0.17982178
-
-

-

-# This should give 0.07434 according to test data from Dintest, which 
-# was collected from Procontrol 3.1 (isomehr GmbH) in this case
-round(prediction$Confidence,5)

-
[1] 0.07434
-

-

-## Critical value:
-(crit <- lod(m, alpha = 0.01, beta = 0.5))

-
$x
-[1] 0.0698127
-
-$y
-       1 
-3155.393 
-
-

-

-# According to DIN 32645, we should get 0.07 for the critical value
-# (decision limit, "Nachweisgrenze")
-round(crit$x, 2)

-
[1] 0.07
-

-
# and according to Dintest test data, we should get 0.0698 from
-round(crit$x, 4)

-
[1] 0.0698
-

-

-## Limit of detection (smallest detectable value given alpha and beta)
-# In German, the smallest detectable value is the "Erfassungsgrenze", and we
-# should get 0.14 according to DIN, which we achieve by using the method 
-# described in it:
-lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
-round(lod.din$x, 2)

-
[1] 0.14
-

-

-## Limit of quantification
-# This accords to the test data coming with the test data from Dintest again, 
-# except for the last digits of the value cited for Procontrol 3.1 (0.2121)
-(loq <- loq(m, alpha = 0.01))

-
$x
-[1] 0.2119575
-
-$y
-       1 
-4528.787 
-
-

-
round(loq$x,4)

-
[1] 0.212
-

-

-# A similar value is obtained using the approximation 
-# LQ = 3.04 * LC (Currie 1999, p. 120)
-3.04 * lod(m,alpha = 0.01, beta = 0.5)$x

-
[1] 0.2122306
-
-
-
- - - - - -
-
- - -
- - \ No newline at end of file diff --git a/docs/img/glyphicons-halflings-white.png b/docs/img/glyphicons-halflings-white.png deleted file mode 100644 index 3bf6484..0000000 Binary files a/docs/img/glyphicons-halflings-white.png and /dev/null differ diff --git a/docs/img/glyphicons-halflings.png b/docs/img/glyphicons-halflings.png deleted file mode 100644 index 79bc568..0000000 Binary files a/docs/img/glyphicons-halflings.png and /dev/null differ diff --git a/docs/index.html b/docs/index.html index 7aeb5e9..c31f638 100644 --- a/docs/index.html +++ b/docs/index.html @@ -1,81 +1,91 @@ - - - -Home. chemCal 0.1-37 + + + + + - - - - - - - - + + + - - - - - - -
-
-
- chemCal 0.1-37 -
- -
+ + +
+
+ - -
-
- -
-
-
- Simple functions for plotting linear -calibration functions and estimating standard errors for measurements -according to the Handbook of Chemometrics and Qualimetrics: Part A -by Massart et al. There are also functions estimating the limit -of detection (LOD) and limit of quantification (LOQ). -The functions work on model objects from - optionally weighted - linear -regression (lm) or robust linear regression ('rlm' from the 'MASS' package). -
+
+
+
+

+ chemCal

-
-

Vignettes

- -

Authors

- +

Static documentation of this R package can be found unter http://jranke.github.io/chemCal

+
+ + - -
+ + +
+

Developed by Johannes Ranke.

+
+ +
+

Site built with pkgdown.

+
+
-
+
+ - \ No newline at end of file + diff --git a/docs/inverse.predict.html b/docs/inverse.predict.html deleted file mode 100644 index 4d66549..0000000 --- a/docs/inverse.predict.html +++ /dev/null @@ -1,204 +0,0 @@ - - - - -inverse.predict. chemCal 0.1-37 - - - - - - - - - - - - - - - -
-
-
- chemCal 0.1-37 -
- -
-
-
-
- - -
-
- -
- -

Predict x from y for a linear calibration

- -
-
-

Usage

- 
inverse.predict(object, newdata, ...,
-  ws, alpha=0.05, var.s = "auto")
- -

Arguments

-
-
object
-
- A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1. -
-
newdata
-
- A vector of observed y values for one sample. -
-
...
-
- Placeholder for further arguments that might be needed by - future implementations. -
-
ws
-
- The weight attributed to the sample. This argument is obligatory - if object has weights. -
-
alpha
-
- The error tolerance level for the confidence interval to be reported. -
-
var.s
-
- The estimated variance of the sample measurements. The default is to take - the residual standard error from the calibration and to adjust it - using ws, if applicable. This means that var.s - overrides ws. -
-
- -
-

Value

- -

- A list containing the predicted x value, its standard error and a - confidence interval. -

- -
- -
-

Description

- -

This function predicts x values using a univariate linear model that has been - generated for the purpose of calibrating a measurement method. Prediction - intervals are given at the specified confidence level. - The calculation method was taken from Massart et al. (1997). In particular, - Equations 8.26 and 8.28 were combined in order to yield a general treatment - of inverse prediction for univariate linear models, taking into account - weights that have been used to create the linear model, and at the same - time providing the possibility to specify a precision in sample measurements - differing from the precision in standard samples used for the calibration. - This is elaborated in the package vignette.

- -
- -
-

Note

- -

The function was validated with examples 7 and 8 from Massart et al. (1997).

- -
- -
-

References

- -

Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., - Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, - p. 200

- -
- -

Examples

- 
# This is example 7 from Chapter 8 in Massart et al. (1997)
-data(massart97ex1)
-m <- lm(y ~ x, data = massart97ex1)
-inverse.predict(m, 15)        #  6.1 +- 4.9

-
$Prediction
-[1] 6.09381
-
-$`Standard Error`
-[1] 1.767278
-
-$Confidence
-[1] 4.906751
-
-$`Confidence Limits`
-[1]  1.187059 11.000561
-
-

-
inverse.predict(m, 90)        # 43.9 +- 4.9

-
$Prediction
-[1] 43.93983
-
-$`Standard Error`
-[1] 1.767747
-
-$Confidence
-[1] 4.908053
-
-$`Confidence Limits`
-[1] 39.03178 48.84788
-
-

-
inverse.predict(m, rep(90,5)) # 43.9 +- 3.2

-
$Prediction
-[1] 43.93983
-
-$`Standard Error`
-[1] 1.141204
-
-$Confidence
-[1] 3.168489
-
-$`Confidence Limits`
-[1] 40.77134 47.10832
-
-
-
-
- - - - - -
-
- - -
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'addClass' : 'removeClass']('collapse') - - return this - } - - , transition: function (method, startEvent, completeEvent) { - var that = this - , complete = function () { - if (startEvent.type == 'show') that.reset() - that.transitioning = 0 - that.$element.trigger(completeEvent) - } - - this.$element.trigger(startEvent) - - if (startEvent.isDefaultPrevented()) return - - this.transitioning = 1 - - this.$element[method]('in') - - $.support.transition && this.$element.hasClass('collapse') ? - this.$element.one($.support.transition.end, complete) : - complete() - } - - , toggle: function () { - this[this.$element.hasClass('in') ? 'hide' : 'show']() - } - - } - - - /* COLLAPSIBLE PLUGIN DEFINITION - * ============================== */ - - $.fn.collapse = function (option) { - return this.each(function () { - var $this = $(this) - , data = $this.data('collapse') - , options = typeof option == 'object' && option - if (!data) $this.data('collapse', (data = new Collapse(this, options))) - if (typeof option == 'string') data[option]() - }) - } - - $.fn.collapse.defaults = { - toggle: true - } - - $.fn.collapse.Constructor = Collapse - - - /* COLLAPSIBLE DATA-API - * ==================== */ - - $(function () { - $('body').on('click.collapse.data-api', '[data-toggle=collapse]', function ( e ) { - var $this = $(this), href - , target = $this.attr('data-target') - || e.preventDefault() - || (href = $this.attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '') //strip for ie7 - , option = $(target).data('collapse') ? 'toggle' : $this.data() - $(target).collapse(option) - }) - }) - -}(window.jQuery);/* ============================================================ - * bootstrap-dropdown.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#dropdowns - * ============================================================ - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ============================================================ */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* DROPDOWN CLASS DEFINITION - * ========================= */ - - var toggle = '[data-toggle="dropdown"]' - , Dropdown = function (element) { - var $el = $(element).on('click.dropdown.data-api', this.toggle) - $('html').on('click.dropdown.data-api', function () { - $el.parent().removeClass('open') - }) - } - - Dropdown.prototype = { - - constructor: Dropdown - - , toggle: function (e) { - var $this = $(this) - , $parent - , selector - , isActive - - if ($this.is('.disabled, :disabled')) return - - selector = $this.attr('data-target') - - if (!selector) { - selector = $this.attr('href') - selector = selector && selector.replace(/.*(?=#[^\s]*$)/, '') //strip for ie7 - } - - $parent = $(selector) - $parent.length || ($parent = $this.parent()) - - isActive = $parent.hasClass('open') - - clearMenus() - - if (!isActive) $parent.toggleClass('open') - - return false - } - - } - - function clearMenus() { - $(toggle).parent().removeClass('open') - } - - - /* DROPDOWN PLUGIN DEFINITION - * ========================== */ - - $.fn.dropdown = function (option) { - return this.each(function () { - var $this = $(this) - , data = $this.data('dropdown') - if (!data) $this.data('dropdown', (data = new Dropdown(this))) - if (typeof option == 'string') data[option].call($this) - }) - } - - $.fn.dropdown.Constructor = Dropdown - - - /* APPLY TO STANDARD DROPDOWN ELEMENTS - * =================================== */ - - $(function () { - $('html').on('click.dropdown.data-api', clearMenus) - $('body') - .on('click.dropdown', '.dropdown form', function (e) { e.stopPropagation() }) - .on('click.dropdown.data-api', toggle, Dropdown.prototype.toggle) - }) - -}(window.jQuery);/* ========================================================= - * bootstrap-modal.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#modals - * ========================================================= - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ========================================================= */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* MODAL CLASS DEFINITION - * ====================== */ - - var Modal = function (content, options) { - this.options = options - this.$element = $(content) - .delegate('[data-dismiss="modal"]', 'click.dismiss.modal', $.proxy(this.hide, this)) - } - - Modal.prototype = { - - constructor: Modal - - , toggle: function () { - return this[!this.isShown ? 'show' : 'hide']() - } - - , show: function () { - var that = this - , e = $.Event('show') - - this.$element.trigger(e) - - if (this.isShown || e.isDefaultPrevented()) return - - $('body').addClass('modal-open') - - this.isShown = true - - escape.call(this) - backdrop.call(this, function () { - var transition = $.support.transition && that.$element.hasClass('fade') - - if (!that.$element.parent().length) { - that.$element.appendTo(document.body) //don't move modals dom position - } - - that.$element - .show() - - if (transition) { - that.$element[0].offsetWidth // force reflow - } - - that.$element.addClass('in') - - transition ? - that.$element.one($.support.transition.end, function () { that.$element.trigger('shown') }) : - that.$element.trigger('shown') - - }) - } - - , hide: function (e) { - e && e.preventDefault() - - var that = this - - e = $.Event('hide') - - this.$element.trigger(e) - - if (!this.isShown || e.isDefaultPrevented()) return - - this.isShown = false - - $('body').removeClass('modal-open') - - escape.call(this) - - this.$element.removeClass('in') - - $.support.transition && this.$element.hasClass('fade') ? - hideWithTransition.call(this) : - hideModal.call(this) - } - - } - - - /* MODAL PRIVATE METHODS - * ===================== */ - - function hideWithTransition() { - var that = this - , timeout = setTimeout(function () { - that.$element.off($.support.transition.end) - hideModal.call(that) - }, 500) - - this.$element.one($.support.transition.end, function () { - clearTimeout(timeout) - hideModal.call(that) - }) - } - - function hideModal(that) { - this.$element - .hide() - .trigger('hidden') - - backdrop.call(this) - } - - function backdrop(callback) { - var that = this - , animate = this.$element.hasClass('fade') ? 'fade' : '' - - if (this.isShown && this.options.backdrop) { - var doAnimate = $.support.transition && animate - - this.$backdrop = $('
') - .appendTo(document.body) - - if (this.options.backdrop != 'static') { - this.$backdrop.click($.proxy(this.hide, this)) - } - - if (doAnimate) this.$backdrop[0].offsetWidth // force reflow - - this.$backdrop.addClass('in') - - doAnimate ? - this.$backdrop.one($.support.transition.end, callback) : - callback() - - } else if (!this.isShown && this.$backdrop) { - this.$backdrop.removeClass('in') - - $.support.transition && this.$element.hasClass('fade')? - this.$backdrop.one($.support.transition.end, $.proxy(removeBackdrop, this)) : - removeBackdrop.call(this) - - } else if (callback) { - callback() - } - } - - function removeBackdrop() { - this.$backdrop.remove() - this.$backdrop = null - } - - function escape() { - var that = this - if (this.isShown && this.options.keyboard) { - $(document).on('keyup.dismiss.modal', function ( e ) { - e.which == 27 && that.hide() - }) - } else if (!this.isShown) { - $(document).off('keyup.dismiss.modal') - } - } - - - /* MODAL PLUGIN DEFINITION - * ======================= */ - - $.fn.modal = function (option) { - return this.each(function () { - var $this = $(this) - , data = $this.data('modal') - , options = $.extend({}, $.fn.modal.defaults, $this.data(), typeof option == 'object' && option) - if (!data) $this.data('modal', (data = new Modal(this, options))) - if (typeof option == 'string') data[option]() - else if (options.show) data.show() - }) - } - - $.fn.modal.defaults = { - backdrop: true - , keyboard: true - , show: true - } - - $.fn.modal.Constructor = Modal - - - /* MODAL DATA-API - * ============== */ - - $(function () { - $('body').on('click.modal.data-api', '[data-toggle="modal"]', function ( e ) { - var $this = $(this), href - , $target = $($this.attr('data-target') || (href = $this.attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '')) //strip for ie7 - , option = $target.data('modal') ? 'toggle' : $.extend({}, $target.data(), $this.data()) - - e.preventDefault() - $target.modal(option) - }) - }) - -}(window.jQuery);/* =========================================================== - * bootstrap-tooltip.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#tooltips - * Inspired by the original jQuery.tipsy by Jason Frame - * =========================================================== - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ========================================================== */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* TOOLTIP PUBLIC CLASS DEFINITION - * =============================== */ - - var Tooltip = function (element, options) { - this.init('tooltip', element, options) - } - - Tooltip.prototype = { - - constructor: Tooltip - - , init: function (type, element, options) { - var eventIn - , eventOut - - this.type = type - this.$element = $(element) - this.options = this.getOptions(options) - this.enabled = true - - if (this.options.trigger != 'manual') { - eventIn = this.options.trigger == 'hover' ? 'mouseenter' : 'focus' - eventOut = this.options.trigger == 'hover' ? 'mouseleave' : 'blur' - this.$element.on(eventIn, this.options.selector, $.proxy(this.enter, this)) - this.$element.on(eventOut, this.options.selector, $.proxy(this.leave, this)) - } - - this.options.selector ? - (this._options = $.extend({}, this.options, { trigger: 'manual', selector: '' })) : - this.fixTitle() - } - - , getOptions: function (options) { - options = $.extend({}, $.fn[this.type].defaults, options, this.$element.data()) - - if (options.delay && typeof options.delay == 'number') { - options.delay = { - show: options.delay - , hide: options.delay - } - } - - return options - } - - , enter: function (e) { - var self = $(e.currentTarget)[this.type](this._options).data(this.type) - - if (!self.options.delay || !self.options.delay.show) return self.show() - - clearTimeout(this.timeout) - self.hoverState = 'in' - this.timeout = setTimeout(function() { - if (self.hoverState == 'in') self.show() - }, self.options.delay.show) - } - - , leave: function (e) { - var self = $(e.currentTarget)[this.type](this._options).data(this.type) - - if (this.timeout) clearTimeout(this.timeout) - if (!self.options.delay || !self.options.delay.hide) return self.hide() - - self.hoverState = 'out' - this.timeout = setTimeout(function() { - if (self.hoverState == 'out') self.hide() - }, self.options.delay.hide) - } - - , show: function () { - var $tip - , inside - , pos - , actualWidth - , actualHeight - , placement - , tp - - if (this.hasContent() && this.enabled) { - $tip = this.tip() - this.setContent() - - if (this.options.animation) { - $tip.addClass('fade') - } - - placement = typeof this.options.placement == 'function' ? - this.options.placement.call(this, $tip[0], this.$element[0]) : - this.options.placement - - inside = /in/.test(placement) - - $tip - .remove() - .css({ top: 0, left: 0, display: 'block' }) - .appendTo(inside ? this.$element : document.body) - - pos = this.getPosition(inside) - - actualWidth = $tip[0].offsetWidth - actualHeight = $tip[0].offsetHeight - - switch (inside ? placement.split(' ')[1] : placement) { - case 'bottom': - tp = {top: pos.top + pos.height, left: pos.left + pos.width / 2 - actualWidth / 2} - break - case 'top': - tp = {top: pos.top - actualHeight, left: pos.left + pos.width / 2 - actualWidth / 2} - break - case 'left': - tp = {top: pos.top + pos.height / 2 - actualHeight / 2, left: pos.left - actualWidth} - break - case 'right': - tp = {top: pos.top + pos.height / 2 - actualHeight / 2, left: pos.left + pos.width} - break - } - - $tip - .css(tp) - .addClass(placement) - .addClass('in') - } - } - - , isHTML: function(text) { - // html string detection logic adapted from jQuery - return typeof text != 'string' - || ( text.charAt(0) === "<" - && text.charAt( text.length - 1 ) === ">" - && text.length >= 3 - ) || /^(?:[^<]*<[\w\W]+>[^>]*$)/.exec(text) - } - - , setContent: function () { - var $tip = this.tip() - , title = this.getTitle() - - $tip.find('.tooltip-inner')[this.isHTML(title) ? 'html' : 'text'](title) - $tip.removeClass('fade in top bottom left right') - } - - , hide: function () { - var that = this - , $tip = this.tip() - - $tip.removeClass('in') - - function removeWithAnimation() { - var timeout = setTimeout(function () { - $tip.off($.support.transition.end).remove() - }, 500) - - $tip.one($.support.transition.end, function () { - clearTimeout(timeout) - $tip.remove() - }) - } - - $.support.transition && this.$tip.hasClass('fade') ? - removeWithAnimation() : - $tip.remove() - } - - , fixTitle: function () { - var $e = this.$element - if ($e.attr('title') || typeof($e.attr('data-original-title')) != 'string') { - $e.attr('data-original-title', $e.attr('title') || '').removeAttr('title') - } - } - - , hasContent: function () { - return this.getTitle() - } - - , getPosition: function (inside) { - return $.extend({}, (inside ? {top: 0, left: 0} : this.$element.offset()), { - width: this.$element[0].offsetWidth - , height: this.$element[0].offsetHeight - }) - } - - , getTitle: function () { - var title - , $e = this.$element - , o = this.options - - title = $e.attr('data-original-title') - || (typeof o.title == 'function' ? o.title.call($e[0]) : o.title) - - return title - } - - , tip: function () { - return this.$tip = this.$tip || $(this.options.template) - } - - , validate: function () { - if (!this.$element[0].parentNode) { - this.hide() - this.$element = null - this.options = null - } - } - - , enable: function () { - this.enabled = true - } - - , disable: function () { - this.enabled = false - } - - , toggleEnabled: function () { - this.enabled = !this.enabled - } - - , toggle: function () { - this[this.tip().hasClass('in') ? 'hide' : 'show']() - } - - } - - - /* TOOLTIP PLUGIN DEFINITION - * ========================= */ - - $.fn.tooltip = function ( option ) { - return this.each(function () { - var $this = $(this) - , data = $this.data('tooltip') - , options = typeof option == 'object' && option - if (!data) $this.data('tooltip', (data = new Tooltip(this, options))) - if (typeof option == 'string') data[option]() - }) - } - - $.fn.tooltip.Constructor = Tooltip - - $.fn.tooltip.defaults = { - animation: true - , placement: 'top' - , selector: false - , template: '
' - , trigger: 'hover' - , title: '' - , delay: 0 - } - -}(window.jQuery); -/* =========================================================== - * bootstrap-popover.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#popovers - * =========================================================== - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * =========================================================== */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* POPOVER PUBLIC CLASS DEFINITION - * =============================== */ - - var Popover = function ( element, options ) { - this.init('popover', element, options) - } - - - /* NOTE: POPOVER EXTENDS BOOTSTRAP-TOOLTIP.js - ========================================== */ - - Popover.prototype = $.extend({}, $.fn.tooltip.Constructor.prototype, { - - constructor: Popover - - , setContent: function () { - var $tip = this.tip() - , title = this.getTitle() - , content = this.getContent() - - $tip.find('.popover-title')[this.isHTML(title) ? 'html' : 'text'](title) - $tip.find('.popover-content > *')[this.isHTML(content) ? 'html' : 'text'](content) - - $tip.removeClass('fade top bottom left right in') - } - - , hasContent: function () { - return this.getTitle() || this.getContent() - } - - , getContent: function () { - var content - , $e = this.$element - , o = this.options - - content = $e.attr('data-content') - || (typeof o.content == 'function' ? o.content.call($e[0]) : o.content) - - return content - } - - , tip: function () { - if (!this.$tip) { - this.$tip = $(this.options.template) - } - return this.$tip - } - - }) - - - /* POPOVER PLUGIN DEFINITION - * ======================= */ - - $.fn.popover = function (option) { - return this.each(function () { - var $this = $(this) - , data = $this.data('popover') - , options = typeof option == 'object' && option - if (!data) $this.data('popover', (data = new Popover(this, options))) - if (typeof option == 'string') data[option]() - }) - } - - $.fn.popover.Constructor = Popover - - $.fn.popover.defaults = $.extend({} , $.fn.tooltip.defaults, { - placement: 'right' - , content: '' - , template: '

' - }) - -}(window.jQuery);/* ============================================================= - * bootstrap-scrollspy.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#scrollspy - * ============================================================= - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ============================================================== */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* SCROLLSPY CLASS DEFINITION - * ========================== */ - - function ScrollSpy( element, options) { - var process = $.proxy(this.process, this) - , $element = $(element).is('body') ? $(window) : $(element) - , href - this.options = $.extend({}, $.fn.scrollspy.defaults, options) - this.$scrollElement = $element.on('scroll.scroll.data-api', process) - this.selector = (this.options.target - || ((href = $(element).attr('href')) && href.replace(/.*(?=#[^\s]+$)/, '')) //strip for ie7 - || '') + ' .nav li > a' - this.$body = $('body') - this.refresh() - this.process() - } - - ScrollSpy.prototype = { - - constructor: ScrollSpy - - , refresh: function () { - var self = this - , $targets - - this.offsets = $([]) - this.targets = $([]) - - $targets = this.$body - .find(this.selector) - .map(function () { - var $el = $(this) - , href = $el.data('target') || $el.attr('href') - , $href = /^#\w/.test(href) && $(href) - return ( $href - && href.length - && [[ $href.position().top, href ]] ) || null - }) - .sort(function (a, b) { return a[0] - b[0] }) - .each(function () { - self.offsets.push(this[0]) - self.targets.push(this[1]) - }) - } - - , process: function () { - var scrollTop = this.$scrollElement.scrollTop() + this.options.offset - , scrollHeight = this.$scrollElement[0].scrollHeight || this.$body[0].scrollHeight - , maxScroll = scrollHeight - this.$scrollElement.height() - , offsets = this.offsets - , targets = this.targets - , activeTarget = this.activeTarget - , i - - if (scrollTop >= maxScroll) { - return activeTarget != (i = targets.last()[0]) - && this.activate ( i ) - } - - for (i = offsets.length; i--;) { - activeTarget != targets[i] - && scrollTop >= offsets[i] - && (!offsets[i + 1] || scrollTop <= offsets[i + 1]) - && this.activate( targets[i] ) - } - } - - , activate: function (target) { - var active - , selector - - this.activeTarget = target - - $(this.selector) - .parent('.active') - .removeClass('active') - - selector = this.selector - + '[data-target="' + target + '"],' - + this.selector + '[href="' + target + '"]' - - active = $(selector) - .parent('li') - .addClass('active') - - if (active.parent('.dropdown-menu')) { - active = active.closest('li.dropdown').addClass('active') - } - - active.trigger('activate') - } - - } - - - /* SCROLLSPY PLUGIN DEFINITION - * =========================== */ - - $.fn.scrollspy = function ( option ) { - return this.each(function () { - var $this = $(this) - , data = $this.data('scrollspy') - , options = typeof option == 'object' && option - if (!data) $this.data('scrollspy', (data = new ScrollSpy(this, options))) - if (typeof option == 'string') data[option]() - }) - } - - $.fn.scrollspy.Constructor = ScrollSpy - - $.fn.scrollspy.defaults = { - offset: 10 - } - - - /* SCROLLSPY DATA-API - * ================== */ - - $(function () { - $('[data-spy="scroll"]').each(function () { - var $spy = $(this) - $spy.scrollspy($spy.data()) - }) - }) - -}(window.jQuery);/* ======================================================== - * bootstrap-tab.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#tabs - * ======================================================== - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ======================================================== */ - - -!function ($) { - - "use strict"; // jshint ;_; - - - /* TAB CLASS DEFINITION - * ==================== */ - - var Tab = function ( element ) { - this.element = $(element) - } - - Tab.prototype = { - - constructor: Tab - - , show: function () { - var $this = this.element - , $ul = $this.closest('ul:not(.dropdown-menu)') - , selector = $this.attr('data-target') - , previous - , $target - , e - - if (!selector) { - selector = $this.attr('href') - selector = selector && selector.replace(/.*(?=#[^\s]*$)/, '') //strip for ie7 - } - - if ( $this.parent('li').hasClass('active') ) return - - previous = $ul.find('.active a').last()[0] - - e = $.Event('show', { - relatedTarget: previous - }) - - $this.trigger(e) - - if (e.isDefaultPrevented()) return - - $target = $(selector) - - this.activate($this.parent('li'), $ul) - this.activate($target, $target.parent(), function () { - $this.trigger({ - type: 'shown' - , relatedTarget: previous - }) - }) - } - - , activate: function ( element, container, callback) { - var $active = container.find('> .active') - , transition = callback - && $.support.transition - && $active.hasClass('fade') - - function next() { - $active - .removeClass('active') - .find('> .dropdown-menu > .active') - .removeClass('active') - - element.addClass('active') - - if (transition) { - element[0].offsetWidth // reflow for transition - element.addClass('in') - } else { - element.removeClass('fade') - } - - if ( element.parent('.dropdown-menu') ) { - element.closest('li.dropdown').addClass('active') - } - - callback && callback() - } - - transition ? - $active.one($.support.transition.end, next) : - next() - - $active.removeClass('in') - } - } - - - /* TAB PLUGIN DEFINITION - * ===================== */ - - $.fn.tab = function ( option ) { - return this.each(function () { - var $this = $(this) - , data = $this.data('tab') - if (!data) $this.data('tab', (data = new Tab(this))) - if (typeof option == 'string') data[option]() - }) - } - - $.fn.tab.Constructor = Tab - - - /* TAB DATA-API - * ============ */ - - $(function () { - $('body').on('click.tab.data-api', '[data-toggle="tab"], [data-toggle="pill"]', function (e) { - e.preventDefault() - $(this).tab('show') - }) - }) - -}(window.jQuery);/* ============================================================= - * bootstrap-typeahead.js v2.0.4 - * http://twitter.github.com/bootstrap/javascript.html#typeahead - * ============================================================= - * Copyright 2012 Twitter, Inc. - * - * Licensed under the Apache License, Version 2.0 (the "License"); - * you may not use this file except in compliance with the License. - * You may obtain a copy of the License at - * - * http://www.apache.org/licenses/LICENSE-2.0 - * - * Unless required by applicable law or agreed to in writing, software - * distributed under the License is distributed on an "AS IS" BASIS, - * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. - * See the License for the specific language governing permissions and - * limitations under the License. - * ============================================================ */ - - -!function($){ - - "use strict"; // jshint ;_; - - - /* TYPEAHEAD PUBLIC CLASS DEFINITION - * ================================= */ - - var Typeahead = function (element, options) { - this.$element = $(element) - this.options = $.extend({}, $.fn.typeahead.defaults, options) - this.matcher = this.options.matcher || this.matcher - this.sorter = this.options.sorter || this.sorter - this.highlighter = this.options.highlighter || this.highlighter - this.updater = this.options.updater || this.updater - this.$menu = $(this.options.menu).appendTo('body') - this.source = this.options.source - this.shown = false - this.listen() - } - - Typeahead.prototype = { - - constructor: Typeahead - - , select: function () { - var val = this.$menu.find('.active').attr('data-value') - this.$element - .val(this.updater(val)) - .change() - return this.hide() - } - - , updater: function (item) { - return item - } - - , show: function () { - var pos = $.extend({}, this.$element.offset(), { - height: this.$element[0].offsetHeight - }) - - this.$menu.css({ - top: pos.top + pos.height - , left: pos.left - }) - - this.$menu.show() - this.shown = true - return this - } - - , hide: function () { - 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      ',item:'
      • '},a.fn.typeahead.Constructor=b,a(function(){a("body").on("focus.typeahead.data-api",'[data-provide="typeahead"]',function(b){var c=a(this);if(c.data("typeahead"))return;b.preventDefault(),c.typeahead(c.data())})})}(window.jQuery); \ No newline at end of file diff --git a/docs/link.svg b/docs/link.svg new file mode 100644 index 0000000..88ad827 --- /dev/null +++ b/docs/link.svg @@ -0,0 +1,12 @@ + + + + + + diff --git a/docs/lod.html b/docs/lod.html deleted file mode 100644 index e5eb135..0000000 --- a/docs/lod.html +++ /dev/null @@ -1,199 +0,0 @@ - - - - -lod. chemCal 0.1-37 - - - - - - - - - - - - - - - -
      -
      -
      - chemCal 0.1-37 -
      - -
      -
      -
      -
      - - -
      -
      - -
      - -

      Estimate a limit of detection (LOD)

      - -
      -
      -

      Usage

      - 
      lod(object, ..., alpha = 0.05, beta = 0.05, method = "default", tol = "default")
      - -

      Arguments

      -
      -
      object
      -
      - A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1, - optionally from a weighted regression. -
      -
      ...
      -
      - Placeholder for further arguments that might be needed by - future implementations. -
      -
      alpha
      -
      - The error tolerance for the decision limit (critical value). -
      -
      beta
      -
      - The error tolerance beta for the detection limit. -
      -
      method
      -
      - The “default” method uses a prediction interval at the LOD - for the estimation of the LOD, which obviously requires - iteration. This is described for example in Massart, p. 432 ff. - The “din” method uses the prediction interval at - x = 0 as an approximation. -
      -
      tol
      -
      - When the “default” method is used, the default tolerance - for the LOD on the x scale is the value of the smallest non-zero standard - divided by 1000. Can be set to a numeric value to override this. -
      -
      - -
      -

      Value

      - -

      - A list containig the corresponding x and y values of the estimated limit of - detection of a model used for calibration. -

      - -
      - -
      -

      Description

      - -

      The decision limit (German: Nachweisgrenze) is defined as the signal or - analyte concentration that is significantly different from the blank signal - with a first order error alpha (one-sided significance test). - The detection limit, or more precise, the minimum detectable value - (German: Erfassungsgrenze), is then defined as the signal or analyte - concentration where the probability that the signal is not detected although - the analyte is present (type II or false negative error), is beta (also a - one-sided significance test).

      - -
      - -
      -

      Note

      - -

      - The default values for alpha and beta are the ones recommended by IUPAC. - - The estimation of the LOD in terms of the analyte amount/concentration - xD from the LOD in the signal domain SD is done by simply inverting the - calibration function (i.e. assuming a known calibration function). - - The calculation of a LOD from weighted calibration models requires - a weights argument for the internally used predict.lm - function, which is currently not supported in R.

      - -
      - -
      -

      References

      - -

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., - Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, - Chapter 13.7.8

      - -

      J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and - Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. - Web edition.

      - -

      Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including - detection and quantification capabilities (IUPAC Recommendations 1995). - Analytica Chimica Acta 391, 105 - 126.

      - -
      - -

      Examples

      - 
      data(din32645)
-m <- lm(y ~ x, data = din32645)
-lod(m)
      
-
      $x
-[1] 0.08655484
-
-$y
-       1 
-3317.154 
-
-
      
-
      
-# The critical value (decision limit, German Nachweisgrenze) can be obtained
-# by using beta = 0.5:
-lod(m, alpha = 0.01, beta = 0.5)
      
-
      $x
-[1] 0.0698127
-
-$y
-       1 
-3155.393 
-
-
      -
      -
      - - -

      See also

      -

      Examples for din32645

      - - - - -
      -
      - - -
      - - \ No newline at end of file diff --git a/docs/loq.html b/docs/loq.html deleted file mode 100644 index 352737f..0000000 --- a/docs/loq.html +++ /dev/null @@ -1,191 +0,0 @@ - - - - -loq. chemCal 0.1-37 - - - - - - - - - - - - - - - -
      -
      -
      - chemCal 0.1-37 -
      - -
      -
      -
      -
      - - -
      -
      - -
      - -

      Estimate a limit of quantification (LOQ)

      - -
      -
      -

      Usage

      - 
      loq(object, ..., alpha = 0.05, k = 3, n = 1, w.loq = "auto",
-    var.loq = "auto", tol = "default")
      - -

      Arguments

      -
      -
      object
      -
      - A univariate model object of class lm or - rlm - with model formula y ~ x or y ~ x - 1, - optionally from a weighted regression. If weights are specified - in the model, either w.loq or var.loq have to - be specified. -
      -
      alpha
      -
      - The error tolerance for the prediction of x values in the calculation. -
      -
      ...
      -
      - Placeholder for further arguments that might be needed by - future implementations. -
      -
      k
      -
      - The inverse of the maximum relative error tolerated at the - desired LOQ. -
      -
      n
      -
      - The number of replicate measurements for which the LOQ should be - specified. -
      -
      w.loq
      -
      - The weight that should be attributed to the LOQ. Defaults - to one for unweighted regression, and to the mean of the weights - for weighted regression. See massart97ex3 for - an example how to take advantage of knowledge about the - variance function. -
      -
      var.loq
      -
      - The approximate variance at the LOQ. The default value is - calculated from the model. -
      -
      tol
      -
      - The default tolerance for the LOQ on the x scale is the value of the - smallest non-zero standard divided by 1000. Can be set to a - numeric value to override this. -
      -
      - -
      -

      Value

      - -

      - The estimated limit of quantification for a model used for calibration. -

      - -
      - -
      -

      Description

      - -

      The limit of quantification is the x value, where the relative error - of the quantification given the calibration model reaches a prespecified - value 1/k. Thus, it is the solution of the equation - $$L = k c(L)$$ - where c(L) is half of the length of the confidence interval at the limit L - (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by - inverse.predict, and L is obtained by iteration.

      - -
      - -
      -

      Note

      - -

      - IUPAC recommends to base the LOQ on the standard deviation of the signal - where x = 0. - - The calculation of a LOQ based on weighted regression is non-standard - and therefore not tested. Feedback is welcome.

      - -
      - -

      Examples

      - 
      data(massart97ex3)
-attach(massart97ex3)
-m <- lm(y ~ x)
-loq(m)
      
-
      $x
-[1] 13.97764
-
-$y
-      1 
-30.6235 
-
-
      
-
      
-# We can get better by using replicate measurements
-loq(m, n = 3)
      
-
      $x
-[1] 9.971963
-
-$y
-       1 
-22.68539 
-
-
      -
      -
      - - -

      See also

      -

      Examples for din32645

      - - - - -
      -
      - - -
      - - \ No newline at end of file diff --git a/docs/massart97ex1.html b/docs/massart97ex1.html deleted file mode 100644 index 00fde33..0000000 --- a/docs/massart97ex1.html +++ /dev/null @@ -1,102 +0,0 @@ - - - - -massart97ex1. chemCal 0.1-37 - - - - - - - - - - - - - - - -
      -
      -
      - chemCal 0.1-37 -
      - -
      -
      -
      -
      - - -
      -
      - -
      - -

      Calibration data from Massart et al. (1997), example 1

      - -
      -
      -

      Usage

      - 
      data(massart97ex1)
      - -
      -

      Description

      - -

      Sample dataset from p. 175 to test the package.

      - -
      - -
      -

      Format

      - -

      A dataframe containing 6 observations of x and y data.

      - -
      - -
      -

      Source

      - -

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., - Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, - Chapter 8.

      - -
      -
      -
      - - - - - -
      -
      - - -
      - - \ No newline at end of file diff --git a/docs/massart97ex3-5.png b/docs/massart97ex3-5.png deleted file mode 100644 index c6c080e..0000000 Binary files a/docs/massart97ex3-5.png and /dev/null differ diff --git a/docs/massart97ex3.html b/docs/massart97ex3.html deleted file mode 100644 index 7e4d510..0000000 --- a/docs/massart97ex3.html +++ /dev/null @@ -1,194 +0,0 @@ - - - - -massart97ex3. chemCal 0.1-37 - - - - - - - - - - - - - - - -
      -
      -
      - chemCal 0.1-37 -
      - -
      -
      -
      -
      - - -
      -
      - -
      - -

      Calibration data from Massart et al. (1997), example 3

      - -
      -
      -

      Usage

      - 
      data(massart97ex3)
      - -
      -

      Description

      - -

      Sample dataset from p. 188 to test the package.

      - -
      - -
      -

      Format

      - -

      A dataframe containing 6 levels of x values with 5 - observations of y for each level.

      - -
      - -
      -

      Source

      - -

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., - Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, - Chapter 8.

      - -
      - -

      Examples

      - 
      data(massart97ex3)
-attach(massart97ex3)
      
-The following objects are masked from massart97ex3 (pos = 3):
-
-    x, y
-
-
      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)
      
-Warning message:
-Assuming constant prediction variance even though model fit is weighted
-
-
      
-
      
-# The following concords with the book p. 200
-inverse.predict(m, 15, ws = 1.67)  # 5.9 +- 2.5
      
-
      $Prediction
-[1] 5.865367
-
-$`Standard Error`
-[1] 0.8926109
-
-$Confidence
-[1] 2.478285
-
-$`Confidence Limits`
-[1] 3.387082 8.343652
-
-
      
-
      inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
      
-
      $Prediction
-[1] 44.06025
-
-$`Standard Error`
-[1] 2.829162
-
-$Confidence
-[1] 7.855012
-
-$`Confidence Limits`
-[1] 36.20523 51.91526
-
-
      
-
      
-# The LOD is only calculated for models from unweighted regression
-# with this version of chemCal
-m0 <- lm(y ~ x)
-lod(m0)
      
-
      $x
-[1] 5.407085
-
-$y
-       1 
-13.63911 
-
-
      
-
      
-# Limit of quantification from unweighted regression
-loq(m0)
      
-
      $x
-[1] 13.97764
-
-$y
-      1 
-30.6235 
-
-
      
-
      
-# For calculating the limit of quantification from a model from weighted
-# regression, we need to supply weights, internally used for inverse.predict
-# If we are not using a variance function, we can use the weight from
-# the above example as a first approximation (x = 15 is close to our
-# loq approx 14 from above).
-loq(m, w.loq = 1.67)
      
-
      $x
-[1] 7.346195
-
-$y
-       1 
-17.90777 
-
-
      
-
      # The weight for the loq should therefore be derived at x = 7.3 instead
-# of 15, but the graphical procedure of Massart (p. 201) to derive the 
-# variances on which the weights are based is quite inaccurate anyway.
      -
      -
      - - - - - -
      -
      - - -
      - - \ No newline at end of file diff --git a/docs/pkgdown.css b/docs/pkgdown.css new file mode 100644 index 0000000..fd7b0ba --- /dev/null +++ b/docs/pkgdown.css @@ -0,0 +1,113 @@ +/* Sticker footer */ +body > .container { + display: flex; + padding-top: 60px; + min-height: calc(100vh); + flex-direction: column; +} + +body > .container .row { + flex: 1; +} + +footer { + margin-top: 45px; + padding: 35px 0 36px; + border-top: 1px solid #e5e5e5; + color: #666; + display: flex; +} +footer p { + margin-bottom: 0; +} +footer div { + flex: 1; +} +footer .pkgdown { + text-align: right; +} +footer p { + margin-bottom: 0; +} + +img.icon { + float: right; +} + +/* Section anchors ---------------------------------*/ + +.hasAnchor { + margin-left: -30px; +} + +a.anchor { + display:inline-block; + width: 30px; + height: 30px; + visibility: hidden; + + background-image: url(./link.svg); + background-repeat: no-repeat; + background-size: 20px 20px; + background-position: center center; +} + +.hasAnchor:hover a.anchor { + visibility: visible; +} + +/* Fixes for fixed navbar --------------------------*/ + +.contents h1, .contents h2, .contents h3, .contents h4 { + padding-top: 60px; + margin-top: -60px; +} + +/* Sidebar --------------------------*/ + +#sidebar { + margin-top: 30px; +} +#sidebar h2 { + font-size: 1.5em; + margin-top: 1em; +} + +#sidebar h2:first-child { + margin-top: 0; +} + +#sidebar .list-unstyled li { + margin-bottom: 0.5em; +} + +/* Syntax highlighting ---------------------------------------------------- */ + +code { + background-color: #f7f7f7; + color: #333; +} +code a { + color: #375f84; +} + +.warning { color: red; } +.message { font-weight: bolder; } +.error { color: red; font-weight: bolder; } + +.fl,.number {color:rgb(21,20,181);} +.fu,.functioncall {color:#264D66 ;} +.ch,.st,.string {color:#375D81 ;} +.kw,.keyword {color:black;} +.argument {color:#264D66 ;} +.co,.comment {color: #777;} +.formalargs {color: #264D66;} +.eqformalargs {color:#264D66;} +.slot {font-style:italic;} +.symbol {color:black ;} +.prompt {color:black ;} + +pre img { + background-color: #fff; + display: block; +} diff --git a/docs/pkgdown.js b/docs/pkgdown.js new file mode 100644 index 0000000..c8b38c4 --- /dev/null +++ b/docs/pkgdown.js @@ -0,0 +1,8 @@ +$(function() { + $("#sidebar").stick_in_parent({offset_top: 40}); + $('body').scrollspy({ + target: '#sidebar', + offset: 60 + }); + +}); diff --git a/docs/reference.html b/docs/reference.html deleted file mode 100644 index 6c99033..0000000 --- a/docs/reference.html +++ /dev/null @@ -1,118 +0,0 @@ - - - - -Function reference. chemCal 0.1-37 - - - - - - - - - - - - - - - -
      -
      -
      - chemCal 0.1-37 -
      - -
      -
      -
      -
      - - -
      -
      - -
      - -
      -
      -

      Function reference

      - -

      Main functions

      -

      Essential functionality

      - - -
        - -
      • - inverse.predict(inverse.predict.lm, inverse.predict.rlm, inverse.predict.default)
        Predict x from y for a linear calibration
        • - -
      • - calplot(calplot.default, calplot.lm)
        Plot calibration graphs from univariate linear models
        • - -
      -

      LOD and LOQ

      -

      Limit of detection and limit of quantification

      - - -
        - -
      • - lod(lod.lm, lod.rlm, lod.default)
        Estimate a limit of detection (LOD)
        • - -
      • - loq(loq.lm, loq.rlm, loq.default)
        Estimate a limit of quantification (LOQ)
        • - -
      -

      Datasets

      -

      Example data

      - - -
        - -
      • - din32645
        Calibration data from DIN 32645
        • - -
      • - massart97ex1
        Calibration data from Massart et al. (1997), example 1
        • - -
      -

      Other

      - - -
        - -
      • - chemCal-package
        - Calibration functions for analytical chemistry -
        • - -
      • - massart97ex3
        Calibration data from Massart et al. (1997), example 3
        • - -
      -
      -
      - - -
      - - \ No newline at end of file diff --git a/docs/reference/calplot-2.png b/docs/reference/calplot-2.png new file mode 100644 index 0000000..7e40a4b Binary files /dev/null and b/docs/reference/calplot-2.png differ diff --git a/docs/reference/calplot.lm.html b/docs/reference/calplot.lm.html new file mode 100644 index 0000000..f66e636 --- /dev/null +++ b/docs/reference/calplot.lm.html @@ -0,0 +1,177 @@ + + + + + + + + +Plot calibration graphs from univariate linear models — calplot • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Plot calibration graphs from univariate linear models

      +
      + + +

      Produce graphics of calibration data, the fitted model as well + as confidence, and, for unweighted regression, prediction bands.

      + + + 
      calplot(object, xlim = c("auto", "auto"), ylim = c("auto", "auto"),
+    xlab = "Concentration", ylab = "Response", alpha=0.05, varfunc = NULL)
      + +

      Arguments

      +
      +
      object
      +
      + A univariate model object of class lm or + rlm + with model formula y ~ x or y ~ x - 1. +
      +
      xlim
      +
      + The limits of the plot on the x axis. +
      +
      ylim
      +
      + The limits of the plot on the y axis. +
      +
      xlab
      +
      + The label of the x axis. +
      +
      ylab
      +
      + The label of the y axis. +
      +
      alpha
      +
      + The error tolerance level for the confidence and prediction bands. Note that this + includes both tails of the Gaussian distribution, unlike the alpha and beta parameters + used in lod (see note below). +
      +
      varfunc
      +
      + The variance function for generating the weights in the model. + Currently, this argument is ignored (see note below). +
      +
      + +

      Value

      + +

      A plot of the calibration data, of your fitted model as well as lines showing + the confidence limits. Prediction limits are only shown for models from + unweighted regression.

      + +

      Note

      + +

      Prediction bands for models from weighted linear regression require weights + for the data, for which responses should be predicted. Prediction intervals + using weights e.g. from a variance function are currently not supported by + the internally used function predict.lm, therefore, + calplot does not draw prediction bands for such models.

      +

      It is possible to compare the calplot prediction bands with the + lod values if the lod() alpha and beta parameters are + half the value of the calplot() alpha parameter.

      + + +

      Examples

      + 
      data(massart97ex3)
+m <- lm(y ~ x, data = massart97ex3)
+calplot(m)
      +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/chemCal-package.html b/docs/reference/chemCal-package.html new file mode 100644 index 0000000..18e3822 --- /dev/null +++ b/docs/reference/chemCal-package.html @@ -0,0 +1,115 @@ + + + + + + + + + + — chemCal-package • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      +

      +
      + + +

      See ../DESCRIPTION

      + + + +

      Details

      + +

      There is a package vignette located in ../doc/chemCal.pdf.

      + + +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/din32645-2.png b/docs/reference/din32645-2.png new file mode 100644 index 0000000..1d1e8ab Binary files /dev/null and b/docs/reference/din32645-2.png differ diff --git a/docs/reference/din32645.html b/docs/reference/din32645.html new file mode 100644 index 0000000..1b64592 --- /dev/null +++ b/docs/reference/din32645.html @@ -0,0 +1,175 @@ + + + + + + + + +Calibration data from DIN 32645 — din32645 • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Calibration data from DIN 32645

      +
      + + +

      Sample dataset to test the package.

      + + + 
      data(din32645)
      + +

      Format

      + +

      A dataframe containing 10 rows of x and y values.

      + +

      References

      + +

      DIN 32645 (equivalent to ISO 11843), Beuth Verlag, Berlin, 1994

      +

      Dintest. Plugin for MS Excel for evaluations of calibration data. Written + by Georg Schmitt, University of Heidelberg. Formerly available from + the Website of the University of Heidelberg.

      +

      Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including + detection and quantification capabilities (IUPAC Recommendations 1995). + Analytica Chimica Acta 391, 105 - 126.

      + + +

      Examples

      + 
      data(din32645)
+m <- lm(y ~ x, data = din32645)
+calplot(m)
      
+## Prediction of x with confidence interval
+(prediction <- inverse.predict(m, 3500, alpha = 0.01))
      #> $Prediction
+#> [1] 0.1054792
+#> 
+#> $`Standard Error`
+#> [1] 0.02215619
+#> 
+#> $Confidence
+#> [1] 0.07434261
+#> 
+#> $`Confidence Limits`
+#> [1] 0.03113656 0.17982178
+#> 
      
+# This should give 0.07434 according to test data from Dintest, which 
+# was collected from Procontrol 3.1 (isomehr GmbH) in this case
+round(prediction$Confidence,5)
      #> [1] 0.07434
      
+## Critical value:
+(crit <- lod(m, alpha = 0.01, beta = 0.5))
      #> $x
+#> [1] 0.0698127
+#> 
+#> $y
+#>        1 
+#> 3155.393 
+#> 
      
+# According to DIN 32645, we should get 0.07 for the critical value
+# (decision limit, "Nachweisgrenze")
+round(crit$x, 2)
      #> [1] 0.07
      # and according to Dintest test data, we should get 0.0698 from
+round(crit$x, 4)
      #> [1] 0.0698
      
+## Limit of detection (smallest detectable value given alpha and beta)
+# In German, the smallest detectable value is the "Erfassungsgrenze", and we
+# should get 0.14 according to DIN, which we achieve by using the method 
+# described in it:
+lod.din <- lod(m, alpha = 0.01, beta = 0.01, method = "din")
+round(lod.din$x, 2)
      #> [1] 0.14
      
+## Limit of quantification
+# This accords to the test data coming with the test data from Dintest again, 
+# except for the last digits of the value cited for Procontrol 3.1 (0.2121)
+(loq <- loq(m, alpha = 0.01))
      #> $x
+#> [1] 0.2119575
+#> 
+#> $y
+#>        1 
+#> 4528.787 
+#> 
      round(loq$x,4)
      #> [1] 0.212
      
+# A similar value is obtained using the approximation 
+# LQ = 3.04 * LC (Currie 1999, p. 120)
+3.04 * lod(m,alpha = 0.01, beta = 0.5)$x
      #> [1] 0.2122306
      +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/index.html b/docs/reference/index.html new file mode 100644 index 0000000..b55336a --- /dev/null +++ b/docs/reference/index.html @@ -0,0 +1,146 @@ + + + + + + + + +Function reference • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Function reference

      +

      version 0.1-37.9000

      +
      + +
      +

      All functions

      +

      + + +

      Plot calibration graphs from univariate linear models

      + + +

      +

      + + +

      Calibration data from DIN 32645

      + + +

      Predict x from y for a linear calibration

      + + +

      Estimate a limit of detection (LOD)

      + + +

      Estimate a limit of quantification (LOQ)

      + + +

      Calibration data from Massart et al. (1997), example 1

      + + +

      Calibration data from Massart et al. (1997), example 3

      + + +
      +
      + + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/inverse.predict.html b/docs/reference/inverse.predict.html new file mode 100644 index 0000000..60d169c --- /dev/null +++ b/docs/reference/inverse.predict.html @@ -0,0 +1,211 @@ + + + + + + + + +Predict x from y for a linear calibration — inverse.predict • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Predict x from y for a linear calibration

      +
      + + +

      This function predicts x values using a univariate linear model that has been + generated for the purpose of calibrating a measurement method. Prediction + intervals are given at the specified confidence level. + The calculation method was taken from Massart et al. (1997). In particular, + Equations 8.26 and 8.28 were combined in order to yield a general treatment + of inverse prediction for univariate linear models, taking into account + weights that have been used to create the linear model, and at the same + time providing the possibility to specify a precision in sample measurements + differing from the precision in standard samples used for the calibration. + This is elaborated in the package vignette.

      + + + 
      inverse.predict(object, newdata, …,
+  ws, alpha=0.05, var.s = "auto")
      + +

      Arguments

      +
      +
      object
      +
      + A univariate model object of class lm or + rlm + with model formula y ~ x or y ~ x - 1. +
      +
      newdata
      +
      + A vector of observed y values for one sample. +
      +
      …
      +
      + Placeholder for further arguments that might be needed by + future implementations. +
      +
      ws
      +
      + The weight attributed to the sample. This argument is obligatory + if object has weights. +
      +
      alpha
      +
      + The error tolerance level for the confidence interval to be reported. +
      +
      var.s
      +
      + The estimated variance of the sample measurements. The default is to take + the residual standard error from the calibration and to adjust it + using ws, if applicable. This means that var.s + overrides ws. +
      +
      + +

      Value

      + +

      A list containing the predicted x value, its standard error and a + confidence interval.

      + +

      Note

      + +

      The function was validated with examples 7 and 8 from Massart et al. (1997).

      + +

      References

      + +

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., + Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, + p. 200

      + + +

      Examples

      + 
      # This is example 7 from Chapter 8 in Massart et al. (1997)
+data(massart97ex1)
+m <- lm(y ~ x, data = massart97ex1)
+inverse.predict(m, 15)        #  6.1 +- 4.9
      #> $Prediction
+#> [1] 6.09381
+#> 
+#> $`Standard Error`
+#> [1] 1.767278
+#> 
+#> $Confidence
+#> [1] 4.906751
+#> 
+#> $`Confidence Limits`
+#> [1]  1.187059 11.000561
+#> 
      inverse.predict(m, 90)        # 43.9 +- 4.9
      #> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 1.767747
+#> 
+#> $Confidence
+#> [1] 4.908053
+#> 
+#> $`Confidence Limits`
+#> [1] 39.03178 48.84788
+#> 
      inverse.predict(m, rep(90,5)) # 43.9 +- 3.2
      #> $Prediction
+#> [1] 43.93983
+#> 
+#> $`Standard Error`
+#> [1] 1.141204
+#> 
+#> $Confidence
+#> [1] 3.168489
+#> 
+#> $`Confidence Limits`
+#> [1] 40.77134 47.10832
+#>
      +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/lod.html b/docs/reference/lod.html new file mode 100644 index 0000000..7c33d47 --- /dev/null +++ b/docs/reference/lod.html @@ -0,0 +1,210 @@ + + + + + + + + +Estimate a limit of detection (LOD) — lod • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Estimate a limit of detection (LOD)

      +
      + + +

      The decision limit (German: Nachweisgrenze) is defined as the signal or + analyte concentration that is significantly different from the blank signal + with a first order error alpha (one-sided significance test). + The detection limit, or more precise, the minimum detectable value + (German: Erfassungsgrenze), is then defined as the signal or analyte + concentration where the probability that the signal is not detected although + the analyte is present (type II or false negative error), is beta (also a + one-sided significance test).

      + + + 
      lod(object, …, alpha = 0.05, beta = 0.05, method = "default", tol = "default")
      + +

      Arguments

      +
      +
      object
      +
      + A univariate model object of class lm or + rlm + with model formula y ~ x or y ~ x - 1, + optionally from a weighted regression. +
      +
      …
      +
      + Placeholder for further arguments that might be needed by + future implementations. +
      +
      alpha
      +
      + The error tolerance for the decision limit (critical value). +
      +
      beta
      +
      + The error tolerance beta for the detection limit. +
      +
      method
      +
      + The “default” method uses a prediction interval at the LOD + for the estimation of the LOD, which obviously requires + iteration. This is described for example in Massart, p. 432 ff. + The “din” method uses the prediction interval at + x = 0 as an approximation. +
      +
      tol
      +
      + When the “default” method is used, the default tolerance + for the LOD on the x scale is the value of the smallest non-zero standard + divided by 1000. Can be set to a numeric value to override this. +
      +
      + +

      Value

      + +

      A list containig the corresponding x and y values of the estimated limit of + detection of a model used for calibration.

      + +

      Note

      + +

      - The default values for alpha and beta are the ones recommended by IUPAC. + - The estimation of the LOD in terms of the analyte amount/concentration + xD from the LOD in the signal domain SD is done by simply inverting the + calibration function (i.e. assuming a known calibration function). + - The calculation of a LOD from weighted calibration models requires + a weights argument for the internally used predict.lm + function, which is currently not supported in R.

      + +

      References

      + +

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., + Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, + Chapter 13.7.8

      +

      J. Inczedy, T. Lengyel, and A.M. Ure (2002) International Union of Pure and + Applied Chemistry Compendium of Analytical Nomenclature: Definitive Rules. + Web edition.

      +

      Currie, L. A. (1997) Nomenclature in evaluation of analytical methods including + detection and quantification capabilities (IUPAC Recommendations 1995). + Analytica Chimica Acta 391, 105 - 126.

      + +

      See also

      + +

      Examples for din32645

      + + +

      Examples

      + 
      data(din32645)
+m <- lm(y ~ x, data = din32645)
+lod(m)
      #> $x
+#> [1] 0.08655484
+#> 
+#> $y
+#>        1 
+#> 3317.154 
+#> 
      
+# The critical value (decision limit, German Nachweisgrenze) can be obtained
+# by using beta = 0.5:
+lod(m, alpha = 0.01, beta = 0.5)
      #> $x
+#> [1] 0.0698127
+#> 
+#> $y
+#>        1 
+#> 3155.393 
+#>
      +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/loq.html b/docs/reference/loq.html new file mode 100644 index 0000000..bc62e75 --- /dev/null +++ b/docs/reference/loq.html @@ -0,0 +1,205 @@ + + + + + + + + +Estimate a limit of quantification (LOQ) — loq • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Estimate a limit of quantification (LOQ)

      +
      + + +

      The limit of quantification is the x value, where the relative error + of the quantification given the calibration model reaches a prespecified + value 1/k. Thus, it is the solution of the equation + $$L = k c(L)$$ + where c(L) is half of the length of the confidence interval at the limit L + (DIN 32645, equivalent to ISO 11843). c(L) is internally estimated by + inverse.predict, and L is obtained by iteration.

      + + + 
      loq(object, …, alpha = 0.05, k = 3, n = 1, w.loq = "auto",
+    var.loq = "auto", tol = "default")
      + +

      Arguments

      +
      +
      object
      +
      + A univariate model object of class lm or + rlm + with model formula y ~ x or y ~ x - 1, + optionally from a weighted regression. If weights are specified + in the model, either w.loq or var.loq have to + be specified. +
      +
      alpha
      +
      + The error tolerance for the prediction of x values in the calculation. +
      +
      …
      +
      + Placeholder for further arguments that might be needed by + future implementations. +
      +
      k
      +
      + The inverse of the maximum relative error tolerated at the + desired LOQ. +
      +
      n
      +
      + The number of replicate measurements for which the LOQ should be + specified. +
      +
      w.loq
      +
      + The weight that should be attributed to the LOQ. Defaults + to one for unweighted regression, and to the mean of the weights + for weighted regression. See massart97ex3 for + an example how to take advantage of knowledge about the + variance function. +
      +
      var.loq
      +
      + The approximate variance at the LOQ. The default value is + calculated from the model. +
      +
      tol
      +
      + The default tolerance for the LOQ on the x scale is the value of the + smallest non-zero standard divided by 1000. Can be set to a + numeric value to override this. +
      +
      + +

      Value

      + +

      The estimated limit of quantification for a model used for calibration.

      + +

      Note

      + +

      - IUPAC recommends to base the LOQ on the standard deviation of the signal + where x = 0. + - The calculation of a LOQ based on weighted regression is non-standard + and therefore not tested. Feedback is welcome.

      + +

      See also

      + +

      Examples for din32645

      + + +

      Examples

      + 
      data(massart97ex3)
+attach(massart97ex3)
+m <- lm(y ~ x)
+loq(m)
      #> $x
+#> [1] 13.97764
+#> 
+#> $y
+#>       1 
+#> 30.6235 
+#> 
      
+# We can get better by using replicate measurements
+loq(m, n = 3)
      #> $x
+#> [1] 9.971963
+#> 
+#> $y
+#>        1 
+#> 22.68539 
+#>
      +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/massart97ex1.html b/docs/reference/massart97ex1.html new file mode 100644 index 0000000..9b95a5f --- /dev/null +++ b/docs/reference/massart97ex1.html @@ -0,0 +1,118 @@ + + + + + + + + +Calibration data from Massart et al. (1997), example 1 — massart97ex1 • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Calibration data from Massart et al. (1997), example 1

      +
      + + +

      Sample dataset from p. 175 to test the package.

      + + + 
      data(massart97ex1)
      + +

      Format

      + +

      A dataframe containing 6 observations of x and y data.

      + +

      Source

      + +

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., + Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, + Chapter 8.

      + + +
      + +
      + +
      +
      +

      Developed by Johannes Ranke.

      +
      + +
      +

      Site built with pkgdown.

      +
      + +
      +
      + + + diff --git a/docs/reference/massart97ex3-5.png b/docs/reference/massart97ex3-5.png new file mode 100644 index 0000000..c6c080e Binary files /dev/null and b/docs/reference/massart97ex3-5.png differ diff --git a/docs/reference/massart97ex3.html b/docs/reference/massart97ex3.html new file mode 100644 index 0000000..2ec8f6f --- /dev/null +++ b/docs/reference/massart97ex3.html @@ -0,0 +1,188 @@ + + + + + + + + +Calibration data from Massart et al. (1997), example 3 — massart97ex3 • chemCal + + + + + + + + + + + + + + + + + + + + + + + + +
      +
      + + + +
      + +
      +
      +
      +

      Calibration data from Massart et al. (1997), example 3

      +
      + + +

      Sample dataset from p. 188 to test the package.

      + + + 
      data(massart97ex3)
      + +

      Format

      + +

      A dataframe containing 6 levels of x values with 5 + observations of y for each level.

      + +

      Source

      + +

      Massart, L.M, Vandenginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., + Smeyers-Verbeke, J. (1997) Handbook of Chemometrics and Qualimetrics: Part A, + Chapter 8.

      + + +

      Examples

      + 
      data(massart97ex3)
+attach(massart97ex3)
      #> The following objects are masked from massart97ex3 (pos = 3):
+#> 
+#>     x, y
      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)
      #> Warning: Assuming constant prediction variance even though model fit is weighted
      
+# The following concords with the book p. 200
+inverse.predict(m, 15, ws = 1.67)  # 5.9 +- 2.5
      #> $Prediction
+#> [1] 5.865367
+#> 
+#> $`Standard Error`
+#> [1] 0.8926109
+#> 
+#> $Confidence
+#> [1] 2.478285
+#> 
+#> $`Confidence Limits`
+#> [1] 3.387082 8.343652
+#> 
      inverse.predict(m, 90, ws = 0.145) # 44.1 +- 7.9
      #> $Prediction
+#> [1] 44.06025
+#> 
+#> $`Standard Error`
+#> [1] 2.829162
+#> 
+#> $Confidence
+#> [1] 7.855012
+#> 
+#> $`Confidence Limits`
+#> [1] 36.20523 51.91526
+#> 
      
+# The LOD is only calculated for models from unweighted regression
+# with this version of chemCal
+m0 <- lm(y ~ x)
+lod(m0)
      #> $x
+#> [1] 5.407085
+#> 
+#> $y
+#>        1 
+#> 13.63911 
+#> 
      
+# Limit of quantification from unweighted regression
+loq(m0)
      #> $x
+#> [1] 13.97764
+#> 
+#> $y
+#>       1 
+#> 30.6235 
+#> 
      
+# For calculating the limit of quantification from a model from weighted
+# regression, we need to supply weights, internally used for inverse.predict
+# If we are not using a variance function, we can use the weight from
+# the above example as a first approximation (x = 15 is close to our
+# loq approx 14 from above).
+loq(m, w.loq = 1.67)
      #> $x
+#> [1] 7.346195
+#> 
+#> $y
+#>        1 
+#> 17.90777 
+#> 
      # The weight for the loq should therefore be derived at x = 7.3 instead
+# of 15, but the graphical procedure of Massart (p. 201) to derive the 
+# variances on which the weights are based is quite inaccurate anyway.
      +
      + +
      + + +
      + + + diff --git a/docs/vignettes/chemCal.pdf b/docs/vignettes/chemCal.pdf deleted file mode 100644 index cc7c5d8..0000000 Binary files a/docs/vignettes/chemCal.pdf and /dev/null differ -- cgit v1.2.1