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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."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> +<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Predict x from y for a linear calibration — inverse.predict • chemCal</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Predict x from y for a linear calibration — inverse.predict"><meta property="og:description" content="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."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> <![endif]--></head><body data-spy="scroll" data-target="#toc"> @@ -56,73 +56,87 @@ <div class="col-md-9 contents"> <div class="page-header"> <h1>Predict x from y for a linear calibration</h1> - + <small class="dont-index">Source: <a href="https://github.com/jranke/chemCal/blob/HEAD/R/inverse.predict.lm.R" class="external-link"><code>R/inverse.predict.lm.R</code></a></small> <div class="hidden name"><code>inverse.predict.Rd</code></div> </div> <div class="ref-description"> - <p>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.</p> + <p>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.</p> </div> <div id="ref-usage"> - <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">object</span>, <span class="va">newdata</span>, <span class="va">...</span>, - <span class="va">ws</span>, alpha<span class="op">=</span><span class="fl">0.05</span>, var.s <span class="op">=</span> <span class="st">"auto"</span><span class="op">)</span></code></pre></div> + <div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">inverse.predict</span><span class="op">(</span> + <span class="va">object</span>, + <span class="va">newdata</span>, + <span class="va">...</span>, + ws <span class="op">=</span> <span class="st">"auto"</span>, + alpha <span class="op">=</span> <span class="fl">0.05</span>, + var.s <span class="op">=</span> <span class="st">"auto"</span> +<span class="op">)</span></code></pre></div> </div> <div id="arguments"> <h2>Arguments</h2> <dl><dt>object</dt> -<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or - <code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> - with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.</p></dd> +<dd><p>A univariate model object of class <code><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></code> or +<code><a href="https://rdrr.io/pkg/MASS/man/rlm.html" class="external-link">rlm</a></code> with model formula <code>y ~ x</code> or <code>y ~ x - +1</code>.</p></dd> <dt>newdata</dt> <dd><p>A vector of observed y values for one sample.</p></dd> <dt>...</dt> -<dd><p>Placeholder for further arguments that might be needed by - future implementations.</p></dd> +<dd><p>Placeholder for further arguments that might be needed by +future implementations.</p></dd> <dt>ws</dt> <dd><p>The weight attributed to the sample. This argument is obligatory - if <code>object</code> has weights.</p></dd> +if <code>object</code> has weights.</p></dd> <dt>alpha</dt> -<dd><p>The error tolerance level for the confidence interval to be reported.</p></dd> +<dd><p>The error tolerance level for the confidence interval to be +reported.</p></dd> <dt>var.s</dt> -<dd><p>The estimated variance of the sample measurements. The default is to take - the residual standard error from the calibration and to adjust it - using <code>ws</code>, if applicable. This means that <code>var.s</code> - overrides <code>ws</code>.</p></dd> +<dd><p>The estimated variance of the sample measurements. The default +is to take the residual standard error from the calibration and to adjust it +using <code>ws</code>, if applicable. This means that <code>var.s</code> overrides +<code>ws</code>.</p></dd> </dl></div> <div id="value"> <h2>Value</h2> <p>A list containing the predicted x value, its standard error and a - confidence interval.</p> +confidence interval.</p> + </div> + <div id="details"> + <h2>Details</h2> + <p>This is an implementation of Equation (8.28) in the Handbook of Chemometrics +and Qualimetrics, Part A, Massart et al (1997), page 200, validated with +Example 8 on the same page, extended as specified in the package vignette</p> </div> <div id="note"> <h2>Note</h2> - <p>The function was validated with examples 7 and 8 from Massart et al. (1997). - Note that the behaviour of inverse.predict changed with chemCal version - 0.2.1. Confidence intervals for x values obtained from calibrations with - replicate measurements did not take the variation about the means into account. - Please refer to the vignette for details.</p> + <p>The function was validated with examples 7 and 8 from Massart et al. +(1997). Note that the behaviour of inverse.predict changed with chemCal +version 0.2.1. Confidence intervals for x values obtained from calibrations +with replicate measurements did not take the variation about the means into +account. Please refer to the vignette for details.</p> </div> <div id="references"> <h2>References</h2> - <p>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</p> + <p>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</p> </div> <div id="ref-examples"> <h2>Examples</h2> - <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="co"># This is example 7 from Chapter 8 in Massart et al. (1997)</span></span> + <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"></span> +<span class="r-in"><span class="co"># This is example 7 from Chapter 8 in Massart et al. (1997)</span></span> <span class="r-in"><span class="va">m</span> <span class="op"><-</span> <span class="fu"><a href="https://rdrr.io/r/stats/lm.html" class="external-link">lm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">massart97ex1</span><span class="op">)</span></span> <span class="r-in"><span class="fu">inverse.predict</span><span class="op">(</span><span class="va">m</span>, <span class="fl">15</span><span class="op">)</span> <span class="co"># 6.1 +- 4.9</span></span> <span class="r-out co"><span class="r-pr">#></span> $Prediction</span> @@ -204,6 +218,7 @@ <span class="r-out co"><span class="r-pr">#></span> [1] 36.20523 51.91526</span> <span class="r-out co"><span class="r-pr">#></span> </span> <span class="r-in"></span> +<span class="r-in"></span> </code></pre></div> </div> </div> |