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authorJohannes Ranke <jranke@uni-bremen.de>2017-03-06 17:00:48 +0100
committerJohannes Ranke <jranke@uni-bremen.de>2017-03-06 17:00:48 +0100
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+ <h1>Predict x from y for a linear calibration</h1>
+ </div>
+
+
+ <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>
+
+
+ <pre>inverse.predict(object, newdata, &#8230;,
+ ws, alpha=0.05, var.s = "auto")</pre>
+
+ <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a> Arguments</h2>
+ <dl class="dl-horizontal">
+ <dt>object</dt>
+ <dd>
+ A univariate model object of class <code>lm</code> or
+ <code><a href='http://www.rdocumentation.org/packages/MASS/topics/rlm'>rlm</a></code>
+ with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.
+ </dd>
+ <dt>newdata</dt>
+ <dd>
+ A vector of observed y values for one sample.
+ </dd>
+ <dt>&#8230;</dt>
+ <dd>
+ Placeholder for further arguments that might be needed by
+ future implementations.
+ </dd>
+ <dt>ws</dt>
+ <dd>
+ The weight attributed to the sample. This argument is obligatory
+ if <code>object</code> has weights.
+ </dd>
+ <dt>alpha</dt>
+ <dd>
+ The error tolerance level for the confidence interval to be reported.
+ </dd>
+ <dt>var.s</dt>
+ <dd>
+ 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>.
+ </dd>
+ </dl>
+
+ <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2>
+
+ <p>A list containing the predicted x value, its standard error and a
+ confidence interval.</p>
+
+ <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2>
+
+ <p>The function was validated with examples 7 and 8 from Massart et al. (1997).</p>
+
+ <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>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>
+
+
+ <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
+ <pre class="examples"><div class='input'><span class='co'># This is example 7 from Chapter 8 in Massart et al. (1997)</span>
+<span class='fu'>data</span>(<span class='no'>massart97ex1</span>)
+<span class='no'>m</span> <span class='kw'>&lt;-</span> <span class='fu'>lm</span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex1</span>)
+<span class='fu'>inverse.predict</span>(<span class='no'>m</span>, <span class='fl'>15</span>) <span class='co'># 6.1 +- 4.9</span></div><div class='output co'>#&gt; $Prediction
+#&gt; [1] 6.09381
+#&gt;
+#&gt; $`Standard Error`
+#&gt; [1] 1.767278
+#&gt;
+#&gt; $Confidence
+#&gt; [1] 4.906751
+#&gt;
+#&gt; $`Confidence Limits`
+#&gt; [1] 1.187059 11.000561
+#&gt; </div><div class='input'><span class='fu'>inverse.predict</span>(<span class='no'>m</span>, <span class='fl'>90</span>) <span class='co'># 43.9 +- 4.9</span></div><div class='output co'>#&gt; $Prediction
+#&gt; [1] 43.93983
+#&gt;
+#&gt; $`Standard Error`
+#&gt; [1] 1.767747
+#&gt;
+#&gt; $Confidence
+#&gt; [1] 4.908053
+#&gt;
+#&gt; $`Confidence Limits`
+#&gt; [1] 39.03178 48.84788
+#&gt; </div><div class='input'><span class='fu'>inverse.predict</span>(<span class='no'>m</span>, <span class='fu'>rep</span>(<span class='fl'>90</span>,<span class='fl'>5</span>)) <span class='co'># 43.9 +- 3.2</span></div><div class='output co'>#&gt; $Prediction
+#&gt; [1] 43.93983
+#&gt;
+#&gt; $`Standard Error`
+#&gt; [1] 1.141204
+#&gt;
+#&gt; $Confidence
+#&gt; [1] 3.168489
+#&gt;
+#&gt; $`Confidence Limits`
+#&gt; [1] 40.77134 47.10832
+#&gt; </div></pre>
+ </div>
+ <div class="col-md-3 hidden-xs hidden-sm" id="sidebar">
+ <h2>Contents</h2>
+ <ul class="nav nav-pills nav-stacked">
+ <li><a href="#arguments">Arguments</a></li>
+
+ <li><a href="#value">Value</a></li>
+
+ <li><a href="#note">Note</a></li>
+
+ <li><a href="#references">References</a></li>
+
+ <li><a href="#examples">Examples</a></li>
+ </ul>
+
+ </div>
+</div>
+
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