docs/reference/inverse.predict.html


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298

<!-- Generated by pkgdown: do not edit by hand -->
<!DOCTYPE html>
<html lang="en">
  <head>
  <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/3.3.1/jquery.min.js" integrity="sha256-FgpCb/KJQlLNfOu91ta32o/NMZxltwRo8QtmkMRdAu8=" crossorigin="anonymous"></script>
<!-- Bootstrap -->

<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/css/bootstrap.min.css" integrity="sha256-916EbMg70RQy9LHiGkXzG8hSg9EdNy97GazNG/aiY1w=" crossorigin="anonymous" />
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.3.7/js/bootstrap.min.js" integrity="sha256-U5ZEeKfGNOja007MMD3YBI0A3OSZOQbeG6z2f2Y0hu8=" crossorigin="anonymous"></script>

<!-- Font Awesome icons -->
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css" integrity="sha256-eZrrJcwDc/3uDhsdt61sL2oOBY362qM3lon1gyExkL0=" crossorigin="anonymous" />

<!-- clipboard.js -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.4/clipboard.min.js" integrity="sha256-FiZwavyI2V6+EXO1U+xzLG3IKldpiTFf3153ea9zikQ=" crossorigin="anonymous"></script>

<!-- sticky kit -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/sticky-kit/1.1.3/sticky-kit.min.js" integrity="sha256-c4Rlo1ZozqTPE2RLuvbusY3+SU1pQaJC0TjuhygMipw=" 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." />
<meta name="twitter:card" content="summary" />


<!-- 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>
    <div class="container template-reference-topic">
      <header>
      <div class="navbar navbar-default navbar-fixed-top" role="navigation">
  <div class="container">
    <div class="navbar-header">
      <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
        <span class="sr-only">Toggle navigation</span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
        <span class="icon-bar"></span>
      </button>
      <span class="navbar-brand">
        <a class="navbar-link" href="../index.html">chemCal</a>
        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">0.2.2</span>
      </span>
    </div>

    <div id="navbar" class="navbar-collapse collapse">
      <ul class="nav navbar-nav">
        <li>
  <a href="../index.html">
    <span class="fa fa-home fa-lg"></span>
     
  </a>
</li>
<li>
  <a href="../articles/chemCal.html">Get started</a>
</li>
<li>
  <a href="../reference/index.html">Reference</a>
</li>
<li>
  <a href="../news/index.html">Changelog</a>
</li>
      </ul>
      
      <ul class="nav navbar-nav navbar-right">
        
      </ul>
      
    </div><!--/.nav-collapse -->
  </div><!--/.container -->
</div><!--/.navbar -->

      
      </header>

<div class="row">
  <div class="col-md-9 contents">
    <div class="page-header">
    <h1>Predict x from y for a linear calibration</h1>
    
    <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>
    
    </div>

    <pre class="usage">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>
    <table class="ref-arguments">
    <colgroup><col class="name" /><col class="desc" /></colgroup>
    <tr>
      <th>object</th>
      <td><p>A univariate model object of class <code><a href='https://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></code> or 
    <code><a href='https://www.rdocumentation.org/packages/MASS/topics/rlm'>rlm</a></code> 
    with model formula <code>y ~ x</code> or <code>y ~ x - 1</code>.</p></td>
    </tr>
    <tr>
      <th>newdata</th>
      <td><p>A vector of observed y values for one sample.</p></td>
    </tr>
    <tr>
      <th>&#8230;</th>
      <td><p>Placeholder for further arguments that might be needed by 
    future implementations.</p></td>
    </tr>
    <tr>
      <th>ws</th>
      <td><p>The weight attributed to the sample. This argument is obligatory
    if <code>object</code> has weights.</p></td>
    </tr>
    <tr>
      <th>alpha</th>
      <td><p>The error tolerance level for the confidence interval to be reported.</p></td>
    </tr>
    <tr>
      <th>var.s</th>
      <td><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></td>
    </tr>
    </table>
    
    <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). 
  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>
    
    <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='no'>m</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></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'><a href='https://www.rdocumentation.org/packages/base/topics/rep'>rep</a></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><div class='input'>
<span class='co'># For reproducing the results for replicate standard measurements in example 8,</span>
<span class='co'># we need to do the calibration on the means when using chemCal &gt; 0.2</span>
<span class='no'>weights</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/with'>with</a></span>(<span class='no'>massart97ex3</span>, {
  <span class='no'>yx</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/split'>split</a></span>(<span class='no'>y</span>, <span class='no'>x</span>)
  <span class='no'>ybar</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/lapply'>sapply</a></span>(<span class='no'>yx</span>, <span class='no'>mean</span>)
  <span class='no'>s</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/Round'>round</a></span>(<span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/lapply'>sapply</a></span>(<span class='no'>yx</span>, <span class='no'>sd</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>2</span>)
  <span class='no'>w</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/base/topics/Round'>round</a></span>(<span class='fl'>1</span> / (<span class='no'>s</span>^<span class='fl'>2</span>), <span class='kw'>digits</span> <span class='kw'>=</span> <span class='fl'>3</span>)
})

<span class='no'>massart97ex3.means</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/aggregate'>aggregate</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='no'>massart97ex3</span>, <span class='no'>mean</span>)

<span class='no'>m3.means</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://www.rdocumentation.org/packages/stats/topics/lm'>lm</a></span>(<span class='no'>y</span> ~ <span class='no'>x</span>, <span class='kw'>w</span> <span class='kw'>=</span> <span class='no'>weights</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>massart97ex3.means</span>)

<span class='fu'>inverse.predict</span>(<span class='no'>m3.means</span>, <span class='fl'>15</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>1.67</span>)  <span class='co'># 5.9 +- 2.5</span></div><div class='output co'>#&gt; $Prediction
#&gt; [1] 5.865367
#&gt; 
#&gt; $`Standard Error`
#&gt; [1] 0.8926109
#&gt; 
#&gt; $Confidence
#&gt; [1] 2.478285
#&gt; 
#&gt; $`Confidence Limits`
#&gt; [1] 3.387082 8.343652
#&gt; </div><div class='input'><span class='fu'>inverse.predict</span>(<span class='no'>m3.means</span>, <span class='fl'>90</span>, <span class='kw'>ws</span> <span class='kw'>=</span> <span class='fl'>0.145</span>) <span class='co'># 44.1 +- 7.9</span></div><div class='output co'>#&gt; $Prediction
#&gt; [1] 44.06025
#&gt; 
#&gt; $`Standard Error`
#&gt; [1] 2.829162
#&gt; 
#&gt; $Confidence
#&gt; [1] 7.855012
#&gt; 
#&gt; $`Confidence Limits`
#&gt; [1] 36.20523 51.91526
#&gt; </div><div class='input'>
</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>

      <footer>
      <div class="copyright">
  <p>Developed by Johannes Ranke.</p>
</div>

<div class="pkgdown">
  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.3.0.</p>
</div>
      </footer>
   </div>

  
  </body>
</html>