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<h1>Lack-of-fit test for models fitted to data with replicates</h1>
- <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/loftest.R'><code>R/loftest.R</code></a></small>
+ <small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/HEAD/R/loftest.R" class="external-link"><code>R/loftest.R</code></a></small>
<div class="hidden name"><code>loftest.Rd</code></div>
</div>
@@ -150,216 +95,231 @@ lrtest.default from the lmtest package." />
<p>This is a generic function with a method currently only defined for mkinfit
objects. It fits an anova model to the data contained in the object and
compares the likelihoods using the likelihood ratio test
-<code><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest.default</a></code> from the lmtest package.</p>
+<code><a href="https://rdrr.io/pkg/lmtest/man/lrtest.html" class="external-link">lrtest.default</a></code> from the lmtest package.</p>
</div>
- <pre class="usage"><span class='fu'>loftest</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span>
+ <div id="ref-usage">
+ <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">loftest</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="co"># S3 method for mkinfit</span></span>
+<span><span class="fu">loftest</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span><span class="op">)</span></span></code></pre></div>
+ </div>
-<span class='co'># S3 method for mkinfit</span>
-<span class='fu'>loftest</span><span class='op'>(</span><span class='va'>object</span>, <span class='va'>...</span><span class='op'>)</span></pre>
+ <div id="arguments">
+ <h2>Arguments</h2>
+ <dl><dt>object</dt>
+<dd><p>A model object with a defined loftest method</p></dd>
- <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 model object with a defined loftest method</p></td>
- </tr>
- <tr>
- <th>...</th>
- <td><p>Not used</p></td>
- </tr>
- </table>
- <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
+<dt>...</dt>
+<dd><p>Not used</p></dd>
+</dl></div>
+ <div id="details">
+ <h2>Details</h2>
<p>The anova model is interpreted as the simplest form of an mkinfit model,
assuming only a constant variance about the means, but not enforcing any
structure of the means, so we have one model parameter for every mean
of replicate samples.</p>
- <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2>
-
- <div class='dont-index'><p>lrtest</p></div>
+ </div>
+ <div id="see-also">
+ <h2>See also</h2>
+ <div class="dont-index"><p>lrtest</p></div>
+ </div>
- <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
- <pre class="examples"><div class='input'><span class='co'># \dontrun{</span>
-<span class='va'>test_data</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[[</span><span class='fl'>12</span><span class='op'>]</span><span class='op'>]</span><span class='op'>$</span><span class='va'>data</span>, <span class='va'>name</span> <span class='op'>==</span> <span class='st'>"parent"</span><span class='op'>)</span>
-<span class='va'>sfo_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='va'>test_data</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
-<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span><span class='op'>(</span><span class='va'>sfo_fit</span><span class='op'>)</span> <span class='co'># We see a clear pattern in the residuals</span>
-</div><div class='img'><img src='loftest-1.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>loftest</span><span class='op'>(</span><span class='va'>sfo_fit</span><span class='op'>)</span> <span class='co'># We have a clear lack of fit</span>
-</div><div class='output co'>#&gt; Likelihood ratio test
-#&gt;
-#&gt; Model 1: ANOVA with error model const
-#&gt; Model 2: SFO with error model const
-#&gt; #Df LogLik Df Chisq Pr(&gt;Chisq)
-#&gt; 1 10 -40.710
-#&gt; 2 3 -63.954 -7 46.487 7.027e-08 ***
-#&gt; ---
-#&gt; Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'>#</span>
-<span class='co'># We try a different model (the one that was used to generate the data)</span>
-<span class='va'>dfop_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='st'>"DFOP"</span>, <span class='va'>test_data</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
-<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span><span class='op'>(</span><span class='va'>dfop_fit</span><span class='op'>)</span> <span class='co'># We don't see systematic deviations, but heteroscedastic residuals</span>
-</div><div class='img'><img src='loftest-2.png' alt='' width='700' height='433' /></div><div class='input'><span class='co'># therefore we should consider adapting the error model, although we have</span>
-<span class='fu'>loftest</span><span class='op'>(</span><span class='va'>dfop_fit</span><span class='op'>)</span> <span class='co'># no lack of fit</span>
-</div><div class='output co'>#&gt; Likelihood ratio test
-#&gt;
-#&gt; Model 1: ANOVA with error model const
-#&gt; Model 2: DFOP with error model const
-#&gt; #Df LogLik Df Chisq Pr(&gt;Chisq)
-#&gt; 1 10 -40.710
-#&gt; 2 5 -42.453 -5 3.485 0.6257</div><div class='input'><span class='co'>#</span>
-<span class='co'># This is the anova model used internally for the comparison</span>
-<span class='va'>test_data_anova</span> <span class='op'>&lt;-</span> <span class='va'>test_data</span>
-<span class='va'>test_data_anova</span><span class='op'>$</span><span class='va'>time</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span><span class='op'>(</span><span class='va'>test_data_anova</span><span class='op'>$</span><span class='va'>time</span><span class='op'>)</span>
-<span class='va'>anova_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span><span class='op'>(</span><span class='va'>value</span> <span class='op'>~</span> <span class='va'>time</span>, data <span class='op'>=</span> <span class='va'>test_data_anova</span><span class='op'>)</span>
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>anova_fit</span><span class='op'>)</span>
-</div><div class='output co'>#&gt;
-#&gt; Call:
-#&gt; lm(formula = value ~ time, data = test_data_anova)
-#&gt;
-#&gt; Residuals:
-#&gt; Min 1Q Median 3Q Max
-#&gt; -6.1000 -0.5625 0.0000 0.5625 6.1000
-#&gt;
-#&gt; Coefficients:
-#&gt; Estimate Std. Error t value Pr(&gt;|t|)
-#&gt; (Intercept) 103.150 2.323 44.409 7.44e-12 ***
-#&gt; time1 -19.950 3.285 -6.073 0.000185 ***
-#&gt; time3 -50.800 3.285 -15.465 8.65e-08 ***
-#&gt; time7 -68.500 3.285 -20.854 6.28e-09 ***
-#&gt; time14 -79.750 3.285 -24.278 1.63e-09 ***
-#&gt; time28 -86.000 3.285 -26.181 8.35e-10 ***
-#&gt; time60 -94.900 3.285 -28.891 3.48e-10 ***
-#&gt; time90 -98.500 3.285 -29.986 2.49e-10 ***
-#&gt; time120 -100.450 3.285 -30.580 2.09e-10 ***
-#&gt; ---
-#&gt; Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-#&gt;
-#&gt; Residual standard error: 3.285 on 9 degrees of freedom
-#&gt; Multiple R-squared: 0.9953, Adjusted R-squared: 0.9912
-#&gt; F-statistic: 240.5 on 8 and 9 DF, p-value: 1.417e-09
-#&gt; </div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/logLik.html'>logLik</a></span><span class='op'>(</span><span class='va'>anova_fit</span><span class='op'>)</span> <span class='co'># We get the same likelihood and degrees of freedom</span>
-</div><div class='output co'>#&gt; 'log Lik.' -40.71015 (df=10)</div><div class='input'><span class='co'>#</span>
-<span class='va'>test_data_2</span> <span class='op'>&lt;-</span> <span class='va'>synthetic_data_for_UBA_2014</span><span class='op'>[[</span><span class='fl'>12</span><span class='op'>]</span><span class='op'>]</span><span class='op'>$</span><span class='va'>data</span>
-<span class='va'>m_synth_SFO_lin</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"M1"</span><span class='op'>)</span>,
- M1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='st'>"M2"</span><span class='op'>)</span>,
- M2 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>sfo_lin_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_SFO_lin</span>, <span class='va'>test_data_2</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
-<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span><span class='op'>(</span><span class='va'>sfo_lin_fit</span><span class='op'>)</span> <span class='co'># not a good model, we try parallel formation</span>
-</div><div class='img'><img src='loftest-3.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>loftest</span><span class='op'>(</span><span class='va'>sfo_lin_fit</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; Likelihood ratio test
-#&gt;
-#&gt; Model 1: ANOVA with error model const
-#&gt; Model 2: m_synth_SFO_lin with error model const and fixed parameter(s) M1_0, M2_0
-#&gt; #Df LogLik Df Chisq Pr(&gt;Chisq)
-#&gt; 1 28 -93.606
-#&gt; 2 7 -171.927 -21 156.64 &lt; 2.2e-16 ***
-#&gt; ---
-#&gt; Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'>#</span>
-<span class='va'>m_synth_SFO_par</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span>, to <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>,
- M1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>,
- M2 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>sfo_par_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_SFO_par</span>, <span class='va'>test_data_2</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
-<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span><span class='op'>(</span><span class='va'>sfo_par_fit</span><span class='op'>)</span> <span class='co'># much better for metabolites</span>
-</div><div class='img'><img src='loftest-4.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>loftest</span><span class='op'>(</span><span class='va'>sfo_par_fit</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; Likelihood ratio test
-#&gt;
-#&gt; Model 1: ANOVA with error model const
-#&gt; Model 2: m_synth_SFO_par with error model const and fixed parameter(s) M1_0, M2_0
-#&gt; #Df LogLik Df Chisq Pr(&gt;Chisq)
-#&gt; 1 28 -93.606
-#&gt; 2 7 -156.331 -21 125.45 &lt; 2.2e-16 ***
-#&gt; ---
-#&gt; Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'>#</span>
-<span class='va'>m_synth_DFOP_par</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>parent <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"DFOP"</span>, to <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"M1"</span>, <span class='st'>"M2"</span><span class='op'>)</span><span class='op'>)</span>,
- M1 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>,
- M2 <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>type <span class='op'>=</span> <span class='st'>"SFO"</span><span class='op'>)</span>, use_of_ff <span class='op'>=</span> <span class='st'>"max"</span><span class='op'>)</span>
-</div><div class='output co'>#&gt; <span class='message'>Temporary DLL for differentials generated and loaded</span></div><div class='input'><span class='va'>dfop_par_fit</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span><span class='op'>(</span><span class='va'>m_synth_DFOP_par</span>, <span class='va'>test_data_2</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
-<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span><span class='op'>(</span><span class='va'>dfop_par_fit</span><span class='op'>)</span> <span class='co'># No visual lack of fit</span>
-</div><div class='img'><img src='loftest-5.png' alt='' width='700' height='433' /></div><div class='input'><span class='fu'>loftest</span><span class='op'>(</span><span class='va'>dfop_par_fit</span><span class='op'>)</span> <span class='co'># no lack of fit found by the test</span>
-</div><div class='output co'>#&gt; Likelihood ratio test
-#&gt;
-#&gt; Model 1: ANOVA with error model const
-#&gt; Model 2: m_synth_DFOP_par with error model const and fixed parameter(s) M1_0, M2_0
-#&gt; #Df LogLik Df Chisq Pr(&gt;Chisq)
-#&gt; 1 28 -93.606
-#&gt; 2 9 -102.763 -19 18.313 0.5016</div><div class='input'><span class='co'>#</span>
-<span class='co'># The anova model used for comparison in the case of transformation products</span>
-<span class='va'>test_data_anova_2</span> <span class='op'>&lt;-</span> <span class='va'>dfop_par_fit</span><span class='op'>$</span><span class='va'>data</span>
-<span class='va'>test_data_anova_2</span><span class='op'>$</span><span class='va'>variable</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span><span class='op'>(</span><span class='va'>test_data_anova_2</span><span class='op'>$</span><span class='va'>variable</span><span class='op'>)</span>
-<span class='va'>test_data_anova_2</span><span class='op'>$</span><span class='va'>time</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span><span class='op'>(</span><span class='va'>test_data_anova_2</span><span class='op'>$</span><span class='va'>time</span><span class='op'>)</span>
-<span class='va'>anova_fit_2</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span><span class='op'>(</span><span class='va'>observed</span> <span class='op'>~</span> <span class='va'>time</span><span class='op'>:</span><span class='va'>variable</span> <span class='op'>-</span> <span class='fl'>1</span>, data <span class='op'>=</span> <span class='va'>test_data_anova_2</span><span class='op'>)</span>
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>anova_fit_2</span><span class='op'>)</span>
-</div><div class='output co'>#&gt;
-#&gt; Call:
-#&gt; lm(formula = observed ~ time:variable - 1, data = test_data_anova_2)
-#&gt;
-#&gt; Residuals:
-#&gt; Min 1Q Median 3Q Max
-#&gt; -6.1000 -0.5875 0.0000 0.5875 6.1000
-#&gt;
-#&gt; Coefficients: (2 not defined because of singularities)
-#&gt; Estimate Std. Error t value Pr(&gt;|t|)
-#&gt; time0:variableparent 103.150 1.573 65.562 &lt; 2e-16 ***
-#&gt; time1:variableparent 83.200 1.573 52.882 &lt; 2e-16 ***
-#&gt; time3:variableparent 52.350 1.573 33.274 &lt; 2e-16 ***
-#&gt; time7:variableparent 34.650 1.573 22.024 &lt; 2e-16 ***
-#&gt; time14:variableparent 23.400 1.573 14.873 6.35e-14 ***
-#&gt; time28:variableparent 17.150 1.573 10.901 5.47e-11 ***
-#&gt; time60:variableparent 8.250 1.573 5.244 1.99e-05 ***
-#&gt; time90:variableparent 4.650 1.573 2.956 0.006717 **
-#&gt; time120:variableparent 2.700 1.573 1.716 0.098507 .
-#&gt; time0:variableM1 NA NA NA NA
-#&gt; time1:variableM1 11.850 1.573 7.532 6.93e-08 ***
-#&gt; time3:variableM1 22.700 1.573 14.428 1.26e-13 ***
-#&gt; time7:variableM1 33.050 1.573 21.007 &lt; 2e-16 ***
-#&gt; time14:variableM1 31.250 1.573 19.863 &lt; 2e-16 ***
-#&gt; time28:variableM1 18.900 1.573 12.013 7.02e-12 ***
-#&gt; time60:variableM1 7.550 1.573 4.799 6.28e-05 ***
-#&gt; time90:variableM1 3.850 1.573 2.447 0.021772 *
-#&gt; time120:variableM1 2.050 1.573 1.303 0.204454
-#&gt; time0:variableM2 NA NA NA NA
-#&gt; time1:variableM2 6.700 1.573 4.259 0.000254 ***
-#&gt; time3:variableM2 16.750 1.573 10.646 8.93e-11 ***
-#&gt; time7:variableM2 25.800 1.573 16.399 6.89e-15 ***
-#&gt; time14:variableM2 28.600 1.573 18.178 6.35e-16 ***
-#&gt; time28:variableM2 25.400 1.573 16.144 9.85e-15 ***
-#&gt; time60:variableM2 21.600 1.573 13.729 3.81e-13 ***
-#&gt; time90:variableM2 17.800 1.573 11.314 2.51e-11 ***
-#&gt; time120:variableM2 14.100 1.573 8.962 2.79e-09 ***
-#&gt; ---
-#&gt; Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-#&gt;
-#&gt; Residual standard error: 2.225 on 25 degrees of freedom
-#&gt; Multiple R-squared: 0.9979, Adjusted R-squared: 0.9957
-#&gt; F-statistic: 469.2 on 25 and 25 DF, p-value: &lt; 2.2e-16
-#&gt; </div><div class='input'><span class='co'># }</span>
-</div></pre>
+ <div id="ref-examples">
+ <h2>Examples</h2>
+ <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># \dontrun{</span></span></span>
+<span class="r-in"><span><span class="va">test_data</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/subset.html" class="external-link">subset</a></span><span class="op">(</span><span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span>, <span class="va">name</span> <span class="op">==</span> <span class="st">"parent"</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">sfo_fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"SFO"</span>, <span class="va">test_data</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">sfo_fit</span><span class="op">)</span> <span class="co"># We see a clear pattern in the residuals</span></span></span>
+<span class="r-plt img"><img src="loftest-1.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu">loftest</span><span class="op">(</span><span class="va">sfo_fit</span><span class="op">)</span> <span class="co"># We have a clear lack of fit</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Likelihood ratio test</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 1: ANOVA with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 2: SFO with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> #Df LogLik Df Chisq Pr(&gt;Chisq) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 1 10 -40.710 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2 3 -63.954 -7 46.487 7.027e-08 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> ---</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="co"># We try a different model (the one that was used to generate the data)</span></span></span>
+<span class="r-in"><span><span class="va">dfop_fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="st">"DFOP"</span>, <span class="va">test_data</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">dfop_fit</span><span class="op">)</span> <span class="co"># We don't see systematic deviations, but heteroscedastic residuals</span></span></span>
+<span class="r-plt img"><img src="loftest-2.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="co"># therefore we should consider adapting the error model, although we have</span></span></span>
+<span class="r-in"><span><span class="fu">loftest</span><span class="op">(</span><span class="va">dfop_fit</span><span class="op">)</span> <span class="co"># no lack of fit</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Likelihood ratio test</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 1: ANOVA with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 2: DFOP with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> #Df LogLik Df Chisq Pr(&gt;Chisq)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 1 10 -40.710 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2 5 -42.453 -5 3.485 0.6257</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="co"># This is the anova model used internally for the comparison</span></span></span>
+<span class="r-in"><span><span class="va">test_data_anova</span> <span class="op">&lt;-</span> <span class="va">test_data</span></span></span>
+<span class="r-in"><span><span class="va">test_data_anova</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">as.factor</a></span><span class="op">(</span><span class="va">test_data_anova</span><span class="op">$</span><span class="va">time</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">anova_fit</span> <span class="op">&lt;-</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">value</span> <span class="op">~</span> <span class="va">time</span>, data <span class="op">=</span> <span class="va">test_data_anova</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">anova_fit</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Call:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> lm(formula = value ~ time, data = test_data_anova)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Residuals:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Min 1Q Median 3Q Max </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> -6.1000 -0.5625 0.0000 0.5625 6.1000 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Coefficients:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Estimate Std. Error t value Pr(&gt;|t|) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> (Intercept) 103.150 2.323 44.409 7.44e-12 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time1 -19.950 3.285 -6.073 0.000185 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time3 -50.800 3.285 -15.465 8.65e-08 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time7 -68.500 3.285 -20.854 6.28e-09 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time14 -79.750 3.285 -24.278 1.63e-09 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time28 -86.000 3.285 -26.181 8.35e-10 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time60 -94.900 3.285 -28.891 3.48e-10 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time90 -98.500 3.285 -29.986 2.49e-10 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time120 -100.450 3.285 -30.580 2.09e-10 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> ---</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Residual standard error: 3.285 on 9 degrees of freedom</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Multiple R-squared: 0.9953, Adjusted R-squared: 0.9912 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> F-statistic: 240.5 on 8 and 9 DF, p-value: 1.417e-09</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/stats/logLik.html" class="external-link">logLik</a></span><span class="op">(</span><span class="va">anova_fit</span><span class="op">)</span> <span class="co"># We get the same likelihood and degrees of freedom</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 'log Lik.' -40.71015 (df=10)</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="va">test_data_2</span> <span class="op">&lt;-</span> <span class="va">synthetic_data_for_UBA_2014</span><span class="op">[[</span><span class="fl">12</span><span class="op">]</span><span class="op">]</span><span class="op">$</span><span class="va">data</span></span></span>
+<span class="r-in"><span><span class="va">m_synth_SFO_lin</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="st">"M1"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="st">"M2"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Temporary DLL for differentials generated and loaded</span>
+<span class="r-in"><span><span class="va">sfo_lin_fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_synth_SFO_lin</span>, <span class="va">test_data_2</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">sfo_lin_fit</span><span class="op">)</span> <span class="co"># not a good model, we try parallel formation</span></span></span>
+<span class="r-plt img"><img src="loftest-3.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu">loftest</span><span class="op">(</span><span class="va">sfo_lin_fit</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Likelihood ratio test</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 1: ANOVA with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 2: m_synth_SFO_lin with error model const and fixed parameter(s) M1_0, M2_0</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> #Df LogLik Df Chisq Pr(&gt;Chisq) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 1 28 -93.606 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2 7 -171.927 -21 156.64 &lt; 2.2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> ---</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="va">m_synth_SFO_par</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span>, to <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Temporary DLL for differentials generated and loaded</span>
+<span class="r-in"><span><span class="va">sfo_par_fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_synth_SFO_par</span>, <span class="va">test_data_2</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">sfo_par_fit</span><span class="op">)</span> <span class="co"># much better for metabolites</span></span></span>
+<span class="r-plt img"><img src="loftest-4.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu">loftest</span><span class="op">(</span><span class="va">sfo_par_fit</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Likelihood ratio test</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 1: ANOVA with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 2: m_synth_SFO_par with error model const and fixed parameter(s) M1_0, M2_0</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> #Df LogLik Df Chisq Pr(&gt;Chisq) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 1 28 -93.606 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2 7 -156.331 -21 125.45 &lt; 2.2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> ---</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="va">m_synth_DFOP_par</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinmod.html">mkinmod</a></span><span class="op">(</span>parent <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"DFOP"</span>, to <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"M1"</span>, <span class="st">"M2"</span><span class="op">)</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span> M2 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span>type <span class="op">=</span> <span class="st">"SFO"</span><span class="op">)</span>, use_of_ff <span class="op">=</span> <span class="st">"max"</span><span class="op">)</span></span></span>
+<span class="r-msg co"><span class="r-pr">#&gt;</span> Temporary DLL for differentials generated and loaded</span>
+<span class="r-in"><span><span class="va">dfop_par_fit</span> <span class="op">&lt;-</span> <span class="fu"><a href="mkinfit.html">mkinfit</a></span><span class="op">(</span><span class="va">m_synth_DFOP_par</span>, <span class="va">test_data_2</span>, quiet <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="plot.mkinfit.html">plot_res</a></span><span class="op">(</span><span class="va">dfop_par_fit</span><span class="op">)</span> <span class="co"># No visual lack of fit</span></span></span>
+<span class="r-plt img"><img src="loftest-5.png" alt="" width="700" height="433"></span>
+<span class="r-in"><span><span class="fu">loftest</span><span class="op">(</span><span class="va">dfop_par_fit</span><span class="op">)</span> <span class="co"># no lack of fit found by the test</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Likelihood ratio test</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 1: ANOVA with error model const</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Model 2: m_synth_DFOP_par with error model const and fixed parameter(s) M1_0, M2_0</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> #Df LogLik Df Chisq Pr(&gt;Chisq)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 1 28 -93.606 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> 2 9 -102.763 -19 18.313 0.5016</span>
+<span class="r-in"><span><span class="co">#</span></span></span>
+<span class="r-in"><span><span class="co"># The anova model used for comparison in the case of transformation products</span></span></span>
+<span class="r-in"><span><span class="va">test_data_anova_2</span> <span class="op">&lt;-</span> <span class="va">dfop_par_fit</span><span class="op">$</span><span class="va">data</span></span></span>
+<span class="r-in"><span><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">variable</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">as.factor</a></span><span class="op">(</span><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">variable</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">time</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/factor.html" class="external-link">as.factor</a></span><span class="op">(</span><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">time</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="va">anova_fit_2</span> <span class="op">&lt;-</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">observed</span> <span class="op">~</span> <span class="va">time</span><span class="op">:</span><span class="va">variable</span> <span class="op">-</span> <span class="fl">1</span>, data <span class="op">=</span> <span class="va">test_data_anova_2</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">anova_fit_2</span><span class="op">)</span></span></span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Call:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> lm(formula = observed ~ time:variable - 1, data = test_data_anova_2)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Residuals:</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Min 1Q Median 3Q Max </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> -6.1000 -0.5875 0.0000 0.5875 6.1000 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Coefficients: (2 not defined because of singularities)</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Estimate Std. Error t value Pr(&gt;|t|) </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time0:variableparent 103.150 1.573 65.562 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time1:variableparent 83.200 1.573 52.882 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time3:variableparent 52.350 1.573 33.274 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time7:variableparent 34.650 1.573 22.024 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time14:variableparent 23.400 1.573 14.873 6.35e-14 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time28:variableparent 17.150 1.573 10.901 5.47e-11 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time60:variableparent 8.250 1.573 5.244 1.99e-05 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time90:variableparent 4.650 1.573 2.956 0.006717 ** </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time120:variableparent 2.700 1.573 1.716 0.098507 . </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time0:variableM1 NA NA NA NA </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time1:variableM1 11.850 1.573 7.532 6.93e-08 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time3:variableM1 22.700 1.573 14.428 1.26e-13 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time7:variableM1 33.050 1.573 21.007 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time14:variableM1 31.250 1.573 19.863 &lt; 2e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time28:variableM1 18.900 1.573 12.013 7.02e-12 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time60:variableM1 7.550 1.573 4.799 6.28e-05 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time90:variableM1 3.850 1.573 2.447 0.021772 * </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time120:variableM1 2.050 1.573 1.303 0.204454 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time0:variableM2 NA NA NA NA </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time1:variableM2 6.700 1.573 4.259 0.000254 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time3:variableM2 16.750 1.573 10.646 8.93e-11 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time7:variableM2 25.800 1.573 16.399 6.89e-15 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time14:variableM2 28.600 1.573 18.178 6.35e-16 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time28:variableM2 25.400 1.573 16.144 9.85e-15 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time60:variableM2 21.600 1.573 13.729 3.81e-13 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time90:variableM2 17.800 1.573 11.314 2.51e-11 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> time120:variableM2 14.100 1.573 8.962 2.79e-09 ***</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> ---</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Residual standard error: 2.225 on 25 degrees of freedom</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> Multiple R-squared: 0.9979, Adjusted R-squared: 0.9957 </span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> F-statistic: 469.2 on 25 and 25 DF, p-value: &lt; 2.2e-16</span>
+<span class="r-out co"><span class="r-pr">#&gt;</span> </span>
+<span class="r-in"><span><span class="co"># }</span></span></span>
+</code></pre></div>
+ </div>
</div>
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+ <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
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