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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/HEAD/R/loftest.R" class="external-link"><code>R/loftest.R</code></a></small>
<div class="hidden name"><code>loftest.Rd</code></div>
</div>
<div class="ref-description">
<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" class="external-link">lrtest.default</a></code> from the lmtest package.</p>
</div>
<div id="ref-usage">
<div class="sourceCode"><pre class="sourceCode r"><code><span class="fu">loftest</span><span class="op">(</span><span class="va">object</span>, <span class="va">...</span><span class="op">)</span>
<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></code></pre></div>
</div>
<div id="arguments">
<h2>Arguments</h2>
<dl><dt>object</dt>
<dd><p>A model object with a defined loftest method</p></dd>
<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>
</div>
<div id="see-also">
<h2>See also</h2>
<div class="dont-index"><p>lrtest</p></div>
</div>
<div id="ref-examples">
<h2>Examples</h2>
<div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span class="co"># \dontrun{</span></span>
<span class="r-in"><span class="va">test_data</span> <span class="op"><-</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 class="r-in"><span class="va">sfo_fit</span> <span class="op"><-</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 class="r-in"><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 class="r-plt img"><img src="loftest-1.png" alt="" width="700" height="433"></span>
<span class="r-in"><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 class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model 1: ANOVA with error model const</span>
<span class="r-out co"><span class="r-pr">#></span> Model 2: SFO with error model const</span>
<span class="r-out co"><span class="r-pr">#></span> #Df LogLik Df Chisq Pr(>Chisq) </span>
<span class="r-out co"><span class="r-pr">#></span> 1 10 -40.710 </span>
<span class="r-out co"><span class="r-pr">#></span> 2 3 -63.954 -7 46.487 7.027e-08 ***</span>
<span class="r-out co"><span class="r-pr">#></span> ---</span>
<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="co"># We try a different model (the one that was used to generate the data)</span></span>
<span class="r-in"><span class="va">dfop_fit</span> <span class="op"><-</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 class="r-in"><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 class="r-plt img"><img src="loftest-2.png" alt="" width="700" height="433"></span>
<span class="r-in"><span class="co"># therefore we should consider adapting the error model, although we have</span></span>
<span class="r-in"><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 class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model 1: ANOVA with error model const</span>
<span class="r-out co"><span class="r-pr">#></span> Model 2: DFOP with error model const</span>
<span class="r-out co"><span class="r-pr">#></span> #Df LogLik Df Chisq Pr(>Chisq)</span>
<span class="r-out co"><span class="r-pr">#></span> 1 10 -40.710 </span>
<span class="r-out co"><span class="r-pr">#></span> 2 5 -42.453 -5 3.485 0.6257</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="co"># This is the anova model used internally for the comparison</span></span>
<span class="r-in"><span class="va">test_data_anova</span> <span class="op"><-</span> <span class="va">test_data</span></span>
<span class="r-in"><span class="va">test_data_anova</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</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 class="r-in"><span class="va">anova_fit</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">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 class="r-in"><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 class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Call:</span>
<span class="r-out co"><span class="r-pr">#></span> lm(formula = value ~ time, data = test_data_anova)</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Residuals:</span>
<span class="r-out co"><span class="r-pr">#></span> Min 1Q Median 3Q Max </span>
<span class="r-out co"><span class="r-pr">#></span> -6.1000 -0.5625 0.0000 0.5625 6.1000 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Coefficients:</span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error t value Pr(>|t|) </span>
<span class="r-out co"><span class="r-pr">#></span> (Intercept) 103.150 2.323 44.409 7.44e-12 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time1 -19.950 3.285 -6.073 0.000185 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time3 -50.800 3.285 -15.465 8.65e-08 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time7 -68.500 3.285 -20.854 6.28e-09 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time14 -79.750 3.285 -24.278 1.63e-09 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time28 -86.000 3.285 -26.181 8.35e-10 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time60 -94.900 3.285 -28.891 3.48e-10 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time90 -98.500 3.285 -29.986 2.49e-10 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time120 -100.450 3.285 -30.580 2.09e-10 ***</span>
<span class="r-out co"><span class="r-pr">#></span> ---</span>
<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Residual standard error: 3.285 on 9 degrees of freedom</span>
<span class="r-out co"><span class="r-pr">#></span> Multiple R-squared: 0.9953, Adjusted R-squared: 0.9912 </span>
<span class="r-out co"><span class="r-pr">#></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">#></span> </span>
<span class="r-in"><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 class="r-out co"><span class="r-pr">#></span> 'log Lik.' -40.71015 (df=10)</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="va">test_data_2</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>
<span class="r-in"><span class="va">m_synth_SFO_lin</span> <span class="op"><-</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 class="r-in"> 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 class="r-in"> 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 class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span class="va">sfo_lin_fit</span> <span class="op"><-</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 class="r-in"><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 class="r-plt img"><img src="loftest-3.png" alt="" width="700" height="433"></span>
<span class="r-in"><span class="fu">loftest</span><span class="op">(</span><span class="va">sfo_lin_fit</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model 1: ANOVA with error model const</span>
<span class="r-out co"><span class="r-pr">#></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">#></span> #Df LogLik Df Chisq Pr(>Chisq) </span>
<span class="r-out co"><span class="r-pr">#></span> 1 28 -93.606 </span>
<span class="r-out co"><span class="r-pr">#></span> 2 7 -171.927 -21 156.64 < 2.2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> ---</span>
<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="va">m_synth_SFO_par</span> <span class="op"><-</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 class="r-in"> 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 class="r-in"> 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 class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span class="va">sfo_par_fit</span> <span class="op"><-</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 class="r-in"><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 class="r-plt img"><img src="loftest-4.png" alt="" width="700" height="433"></span>
<span class="r-in"><span class="fu">loftest</span><span class="op">(</span><span class="va">sfo_par_fit</span><span class="op">)</span></span>
<span class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model 1: ANOVA with error model const</span>
<span class="r-out co"><span class="r-pr">#></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">#></span> #Df LogLik Df Chisq Pr(>Chisq) </span>
<span class="r-out co"><span class="r-pr">#></span> 1 28 -93.606 </span>
<span class="r-out co"><span class="r-pr">#></span> 2 7 -156.331 -21 125.45 < 2.2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> ---</span>
<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="va">m_synth_DFOP_par</span> <span class="op"><-</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 class="r-in"> 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 class="r-in"> 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 class="r-msg co"><span class="r-pr">#></span> Temporary DLL for differentials generated and loaded</span>
<span class="r-in"><span class="va">dfop_par_fit</span> <span class="op"><-</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 class="r-in"><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 class="r-plt img"><img src="loftest-5.png" alt="" width="700" height="433"></span>
<span class="r-in"><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 class="r-out co"><span class="r-pr">#></span> Likelihood ratio test</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Model 1: ANOVA with error model const</span>
<span class="r-out co"><span class="r-pr">#></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">#></span> #Df LogLik Df Chisq Pr(>Chisq)</span>
<span class="r-out co"><span class="r-pr">#></span> 1 28 -93.606 </span>
<span class="r-out co"><span class="r-pr">#></span> 2 9 -102.763 -19 18.313 0.5016</span>
<span class="r-in"><span class="co">#</span></span>
<span class="r-in"><span class="co"># The anova model used for comparison in the case of transformation products</span></span>
<span class="r-in"><span class="va">test_data_anova_2</span> <span class="op"><-</span> <span class="va">dfop_par_fit</span><span class="op">$</span><span class="va">data</span></span>
<span class="r-in"><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">variable</span> <span class="op"><-</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">$</span><span class="va">variable</span><span class="op">)</span></span>
<span class="r-in"><span class="va">test_data_anova_2</span><span class="op">$</span><span class="va">time</span> <span class="op"><-</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 class="r-in"><span class="va">anova_fit_2</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">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 class="r-in"><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 class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Call:</span>
<span class="r-out co"><span class="r-pr">#></span> lm(formula = observed ~ time:variable - 1, data = test_data_anova_2)</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Residuals:</span>
<span class="r-out co"><span class="r-pr">#></span> Min 1Q Median 3Q Max </span>
<span class="r-out co"><span class="r-pr">#></span> -6.1000 -0.5875 0.0000 0.5875 6.1000 </span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Coefficients: (2 not defined because of singularities)</span>
<span class="r-out co"><span class="r-pr">#></span> Estimate Std. Error t value Pr(>|t|) </span>
<span class="r-out co"><span class="r-pr">#></span> time0:variableparent 103.150 1.573 65.562 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time1:variableparent 83.200 1.573 52.882 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time3:variableparent 52.350 1.573 33.274 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time7:variableparent 34.650 1.573 22.024 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time14:variableparent 23.400 1.573 14.873 6.35e-14 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time28:variableparent 17.150 1.573 10.901 5.47e-11 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time60:variableparent 8.250 1.573 5.244 1.99e-05 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time90:variableparent 4.650 1.573 2.956 0.006717 ** </span>
<span class="r-out co"><span class="r-pr">#></span> time120:variableparent 2.700 1.573 1.716 0.098507 . </span>
<span class="r-out co"><span class="r-pr">#></span> time0:variableM1 NA NA NA NA </span>
<span class="r-out co"><span class="r-pr">#></span> time1:variableM1 11.850 1.573 7.532 6.93e-08 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time3:variableM1 22.700 1.573 14.428 1.26e-13 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time7:variableM1 33.050 1.573 21.007 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time14:variableM1 31.250 1.573 19.863 < 2e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time28:variableM1 18.900 1.573 12.013 7.02e-12 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time60:variableM1 7.550 1.573 4.799 6.28e-05 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time90:variableM1 3.850 1.573 2.447 0.021772 * </span>
<span class="r-out co"><span class="r-pr">#></span> time120:variableM1 2.050 1.573 1.303 0.204454 </span>
<span class="r-out co"><span class="r-pr">#></span> time0:variableM2 NA NA NA NA </span>
<span class="r-out co"><span class="r-pr">#></span> time1:variableM2 6.700 1.573 4.259 0.000254 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time3:variableM2 16.750 1.573 10.646 8.93e-11 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time7:variableM2 25.800 1.573 16.399 6.89e-15 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time14:variableM2 28.600 1.573 18.178 6.35e-16 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time28:variableM2 25.400 1.573 16.144 9.85e-15 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time60:variableM2 21.600 1.573 13.729 3.81e-13 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time90:variableM2 17.800 1.573 11.314 2.51e-11 ***</span>
<span class="r-out co"><span class="r-pr">#></span> time120:variableM2 14.100 1.573 8.962 2.79e-09 ***</span>
<span class="r-out co"><span class="r-pr">#></span> ---</span>
<span class="r-out co"><span class="r-pr">#></span> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-out co"><span class="r-pr">#></span> Residual standard error: 2.225 on 25 degrees of freedom</span>
<span class="r-out co"><span class="r-pr">#></span> Multiple R-squared: 0.9979, Adjusted R-squared: 0.9957 </span>
<span class="r-out co"><span class="r-pr">#></span> F-statistic: 469.2 on 25 and 25 DF, p-value: < 2.2e-16</span>
<span class="r-out co"><span class="r-pr">#></span> </span>
<span class="r-in"><span class="co"># }</span></span>
</code></pre></div>
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