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<h1>Lack-of-fit test for models fitted to data with replicates</h1>
<small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/loftest.R'><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'>lrtest.default</a></code> from the lmtest package.</p>
</div>
<pre class="usage"><span class='fu'>loftest</span>(<span class='no'>object</span>, <span class='no'>...</span>)
<span class='co'># S3 method for mkinfit</span>
<span class='fu'>loftest</span>(<span class='no'>object</span>, <span class='no'>...</span>)</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 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>
<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>
<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='no'>test_data</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>12</span>]]$<span class='no'>data</span>, <span class='no'>name</span> <span class='kw'>==</span> <span class='st'>"parent"</span>)
<span class='no'>sfo_fit</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"SFO"</span>, <span class='no'>test_data</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span>(<span class='no'>sfo_fit</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='no'>sfo_fit</span>) <span class='co'># We have a clear lack of fit</span></div><div class='output co'>#> Likelihood ratio test
#>
#> Model 1: ANOVA with error model const
#> Model 2: SFO with error model const
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 10 -40.710
#> 2 3 -63.954 -7 46.487 7.027e-08 ***
#> ---
#> 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='no'>dfop_fit</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='st'>"DFOP"</span>, <span class='no'>test_data</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span>(<span class='no'>dfop_fit</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='no'>dfop_fit</span>) <span class='co'># no lack of fit</span></div><div class='output co'>#> Likelihood ratio test
#>
#> Model 1: ANOVA with error model const
#> Model 2: DFOP with error model const
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 10 -40.710
#> 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='no'>test_data_anova</span> <span class='kw'><-</span> <span class='no'>test_data</span>
<span class='no'>test_data_anova</span>$<span class='no'>time</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span>(<span class='no'>test_data_anova</span>$<span class='no'>time</span>)
<span class='no'>anova_fit</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span>(<span class='no'>value</span> ~ <span class='no'>time</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>test_data_anova</span>)
<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>anova_fit</span>)</div><div class='output co'>#>
#> Call:
#> lm(formula = value ~ time, data = test_data_anova)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.1000 -0.5625 0.0000 0.5625 6.1000
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 103.150 2.323 44.409 7.44e-12 ***
#> time1 -19.950 3.285 -6.073 0.000185 ***
#> time3 -50.800 3.285 -15.465 8.65e-08 ***
#> time7 -68.500 3.285 -20.854 6.28e-09 ***
#> time14 -79.750 3.285 -24.278 1.63e-09 ***
#> time28 -86.000 3.285 -26.181 8.35e-10 ***
#> time60 -94.900 3.285 -28.891 3.48e-10 ***
#> time90 -98.500 3.285 -29.986 2.49e-10 ***
#> time120 -100.450 3.285 -30.580 2.09e-10 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 3.285 on 9 degrees of freedom
#> Multiple R-squared: 0.9953, Adjusted R-squared: 0.9912
#> F-statistic: 240.5 on 8 and 9 DF, p-value: 1.417e-09
#> </div><div class='input'><span class='fu'><a href='https://rdrr.io/r/stats/logLik.html'>logLik</a></span>(<span class='no'>anova_fit</span>) <span class='co'># We get the same likelihood and degrees of freedom</span></div><div class='output co'>#> 'log Lik.' -40.71015 (df=10)</div><div class='input'><span class='co'>#</span>
<span class='no'>test_data_2</span> <span class='kw'><-</span> <span class='no'>synthetic_data_for_UBA_2014</span><span class='kw'>[[</span><span class='fl'>12</span>]]$<span class='no'>data</span>
<span class='no'>m_synth_SFO_lin</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M1"</span>),
<span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"M2"</span>),
<span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>sfo_lin_fit</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_SFO_lin</span>, <span class='no'>test_data_2</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span>(<span class='no'>sfo_lin_fit</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='no'>sfo_lin_fit</span>)</div><div class='output co'>#> Likelihood ratio test
#>
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_SFO_lin with error model const and fixed parameter(s) M1_0, M2_0
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 28 -93.606
#> 2 7 -171.927 -21 156.64 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'>#</span>
<span class='no'>m_synth_SFO_par</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>)),
<span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
<span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>sfo_par_fit</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_SFO_par</span>, <span class='no'>test_data_2</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span>(<span class='no'>sfo_par_fit</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='no'>sfo_par_fit</span>)</div><div class='output co'>#> Likelihood ratio test
#>
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_SFO_par with error model const and fixed parameter(s) M1_0, M2_0
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 28 -93.606
#> 2 7 -156.331 -21 125.45 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'>#</span>
<span class='no'>m_synth_DFOP_par</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>(<span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"DFOP"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"M1"</span>, <span class='st'>"M2"</span>)),
<span class='kw'>M1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>),
<span class='kw'>M2</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>dfop_par_fit</span> <span class='kw'><-</span> <span class='fu'><a href='mkinfit.html'>mkinfit</a></span>(<span class='no'>m_synth_DFOP_par</span>, <span class='no'>test_data_2</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
<span class='fu'><a href='plot.mkinfit.html'>plot_res</a></span>(<span class='no'>dfop_par_fit</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='no'>dfop_par_fit</span>) <span class='co'># no lack of fit found by the test</span></div><div class='output co'>#> Likelihood ratio test
#>
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_DFOP_par with error model const and fixed parameter(s) M1_0, M2_0
#> #Df LogLik Df Chisq Pr(>Chisq)
#> 1 28 -93.606
#> 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='no'>test_data_anova_2</span> <span class='kw'><-</span> <span class='no'>dfop_par_fit</span>$<span class='no'>data</span>
<span class='no'>test_data_anova_2</span>$<span class='no'>variable</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span>(<span class='no'>test_data_anova_2</span>$<span class='no'>variable</span>)
<span class='no'>test_data_anova_2</span>$<span class='no'>time</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/factor.html'>as.factor</a></span>(<span class='no'>test_data_anova_2</span>$<span class='no'>time</span>)
<span class='no'>anova_fit_2</span> <span class='kw'><-</span> <span class='fu'><a href='https://rdrr.io/r/stats/lm.html'>lm</a></span>(<span class='no'>observed</span> ~ <span class='no'>time</span>:<span class='no'>variable</span> - <span class='fl'>1</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='no'>test_data_anova_2</span>)
<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>anova_fit_2</span>)</div><div class='output co'>#>
#> Call:
#> lm(formula = observed ~ time:variable - 1, data = test_data_anova_2)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -6.1000 -0.5875 0.0000 0.5875 6.1000
#>
#> Coefficients: (2 not defined because of singularities)
#> Estimate Std. Error t value Pr(>|t|)
#> time0:variableparent 103.150 1.573 65.562 < 2e-16 ***
#> time1:variableparent 83.200 1.573 52.882 < 2e-16 ***
#> time3:variableparent 52.350 1.573 33.274 < 2e-16 ***
#> time7:variableparent 34.650 1.573 22.024 < 2e-16 ***
#> time14:variableparent 23.400 1.573 14.873 6.35e-14 ***
#> time28:variableparent 17.150 1.573 10.901 5.47e-11 ***
#> time60:variableparent 8.250 1.573 5.244 1.99e-05 ***
#> time90:variableparent 4.650 1.573 2.956 0.006717 **
#> time120:variableparent 2.700 1.573 1.716 0.098507 .
#> time0:variableM1 NA NA NA NA
#> time1:variableM1 11.850 1.573 7.532 6.93e-08 ***
#> time3:variableM1 22.700 1.573 14.428 1.26e-13 ***
#> time7:variableM1 33.050 1.573 21.007 < 2e-16 ***
#> time14:variableM1 31.250 1.573 19.863 < 2e-16 ***
#> time28:variableM1 18.900 1.573 12.013 7.02e-12 ***
#> time60:variableM1 7.550 1.573 4.799 6.28e-05 ***
#> time90:variableM1 3.850 1.573 2.447 0.021772 *
#> time120:variableM1 2.050 1.573 1.303 0.204454
#> time0:variableM2 NA NA NA NA
#> time1:variableM2 6.700 1.573 4.259 0.000254 ***
#> time3:variableM2 16.750 1.573 10.646 8.93e-11 ***
#> time7:variableM2 25.800 1.573 16.399 6.89e-15 ***
#> time14:variableM2 28.600 1.573 18.178 6.35e-16 ***
#> time28:variableM2 25.400 1.573 16.144 9.85e-15 ***
#> time60:variableM2 21.600 1.573 13.729 3.81e-13 ***
#> time90:variableM2 17.800 1.573 11.314 2.51e-11 ***
#> time120:variableM2 14.100 1.573 8.962 2.79e-09 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#>
#> Residual standard error: 2.225 on 25 degrees of freedom
#> Multiple R-squared: 0.9979, Adjusted R-squared: 0.9957
#> F-statistic: 469.2 on 25 and 25 DF, p-value: < 2.2e-16
#> </div><div class='input'># }
</div></pre>
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