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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'>&lt;-</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'>&lt;-</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'>#&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='no'>dfop_fit</span> <span class='kw'>&lt;-</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'>#&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='no'>test_data_anova</span> <span class='kw'>&lt;-</span> <span class='no'>test_data</span>
<span class='no'>test_data_anova</span>$<span class='no'>time</span> <span class='kw'>&lt;-</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'>&lt;-</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'>#&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='no'>anova_fit</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='no'>test_data_2</span> <span class='kw'>&lt;-</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'>&lt;-</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'>#&gt; <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'>&lt;-</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'>#&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='no'>m_synth_SFO_par</span> <span class='kw'>&lt;-</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'>#&gt; <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'>&lt;-</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'>#&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='no'>m_synth_DFOP_par</span> <span class='kw'>&lt;-</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'>#&gt; <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'>&lt;-</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'>#&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='no'>test_data_anova_2</span> <span class='kw'>&lt;-</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'>&lt;-</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'>&lt;-</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'>&lt;-</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'>#&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'># }
</div></pre>
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