<!DOCTYPE html> <!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Lack-of-fit test for models fitted to data with replicates — loftest • mkin</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Lack-of-fit test for models fitted to data with replicates — loftest"><meta property="og:description" content="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 lrtest.default from the lmtest package."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]> <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script> <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script> <![endif]--></head><body data-spy="scroll" data-target="#toc"> <div class="container template-reference-topic"> <header><div class="navbar navbar-default navbar-fixed-top" role="navigation"> <div class="container"> <div class="navbar-header"> <button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar"></span> <span class="icon-bar"></span> <span class="icon-bar"></span> </button> <span class="navbar-brand"> <a class="navbar-link" href="../index.html">mkin</a> <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.2.0</span> </span> </div> <div id="navbar" class="navbar-collapse collapse"> <ul class="nav navbar-nav"><li> <a href="../reference/index.html">Functions and data</a> </li> <li class="dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Articles <span class="caret"></span> </a> <ul class="dropdown-menu" role="menu"><li> <a href="../articles/mkin.html">Introduction to mkin</a> </li> <li> <a href="../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a> </li> <li> <a href="../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a> </li> <li> <a href="../articles/web_only/dimethenamid_2018.html">Example evaluations of dimethenamid data from 2018 with nonlinear mixed-effects models</a> </li> <li> <a href="../articles/web_only/multistart.html">Short demo of the multistart method</a> </li> <li> <a href="../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a> </li> <li> <a href="../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a> </li> <li> <a href="../articles/twa.html">Calculation of time weighted average concentrations with mkin</a> </li> <li> <a href="../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a> </li> <li> <a href="../articles/web_only/benchmarks.html">Benchmark timings for mkin</a> </li> <li> <a href="../articles/web_only/saem_benchmarks.html">Benchmark timings for saem.mmkin</a> </li> </ul></li> <li> <a href="../news/index.html">News</a> </li> </ul><ul class="nav navbar-nav navbar-right"><li> <a href="https://github.com/jranke/mkin/" class="external-link"> <span class="fab fa-github fa-lg"></span> </a> </li> </ul></div><!--/.nav-collapse --> </div><!--/.container --> </div><!--/.navbar --> </header><div class="row"> <div class="col-md-9 contents"> <div class="page-header"> <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><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> <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><span class="co"># \dontrun{</span></span></span> <span class="r-in"><span><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> <span class="r-in"><span><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> <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">#></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><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"><-</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">#></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><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"><-</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"><-</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"><-</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">#></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><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">#></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"><-</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"><-</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">#></span> Temporary DLL for differentials generated and loaded</span> <span class="r-in"><span><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> <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">#></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><span class="co">#</span></span></span> <span class="r-in"><span><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> <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">#></span> Temporary DLL for differentials generated and loaded</span> <span class="r-in"><span><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> <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">#></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><span class="co">#</span></span></span> <span class="r-in"><span><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> <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">#></span> Temporary DLL for differentials generated and loaded</span> <span class="r-in"><span><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> <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">#></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><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"><-</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"><-</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"><-</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"><-</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">#></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><span class="co"># }</span></span></span> </code></pre></div> </div> </div> <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2> </nav></div> </div> <footer><div class="copyright"> <p></p><p>Developed by Johannes Ranke.</p> </div> <div class="pkgdown"> <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p> </div> </footer></div> </body></html>