From 9298a503d8de99dad1f61d6eb8bc228dd4acce6b Mon Sep 17 00:00:00 2001
From: Johannes Ranke <jranke@uni-bremen.de>
Date: Thu, 5 Nov 2020 08:31:21 +0100
Subject: Fix link and update docs

---
 docs/dev/reference/mkinfit.html | 167 ++++++++++++++++++++++------------------
 1 file changed, 94 insertions(+), 73 deletions(-)

(limited to 'docs/dev/reference/mkinfit.html')

diff --git a/docs/dev/reference/mkinfit.html b/docs/dev/reference/mkinfit.html
index 90fb26be..39bd12cb 100644
--- a/docs/dev/reference/mkinfit.html
+++ b/docs/dev/reference/mkinfit.html
@@ -80,7 +80,7 @@ likelihood function." />
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">mkin</a>
-        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.3</span>
+        <span class="version label label-info" data-toggle="tooltip" data-placement="bottom" title="In-development version">0.9.50.4</span>
       </span>
     </div>
 
@@ -128,7 +128,7 @@ likelihood function." />
       </ul>
       <ul class="nav navbar-nav navbar-right">
         <li>
-  <a href="http://github.com/jranke/mkin/">
+  <a href="https://github.com/jranke/mkin/">
     <span class="fab fa fab fa-github fa-lg"></span>
      
   </a>
@@ -147,7 +147,7 @@ likelihood function." />
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Fit a kinetic model to data with one or more state variables</h1>
-    <small class="dont-index">Source: <a href='http://github.com/jranke/mkin/blob/master/R/mkinfit.R'><code>R/mkinfit.R</code></a></small>
+    <small class="dont-index">Source: <a href='https://github.com/jranke/mkin/blob/master/R/mkinfit.R'><code>R/mkinfit.R</code></a></small>
     <div class="hidden name"><code>mkinfit.Rd</code></div>
     </div>
 
@@ -163,32 +163,33 @@ degradation model parameters, as both of them are arguments of the
 likelihood function.</p>
     </div>
 
-    <pre class="usage"><span class='fu'>mkinfit</span>(
-  <span class='no'>mkinmod</span>,
-  <span class='no'>observed</span>,
-  <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>state.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>err.ini</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>fixed_parms</span> <span class='kw'>=</span> <span class='kw'>NULL</span>,
-  <span class='kw'>fixed_initials</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span>(<span class='no'>mkinmod</span>$<span class='no'>diffs</span>)[-<span class='fl'>1</span>],
-  <span class='kw'>from_max_mean</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span>),
-  <span class='kw'>method.ode</span> <span class='kw'>=</span> <span class='st'>"lsoda"</span>,
-  <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='st'>"auto"</span>,
-  <span class='kw'>control</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>eval.max</span> <span class='kw'>=</span> <span class='fl'>300</span>, <span class='kw'>iter.max</span> <span class='kw'>=</span> <span class='fl'>200</span>),
-  <span class='kw'>transform_rates</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>transform_fractions</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>,
-  <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span>),
-  <span class='kw'>error_model_algorithm</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"auto"</span>, <span class='st'>"d_3"</span>, <span class='st'>"direct"</span>, <span class='st'>"twostep"</span>, <span class='st'>"threestep"</span>,
-    <span class='st'>"fourstep"</span>, <span class='st'>"IRLS"</span>, <span class='st'>"OLS"</span>),
-  <span class='kw'>reweight.tol</span> <span class='kw'>=</span> <span class='fl'>1e-08</span>,
-  <span class='kw'>reweight.max.iter</span> <span class='kw'>=</span> <span class='fl'>10</span>,
-  <span class='kw'>trace_parms</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>,
-  <span class='no'>...</span>
-)</pre>
+    <pre class="usage"><span class='fu'>mkinfit</span><span class='op'>(</span>
+  <span class='va'>mkinmod</span>,
+  <span class='va'>observed</span>,
+  parms.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  state.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  err.ini <span class='op'>=</span> <span class='st'>"auto"</span>,
+  fixed_parms <span class='op'>=</span> <span class='cn'>NULL</span>,
+  fixed_initials <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/names.html'>names</a></span><span class='op'>(</span><span class='va'>mkinmod</span><span class='op'>$</span><span class='va'>diffs</span><span class='op'>)</span><span class='op'>[</span><span class='op'>-</span><span class='fl'>1</span><span class='op'>]</span>,
+  from_max_mean <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  solution_type <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"auto"</span>, <span class='st'>"analytical"</span>, <span class='st'>"eigen"</span>, <span class='st'>"deSolve"</span><span class='op'>)</span>,
+  method.ode <span class='op'>=</span> <span class='st'>"lsoda"</span>,
+  use_compiled <span class='op'>=</span> <span class='st'>"auto"</span>,
+  control <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span><span class='op'>(</span>eval.max <span class='op'>=</span> <span class='fl'>300</span>, iter.max <span class='op'>=</span> <span class='fl'>200</span><span class='op'>)</span>,
+  transform_rates <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  transform_fractions <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  quiet <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  atol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  rtol <span class='op'>=</span> <span class='fl'>1e-10</span>,
+  error_model <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"const"</span>, <span class='st'>"obs"</span>, <span class='st'>"tc"</span><span class='op'>)</span>,
+  error_model_algorithm <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"auto"</span>, <span class='st'>"d_3"</span>, <span class='st'>"direct"</span>, <span class='st'>"twostep"</span>, <span class='st'>"threestep"</span>,
+    <span class='st'>"fourstep"</span>, <span class='st'>"IRLS"</span>, <span class='st'>"OLS"</span><span class='op'>)</span>,
+  reweight.tol <span class='op'>=</span> <span class='fl'>1e-08</span>,
+  reweight.max.iter <span class='op'>=</span> <span class='fl'>10</span>,
+  trace_parms <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  test_residuals <span class='op'>=</span> <span class='cn'>FALSE</span>,
+  <span class='va'>...</span>
+<span class='op'>)</span></pre>
 
     <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
     <table class="ref-arguments">
@@ -382,6 +383,10 @@ the error model parameters in IRLS fits.</p></td>
       <th>trace_parms</th>
       <td><p>Should a trace of the parameter values be listed?</p></td>
     </tr>
+    <tr>
+      <th>test_residuals</th>
+      <td><p>Should the residuals be tested for normal distribution?</p></td>
+    </tr>
     <tr>
       <th>...</th>
       <td><p>Further arguments that will be passed on to
@@ -417,22 +422,26 @@ Degradation Data. <em>Environments</em> 6(12) 124
 <code><a href='https://rdrr.io/r/stats/AIC.html'>AIC</a></code> by virtue of the method <code><a href='logLik.mkinfit.html'>logLik.mkinfit</a></code>.</p>
 <p>Fitting of several models to several datasets in a single call to
 <code><a href='mmkin.html'>mmkin</a></code>.</p></div>
+    <h2 class="hasAnchor" id="author"><a class="anchor" href="#author"></a>Author</h2>
+
+    <p>Johannes Ranke</p>
 
     <h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
     <pre class="examples"><div class='input'>
 <span class='co'># Use shorthand notation for parent only degradation</span>
-<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_C</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.3 
-#&gt; R version used for fitting:       4.0.2 
-#&gt; Date of fit:     Thu Oct  8 09:12:15 2020 
-#&gt; Date of summary: Thu Oct  8 09:12:15 2020 
+<span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_C</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.4 
+#&gt; R version used for fitting:       4.0.3 
+#&gt; Date of fit:     Thu Nov  5 08:25:42 2020 
+#&gt; Date of summary: Thu Nov  5 08:25:42 2020 
 #&gt; 
 #&gt; Equations:
 #&gt; d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 #&gt; 
 #&gt; Model predictions using solution type analytical 
 #&gt; 
-#&gt; Fitted using 222 model solutions performed in 0.045 s
+#&gt; Fitted using 222 model solutions performed in 0.049 s
 #&gt; 
 #&gt; Error model: Constant variance 
 #&gt; 
@@ -504,17 +513,20 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt;   119   parent      0.6     1.092  -0.4919</div><div class='input'>
 <span class='co'># One parent compound, one metabolite, both single first order.</span>
 <span class='co'># We remove zero values from FOCUS dataset D in order to avoid warnings</span>
-<span class='no'>FOCUS_D</span> <span class='kw'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span>(<span class='no'>FOCUS_2006_D</span>, <span class='no'>value</span> <span class='kw'>!=</span> <span class='fl'>0</span>)
+<span class='va'>FOCUS_D</span> <span class='op'>&lt;-</span> <span class='fu'><a href='https://rdrr.io/r/base/subset.html'>subset</a></span><span class='op'>(</span><span class='va'>FOCUS_2006_D</span>, <span class='va'>value</span> <span class='op'>!=</span> <span class='fl'>0</span><span class='op'>)</span>
 <span class='co'># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span>
-<span class='no'>SFO_SFO</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='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</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='va'>SFO_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</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='co'># Fit the model quietly to the FOCUS example dataset D using defaults</span>
-<span class='no'>fit</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0165</span></div><div class='input'><span class='co'># Since mkin 0.9.50.3, we get a warning about non-normality of residuals,</span>
+<span class='va'>fit</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='co'># Since mkin 0.9.50.3, we get a warning about non-normality of residuals,</span>
 <span class='co'># so we try an alternative error model</span>
-<span class='no'>fit.tc</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)
+<span class='va'>fit.tc</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
 <span class='co'># This avoids the warning, and the likelihood ratio test confirms it is preferable</span>
-<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span>(<span class='no'>fit.tc</span>, <span class='no'>fit</span>)</div><div class='output co'>#&gt; Likelihood ratio test
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
 #&gt; 
 #&gt; Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0
 #&gt; Model 2: SFO_SFO with error model const and fixed parameter(s) m1_0
@@ -523,10 +535,11 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 2   5 -97.224 -1 64.483  9.737e-16 ***
 #&gt; ---
 #&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='co'># We can also allow for different variances of parent and metabolite as error model</span>
-<span class='no'>fit.obs</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"obs"</span>)
+<span class='va'>fit.obs</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"obs"</span><span class='op'>)</span>
 <span class='co'># This also avoids the warning about non-normality, but the two-component error model</span>
 <span class='co'># has significantly higher likelihood</span>
-<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span>(<span class='no'>fit.obs</span>, <span class='no'>fit.tc</span>)</div><div class='output co'>#&gt; Likelihood ratio test
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.obs</span>, <span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
 #&gt; 
 #&gt; Model 1: SFO_SFO with error model tc and fixed parameter(s) m1_0
 #&gt; Model 2: SFO_SFO with error model obs and fixed parameter(s) m1_0
@@ -534,10 +547,12 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 1   6 -64.983                         
 #&gt; 2   6 -96.936  0 63.907  &lt; 2.2e-16 ***
 #&gt; ---
-#&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span>(<span class='no'>fit.tc</span>)</div><div class='output co'>#&gt;       parent_0       k_parent           k_m1 f_parent_to_m1      sigma_low 
+#&gt; Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1</div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt;       parent_0       k_parent           k_m1 f_parent_to_m1      sigma_low 
 #&gt;   1.007343e+02   1.005562e-01   5.166712e-03   5.083933e-01   3.049891e-03 
 #&gt;       rsd_high 
-#&gt;   7.928117e-02 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.tc</span>)</div><div class='output co'>#&gt; $ff
+#&gt;   7.928117e-02 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span><span class='op'>(</span><span class='va'>fit.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; $ff
 #&gt;   parent_m1 parent_sink 
 #&gt;   0.5083933   0.4916067 
 #&gt; 
@@ -551,27 +566,31 @@ Degradation Data. <em>Environments</em> 6(12) 124
 <span class='co'># uncompiled deSolve, as it is so slow. More benchmarks are found in the</span>
 <span class='co'># benchmark vignette</span>
 <span class='co'># \dontrun{</span>
-<span class='kw'>if</span>(<span class='fu'><a href='https://rdrr.io/r/base/library.html'>require</a></span>(<span class='no'>rbenchmark</span>)) {
-  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span>(<span class='kw'>replications</span> <span class='kw'>=</span> <span class='fl'>1</span>, <span class='kw'>order</span> <span class='kw'>=</span> <span class='st'>"relative"</span>, <span class='kw'>columns</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span>(<span class='st'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span>),
-    <span class='kw'>deSolve_compiled</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, <span class='kw'>use_compiled</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>),
-    <span class='kw'>eigen</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</span>),
-    <span class='kw'>analytical</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>,
-      <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"analytical"</span>))
-}</div><div class='output co'>#&gt;               test relative elapsed
-#&gt; 3       analytical    1.000   0.750
-#&gt; 1 deSolve_compiled    2.288   1.716
-#&gt; 2            eigen    2.821   2.116</div><div class='input'><span class='co'># }</span>
+<span class='kw'>if</span><span class='op'>(</span><span class='kw'><a href='https://rdrr.io/r/base/library.html'>require</a></span><span class='op'>(</span><span class='va'><a href='http://rbenchmark.googlecode.com'>rbenchmark</a></span><span class='op'>)</span><span class='op'>)</span> <span class='op'>{</span>
+  <span class='fu'><a href='https://rdrr.io/pkg/rbenchmark/man/benchmark.html'>benchmark</a></span><span class='op'>(</span>replications <span class='op'>=</span> <span class='fl'>1</span>, order <span class='op'>=</span> <span class='st'>"relative"</span>, columns <span class='op'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/c.html'>c</a></span><span class='op'>(</span><span class='st'>"test"</span>, <span class='st'>"relative"</span>, <span class='st'>"elapsed"</span><span class='op'>)</span>,
+    deSolve_compiled <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"deSolve"</span>, use_compiled <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>,
+    eigen <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"eigen"</span><span class='op'>)</span>,
+    analytical <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>SFO_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span>,
+      solution_type <span class='op'>=</span> <span class='st'>"analytical"</span><span class='op'>)</span><span class='op'>)</span>
+<span class='op'>}</span>
+</div><div class='output co'>#&gt; <span class='message'>Loading required package: rbenchmark</span></div><div class='output co'>#&gt;               test relative elapsed
+#&gt; 3       analytical    1.000   0.746
+#&gt; 1 deSolve_compiled    2.288   1.707
+#&gt; 2            eigen    2.708   2.020</div><div class='input'><span class='co'># }</span>
 
 <span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC-SFO</span>
 <span class='co'># \dontrun{</span>
-<span class='no'>FOMC_SFO</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='mkinsub.html'>mkinsub</a></span>(<span class='st'>"FOMC"</span>, <span class='st'>"m1"</span>),
-  <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span>(<span class='st'>"SFO"</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'>fit.FOMC_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: Shapiro-Wilk test for standardized residuals: p =  0.0499</span></div><div class='input'><span class='co'># Again, we get a warning and try a more sophisticated error model</span>
-<span class='no'>fit.FOMC_SFO.tc</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)
+<span class='va'>FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span><span class='op'>(</span>
+  parent <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='st'>"m1"</span><span class='op'>)</span>,
+  m1 <span class='op'>=</span> <span class='fu'><a href='mkinsub.html'>mkinsub</a></span><span class='op'>(</span><span class='st'>"SFO"</span><span class='op'>)</span><span class='op'>)</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='va'>fit.FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
+<span class='co'># Again, we get a warning and try a more sophisticated error model</span>
+<span class='va'>fit.FOMC_SFO.tc</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
 <span class='co'># This model has a higher likelihood, but not significantly so</span>
-<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span>(<span class='no'>fit.tc</span>, <span class='no'>fit.FOMC_SFO.tc</span>)</div><div class='output co'>#&gt; Likelihood ratio test
+<span class='fu'><a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a></span><span class='op'>(</span><span class='va'>fit.tc</span>, <span class='va'>fit.FOMC_SFO.tc</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; Likelihood ratio test
 #&gt; 
 #&gt; Model 1: FOMC_SFO with error model tc and fixed parameter(s) m1_0
 #&gt; Model 2: SFO_SFO with error model tc and fixed parameter(s) m1_0
@@ -579,10 +598,11 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 1   7 -64.829                     
 #&gt; 2   6 -64.983 -1 0.3075     0.5792</div><div class='input'><span class='co'># Also, the missing standard error for log_beta and the t-tests for alpha</span>
 <span class='co'># and beta indicate overparameterisation</span>
-<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>fit.FOMC_SFO.tc</span>, <span class='kw'>data</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>)</div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: diag(.) had 0 or NA entries; non-finite result is doubtful</span></div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.3 
-#&gt; R version used for fitting:       4.0.2 
-#&gt; Date of fit:     Thu Oct  8 09:12:29 2020 
-#&gt; Date of summary: Thu Oct  8 09:12:29 2020 
+<span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span><span class='op'>(</span><span class='va'>fit.FOMC_SFO.tc</span>, data <span class='op'>=</span> <span class='cn'>FALSE</span><span class='op'>)</span>
+</div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: NaNs produced</span></div><div class='output co'>#&gt; <span class='warning'>Warning: diag(.) had 0 or NA entries; non-finite result is doubtful</span></div><div class='output co'>#&gt; mkin version used for fitting:    0.9.50.4 
+#&gt; R version used for fitting:       4.0.3 
+#&gt; Date of fit:     Thu Nov  5 08:25:56 2020 
+#&gt; Date of summary: Thu Nov  5 08:25:56 2020 
 #&gt; 
 #&gt; Equations:
 #&gt; d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
@@ -591,7 +611,7 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; 
 #&gt; Model predictions using solution type deSolve 
 #&gt; 
-#&gt; Fitted using 3611 model solutions performed in 2.61 s
+#&gt; Fitted using 3611 model solutions performed in 2.673 s
 #&gt; 
 #&gt; Error model: Two-component variance function 
 #&gt; 
@@ -684,10 +704,11 @@ Degradation Data. <em>Environments</em> 6(12) 124
 #&gt; parent   6.812  22.7    6.834
 #&gt; m1     136.661 454.0       NA</div><div class='input'>
 <span class='co'># We can easily use starting parameters from the parent only fit (only for illustration)</span>
-<span class='no'>fit.FOMC</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"FOMC"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)
-<span class='no'>fit.FOMC_SFO</span> <span class='kw'>&lt;-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>,
-  <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.FOMC</span>$<span class='no'>bparms.ode</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>)
-<span class='co'># }</span></div></pre>
+<span class='va'>fit.FOMC</span> <span class='op'>=</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='st'>"FOMC"</span>, <span class='va'>FOCUS_2006_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='va'>fit.FOMC_SFO</span> <span class='op'>&lt;-</span> <span class='fu'>mkinfit</span><span class='op'>(</span><span class='va'>FOMC_SFO</span>, <span class='va'>FOCUS_D</span>, quiet <span class='op'>=</span> <span class='cn'>TRUE</span>,
+  parms.ini <span class='op'>=</span> <span class='va'>fit.FOMC</span><span class='op'>$</span><span class='va'>bparms.ode</span>, error_model <span class='op'>=</span> <span class='st'>"tc"</span><span class='op'>)</span>
+<span class='co'># }</span>
+</div></pre>
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   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
     <nav id="toc" data-toggle="toc" class="sticky-top">
@@ -703,7 +724,7 @@ Degradation Data. <em>Environments</em> 6(12) 124
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-  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p>
+  <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
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