Better initials for error model parameters

- Also make it possible to specify initial values for error model
parameters.
- Run tests
- Rebuild docs

1 files changed, 77 insertions, 77 deletions

diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html
index 8af99f6c..b05963ae 100644
--- a/docs/articles/FOCUS_L.html
+++ b/docs/articles/FOCUS_L.html
@@ -88,7 +88,7 @@
       <h1>Example evaluation of FOCUS Laboratory Data L1 to L3</h1>
                         <h4 class="author">Johannes Ranke</h4>
             
-            <h4 class="date">2019-04-10</h4>
+            <h4 class="date">2019-05-02</h4>
       
       
       <div class="hidden name"><code>FOCUS_L.Rmd</code></div>
@@ -113,19 +113,19 @@
 <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">m.L1.SFO &lt;-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"SFO"</span>, FOCUS_<span class="dv">2006</span>_L1_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a>
 <a class="sourceLine" id="cb2-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L1.SFO)</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:33 2019 
-## Date of summary: Wed Apr 10 10:11:33 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:31 2019 
+## Date of summary: Thu May  2 12:40:31 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 133 model solutions performed in 0.344 s
+## Fitted using 133 model solutions performed in 0.289 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##                   value   type
@@ -163,7 +163,7 @@
 ## k_parent_sink  0.09561   26.57 2.487e-14  0.08824  0.1036
 ## sigma          2.78000    6.00 1.216e-05  1.79200  3.7670
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.424       2  7
 ## parent     3.424       2  7
@@ -214,9 +214,9 @@
 <pre><code>## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
 ## finite result is doubtful</code></pre>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:34 2019 
-## Date of summary: Wed Apr 10 10:11:34 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:33 2019 
+## Date of summary: Thu May  2 12:40:33 2019 
 ## 
 ## 
 ## Warning: Optimisation did not converge:
@@ -228,24 +228,24 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 344 model solutions performed in 0.778 s
+## Fitted using 599 model solutions performed in 1.277 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
-##             value   type
-## parent_0 89.85000  state
-## alpha     1.00000 deparm
-## beta     10.00000 deparm
-## sigma     2.77987  error
+##              value   type
+## parent_0 89.850000  state
+## alpha     1.000000 deparm
+## beta     10.000000 deparm
+## sigma     2.779868  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  89.850000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
-## sigma      2.779870     0   Inf
+## sigma      2.779868     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
@@ -253,16 +253,16 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##           Estimate Std. Error  Lower  Upper
 ## parent_0     92.47     1.2810 89.720 95.220
-## log_alpha    10.60        NaN    NaN    NaN
-## log_beta     12.95        NaN    NaN    NaN
-## sigma         2.78     0.4554  1.803  3.757
+## log_alpha    10.66        NaN    NaN    NaN
+## log_beta     13.01        NaN    NaN    NaN
+## sigma         2.78     0.4599  1.794  3.766
 ## 
 ## Parameter correlation:
 ##           parent_0 log_alpha log_beta    sigma
-## parent_0  1.000000       NaN      NaN 0.008714
+## parent_0  1.000000       NaN      NaN 0.003475
 ## log_alpha      NaN         1      NaN      NaN
 ## log_beta       NaN       NaN        1      NaN
-## sigma     0.008714       NaN      NaN 1.000000
+## sigma     0.003475       NaN      NaN 1.000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -270,11 +270,11 @@
 ## for estimators of untransformed parameters.
 ##           Estimate  t value    Pr(&gt;t)  Lower  Upper
 ## parent_0     92.47 72.13000 1.052e-19 89.720 95.220
-## alpha     40090.00  0.02388 4.906e-01     NA     NA
-## beta     419300.00  0.02388 4.906e-01     NA     NA
-## sigma         2.78  6.00000 1.628e-05  1.803  3.757
+## alpha     42700.00  0.02298 4.910e-01     NA     NA
+## beta     446600.00  0.02298 4.910e-01     NA     NA
+## sigma         2.78  6.00000 1.628e-05  1.794  3.766
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.619       3  6
 ## parent     3.619       3  6
@@ -318,19 +318,19 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p>
 <div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:35 2019 
-## Date of summary: Wed Apr 10 10:11:35 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:34 2019 
+## Date of summary: Thu May  2 12:40:34 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 240 model solutions performed in 0.564 s
+## Fitted using 240 model solutions performed in 0.506 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##              value   type
@@ -373,7 +373,7 @@
 ## beta        1.234   4.012 1.942e-03  0.6945  2.192
 ## sigma       2.276   4.899 5.977e-04  1.2050  3.347
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   6.205       3  3
 ## parent     6.205       3  3
@@ -393,9 +393,9 @@
 <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-10-1.png" width="672"></p>
 <div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb20-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L2.DFOP, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:37 2019 
-## Date of summary: Wed Apr 10 10:11:37 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:35 2019 
+## Date of summary: Thu May  2 12:40:35 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -404,10 +404,10 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 585 model solutions performed in 1.296 s
+## Fitted using 587 model solutions performed in 1.273 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##              value   type
@@ -431,18 +431,18 @@
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0  93.9500  9.998e-01    91.5900   96.3100
-## log_k1     3.1350  2.336e+03 -5522.0000 5528.0000
+## log_k1     3.1330  2.265e+03 -5354.0000 5360.0000
 ## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
 ## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
 ## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0  1.000e+00  5.247e-07 -1.026e-10  2.665e-01 -8.076e-11
-## log_k1    5.247e-07  1.000e+00  8.592e-05 -1.690e-04 -7.938e-06
-## log_k2   -1.026e-10  8.592e-05  1.000e+00 -7.903e-01  5.048e-10
-## g_ilr     2.665e-01 -1.690e-04 -7.903e-01  1.000e+00 -6.476e-10
-## sigma    -8.076e-11 -7.938e-06  5.048e-10 -6.476e-10  1.000e+00
+## parent_0  1.000e+00  5.434e-07 -9.989e-11  2.665e-01 -3.978e-10
+## log_k1    5.434e-07  1.000e+00  8.888e-05 -1.748e-04 -8.207e-06
+## log_k2   -9.989e-11  8.888e-05  1.000e+00 -7.903e-01  5.751e-10
+## g_ilr     2.665e-01 -1.748e-04 -7.903e-01  1.000e+00 -7.109e-10
+## sigma    -3.978e-10 -8.207e-06  5.751e-10 -7.109e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -450,19 +450,19 @@
 ## for estimators of untransformed parameters.
 ##          Estimate   t value    Pr(&gt;t)   Lower   Upper
 ## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        23.0000 4.377e-04 4.998e-01  0.0000     Inf
+## k1        22.9300 4.514e-04 4.998e-01  0.0000     Inf
 ## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
 ## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
 ## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data    2.53       4  2
 ## parent      2.53       4  2
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50_k1 DT50_k2
-## parent 0.5335 5.311 0.03014   2.058</code></pre>
+## parent 0.5335 5.311 0.03023   2.058</code></pre>
 <p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.</p>
 </div>
 </div>
@@ -492,9 +492,9 @@
 <p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.</p>
 <div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]])</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:39 2019 
-## Date of summary: Wed Apr 10 10:11:39 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:37 2019 
+## Date of summary: Thu May  2 12:40:37 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -503,10 +503,10 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 372 model solutions performed in 0.809 s
+## Fitted using 372 model solutions performed in 0.777 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##              value   type
@@ -537,11 +537,11 @@
 ## 
 ## Parameter correlation:
 ##           parent_0     log_k1     log_k2      g_ilr      sigma
-## parent_0 1.000e+00  1.732e-01  2.282e-02  4.009e-01  1.656e-07
-## log_k1   1.732e-01  1.000e+00  4.945e-01 -5.809e-01  6.759e-08
-## log_k2   2.282e-02  4.945e-01  1.000e+00 -6.812e-01  3.867e-07
-## g_ilr    4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -3.839e-07
-## sigma    1.656e-07  6.759e-08  3.867e-07 -3.839e-07  1.000e+00
+## parent_0 1.000e+00  1.732e-01  2.282e-02  4.009e-01  1.660e-07
+## log_k1   1.732e-01  1.000e+00  4.945e-01 -5.809e-01  6.635e-08
+## log_k2   2.282e-02  4.945e-01  1.000e+00 -6.812e-01  3.880e-07
+## g_ilr    4.009e-01 -5.809e-01 -6.812e-01  1.000e+00 -3.822e-07
+## sigma    1.660e-07  6.635e-08  3.880e-07 -3.822e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -554,7 +554,7 @@
 ## g         0.45660  34.920 2.581e-05  0.41540   0.49850
 ## sigma     1.01700   4.000 1.400e-02  0.20790   1.82700
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.225       4  4
 ## parent     2.225       4  4
@@ -597,19 +597,19 @@
 <p>The <span class="math inline">\(\chi^2\)</span> error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the <span class="math inline">\(\chi^2\)</span> test passes is slightly lower for the FOMC model. However, the difference appears negligible.</p>
 <div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"SFO"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:39 2019 
-## Date of summary: Wed Apr 10 10:11:40 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:38 2019 
+## Date of summary: Thu May  2 12:40:38 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent_sink * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 146 model solutions performed in 0.306 s
+## Fitted using 146 model solutions performed in 0.298 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##                  value   type
@@ -634,9 +634,9 @@
 ## 
 ## Parameter correlation:
 ##                    parent_0 log_k_parent_sink      sigma
-## parent_0          1.000e+00         5.938e-01  5.612e-10
-## log_k_parent_sink 5.938e-01         1.000e+00 -4.994e-10
-## sigma             5.612e-10        -4.994e-10  1.000e+00
+## parent_0          1.000e+00         5.938e-01  4.256e-10
+## log_k_parent_sink 5.938e-01         1.000e+00 -7.280e-10
+## sigma             4.256e-10        -7.280e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -647,7 +647,7 @@
 ## k_parent_sink  0.006541   14.17 1.578e-05  0.005455 7.842e-03
 ## sigma          3.162000    4.00 5.162e-03  1.130000 5.194e+00
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   3.287       2  6
 ## parent     3.287       2  6
@@ -661,19 +661,19 @@
 ## parent  106  352</code></pre>
 <div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(mm.L4[[<span class="st">"FOMC"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div>
 <pre><code>## mkin version used for fitting:    0.9.49.4 
-## R version used for fitting:       3.5.3 
-## Date of fit:     Wed Apr 10 10:11:40 2019 
-## Date of summary: Wed Apr 10 10:11:40 2019 
+## R version used for fitting:       3.6.0 
+## Date of fit:     Thu May  2 12:40:38 2019 
+## Date of summary: Thu May  2 12:40:38 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method using 224 model solutions performed in 0.478 s
+## Fitted using 224 model solutions performed in 0.458 s
 ## 
 ## Error model:
-## NULL
+## Constant variance 
 ## 
 ## Starting values for parameters to be optimised:
 ##              value   type
@@ -701,10 +701,10 @@
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.460e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.351e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.079e-08
-## sigma     -2.460e-07  2.351e-08  5.079e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.473e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.429e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.183e-08
+## sigma     -2.473e-07  2.429e-08  5.183e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -716,7 +716,7 @@
 ## beta      64.9800   2.540 3.201e-02 21.7800 193.900
 ## sigma      1.8300   4.000 8.065e-03  0.5598   3.100
 ## 
-## Chi2 error levels in percent:
+## FOCUS Chi2 error levels in percent:
 ##          err.min n.optim df
 ## All data   2.029       3  5
 ## parent     2.029       3  5