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1 files changed, 176 insertions, 151 deletions
diff --git a/docs/articles/FOCUS_L.html b/docs/articles/FOCUS_L.html index 23fa68c6..2cffb323 100644 --- a/docs/articles/FOCUS_L.html +++ b/docs/articles/FOCUS_L.html @@ -112,19 +112,17 @@ <p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code> for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.</p> <div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">m.L1.SFO <-<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>## Warning in summary.mkinfit(m.L1.SFO): Could not calculate correlation; no -## covariance matrix</code></pre> <pre><code>## mkin version used for fitting: 0.9.49.4 ## R version used for fitting: 3.6.0 -## Date of fit: Tue May 7 08:09:13 2019 -## Date of summary: Tue May 7 08:09:13 2019 +## Date of fit: Tue May 7 08:37:48 2019 +## Date of summary: Tue May 7 08:37:48 2019 ## ## Equations: ## d_parent/dt = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted using 41 model solutions performed in 0.088 s +## Fitted using 133 model solutions performed in 0.284 s ## ## Error model: ## Constant variance @@ -145,21 +143,25 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 92.470 NA NA NA -## log_k_parent_sink -2.347 NA NA NA -## sigma 2.780 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 92.470 1.28200 89.740 95.200 +## log_k_parent_sink -2.347 0.03763 -2.428 -2.267 +## sigma 2.780 0.46330 1.792 3.767 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_k_parent_sink sigma +## parent_0 1.000e+00 6.186e-01 -1.712e-09 +## log_k_parent_sink 6.186e-01 1.000e+00 -3.237e-09 +## sigma -1.712e-09 -3.237e-09 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 92.47000 NA NA NA NA -## k_parent_sink 0.09561 NA NA NA NA -## sigma 2.78000 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 92.47000 72.13 8.824e-21 89.74000 95.2000 +## 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 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -195,24 +197,26 @@ ## 30 parent 2.9 5.251 -2.3513 ## 30 parent 4.0 5.251 -1.2513</code></pre> <p>A plot of the fit is obtained with the plot function for mkinfit objects.</p> -<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L1.SFO, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>, <span class="dt">main =</span> <span class="st">"FOCUS L1 - SFO"</span>)</a></code></pre></div> +<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L1.SFO, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>, <span class="dt">main =</span> <span class="st">"FOCUS L1 - SFO"</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-4-1.png" width="576"></p> <p>The residual plot can be easily obtained by</p> -<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1"><span class="kw"><a href="../reference/mkinresplot.html">mkinresplot</a></span>(m.L1.SFO, <span class="dt">ylab =</span> <span class="st">"Observed"</span>, <span class="dt">xlab =</span> <span class="st">"Time"</span>)</a></code></pre></div> +<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" title="1"><span class="kw"><a href="../reference/mkinresplot.html">mkinresplot</a></span>(m.L1.SFO, <span class="dt">ylab =</span> <span class="st">"Observed"</span>, <span class="dt">xlab =</span> <span class="st">"Time"</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-5-1.png" width="576"></p> <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p> -<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb7-1" title="1">m.L1.FOMC <-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L1_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a></code></pre></div> +<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" title="1">m.L1.FOMC <-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L1_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a></code></pre></div> <pre><code>## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge: ## false convergence (8)</code></pre> -<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L1.FOMC, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>, <span class="dt">main =</span> <span class="st">"FOCUS L1 - FOMC"</span>)</a></code></pre></div> +<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L1.FOMC, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>, <span class="dt">main =</span> <span class="st">"FOCUS L1 - FOMC"</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-6-1.png" width="576"></p> -<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L1.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div> -<pre><code>## Warning in summary.mkinfit(m.L1.FOMC, data = FALSE): Could not calculate -## correlation; no covariance matrix</code></pre> +<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb9-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/summary">summary</a></span>(m.L1.FOMC, <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div> +<pre><code>## Warning in sqrt(diag(covar)): NaNs wurden erzeugt</code></pre> +<pre><code>## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt</code></pre> +<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: 3.6.0 -## Date of fit: Tue May 7 08:09:14 2019 -## Date of summary: Tue May 7 08:09:14 2019 +## Date of fit: Tue May 7 08:37:50 2019 +## Date of summary: Tue May 7 08:37:50 2019 ## ## ## Warning: Optimisation did not converge: @@ -224,7 +228,7 @@ ## ## Model predictions using solution type analytical ## -## Fitted using 743 model solutions performed in 1.558 s +## Fitted using 899 model solutions performed in 1.913 s ## ## Error model: ## Constant variance @@ -247,23 +251,28 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 92.47 NA NA NA -## log_alpha 10.58 NA NA NA -## log_beta 12.93 NA NA NA -## sigma 2.78 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 92.47 1.2800 89.730 95.220 +## log_alpha 10.58 NaN NaN NaN +## log_beta 12.93 NaN NaN NaN +## sigma 2.78 0.4507 1.813 3.747 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_alpha log_beta sigma +## parent_0 1.00000 NaN NaN 0.01452 +## log_alpha NaN 1 NaN NaN +## log_beta NaN NaN 1 NaN +## sigma 0.01452 NaN NaN 1.00000 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 92.47 NA NA NA NA -## alpha 39440.00 NA NA NA NA -## beta 412500.00 NA NA NA NA -## sigma 2.78 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 92.47 72.13000 1.052e-19 89.730 95.220 +## alpha 39440.00 0.02397 4.906e-01 NA NA +## beta 412500.00 0.02397 4.906e-01 NA NA +## sigma 2.78 6.00000 1.628e-05 1.813 3.747 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -281,19 +290,19 @@ <h1 class="hasAnchor"> <a href="#laboratory-data-l2" class="anchor"></a>Laboratory Data L2</h1> <p>The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:</p> -<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb13-1" title="1">FOCUS_<span class="dv">2006</span>_L2 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> -<a class="sourceLine" id="cb13-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/rep">rep</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">28</span>), <span class="dt">each =</span> <span class="dv">2</span>),</a> -<a class="sourceLine" id="cb13-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,</a> -<a class="sourceLine" id="cb13-4" title="4"> <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</a> -<a class="sourceLine" id="cb13-5" title="5"> <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))</a> -<a class="sourceLine" id="cb13-6" title="6">FOCUS_<span class="dv">2006</span>_L2_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L2)</a></code></pre></div> +<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1">FOCUS_<span class="dv">2006</span>_L2 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> +<a class="sourceLine" id="cb14-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/rep">rep</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">28</span>), <span class="dt">each =</span> <span class="dv">2</span>),</a> +<a class="sourceLine" id="cb14-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.1</span>, <span class="fl">91.8</span>, <span class="fl">41.4</span>, <span class="fl">38.7</span>,</a> +<a class="sourceLine" id="cb14-4" title="4"> <span class="fl">19.3</span>, <span class="fl">22.3</span>, <span class="fl">4.6</span>, <span class="fl">4.6</span>,</a> +<a class="sourceLine" id="cb14-5" title="5"> <span class="fl">2.6</span>, <span class="fl">1.2</span>, <span class="fl">0.3</span>, <span class="fl">0.6</span>))</a> +<a class="sourceLine" id="cb14-6" title="6">FOCUS_<span class="dv">2006</span>_L2_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L2)</a></code></pre></div> <div id="sfo-fit-for-l2" class="section level2"> <h2 class="hasAnchor"> <a href="#sfo-fit-for-l2" class="anchor"></a>SFO fit for L2</h2> <p>Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument <code>show_residuals</code> to the plot command.</p> -<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" title="1">m.L2.SFO <-<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>_L2_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a> -<a class="sourceLine" id="cb14-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.SFO, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a> -<a class="sourceLine" id="cb14-3" title="3"> <span class="dt">main =</span> <span class="st">"FOCUS L2 - SFO"</span>)</a></code></pre></div> +<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">m.L2.SFO <-<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>_L2_mkin, <span class="dt">quiet=</span><span class="ot">TRUE</span>)</a> +<a class="sourceLine" id="cb15-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.SFO, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>, <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>,</a> +<a class="sourceLine" id="cb15-3" title="3"> <span class="dt">main =</span> <span class="st">"FOCUS L2 - SFO"</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-8-1.png" width="672"></p> <p>The <span class="math inline">\(\chi^2\)</span> error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.</p> <p>In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.</p> @@ -303,24 +312,22 @@ <h2 class="hasAnchor"> <a href="#fomc-fit-for-l2" class="anchor"></a>FOMC fit for L2</h2> <p>For comparison, the FOMC model is fitted as well, and the <span class="math inline">\(\chi^2\)</span> error level is checked.</p> -<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" title="1">m.L2.FOMC <-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> -<a class="sourceLine" id="cb15-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.FOMC, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>,</a> -<a class="sourceLine" id="cb15-3" title="3"> <span class="dt">main =</span> <span class="st">"FOCUS L2 - FOMC"</span>)</a></code></pre></div> +<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" title="1">m.L2.FOMC <-<span class="st"> </span><span class="kw"><a href="../reference/mkinfit.html">mkinfit</a></span>(<span class="st">"FOMC"</span>, FOCUS_<span class="dv">2006</span>_L2_mkin, <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> +<a class="sourceLine" id="cb16-2" title="2"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(m.L2.FOMC, <span class="dt">show_residuals =</span> <span class="ot">TRUE</span>,</a> +<a class="sourceLine" id="cb16-3" title="3"> <span class="dt">main =</span> <span class="st">"FOCUS L2 - FOMC"</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-9-1.png" width="672"></p> -<div class="sourceCode" id="cb16"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb16-1" 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>## Warning in summary.mkinfit(m.L2.FOMC, data = FALSE): Could not calculate -## correlation; no covariance matrix</code></pre> +<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: 3.6.0 -## Date of fit: Tue May 7 08:09:15 2019 -## Date of summary: Tue May 7 08:09:15 2019 +## Date of fit: Tue May 7 08:37:51 2019 +## Date of summary: Tue May 7 08:37:51 2019 ## ## Equations: ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent ## ## Model predictions using solution type analytical ## -## Fitted using 83 model solutions performed in 0.169 s +## Fitted using 239 model solutions performed in 0.494 s ## ## Error model: ## Constant variance @@ -343,23 +350,28 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 93.7700 NA NA NA -## log_alpha 0.3180 NA NA NA -## log_beta 0.2102 NA NA NA -## sigma 2.2760 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 93.7700 1.6130 90.05000 97.4900 +## log_alpha 0.3180 0.1559 -0.04149 0.6776 +## log_beta 0.2102 0.2493 -0.36460 0.7850 +## sigma 2.2760 0.4645 1.20500 3.3470 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_alpha log_beta sigma +## parent_0 1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09 +## log_alpha -1.151e-01 1.000e+00 9.741e-01 -1.617e-07 +## log_beta -2.085e-01 9.741e-01 1.000e+00 -1.387e-07 +## sigma -7.637e-09 -1.617e-07 -1.387e-07 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 93.770 NA NA NA NA -## alpha 1.374 NA NA NA NA -## beta 1.234 NA NA NA NA -## sigma 2.276 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 93.770 58.120 4.267e-12 90.0500 97.490 +## alpha 1.374 6.414 1.030e-04 0.9594 1.969 +## beta 1.234 4.012 1.942e-03 0.6945 2.192 +## sigma 2.276 4.899 5.977e-04 1.2050 3.347 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -380,12 +392,10 @@ <a class="sourceLine" id="cb19-3" title="3"> <span class="dt">main =</span> <span class="st">"FOCUS L2 - DFOP"</span>)</a></code></pre></div> <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>## Warning in summary.mkinfit(m.L2.DFOP, data = FALSE): Could not calculate -## correlation; no covariance matrix</code></pre> <pre><code>## mkin version used for fitting: 0.9.49.4 ## R version used for fitting: 3.6.0 -## Date of fit: Tue May 7 08:09:16 2019 -## Date of summary: Tue May 7 08:09:16 2019 +## Date of fit: Tue May 7 08:37:53 2019 +## Date of summary: Tue May 7 08:37:53 2019 ## ## Equations: ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * @@ -394,7 +404,7 @@ ## ## Model predictions using solution type analytical ## -## Fitted using 336 model solutions performed in 0.708 s +## Fitted using 572 model solutions performed in 1.244 s ## ## Error model: ## Constant variance @@ -419,25 +429,31 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 93.9500 NA NA NA -## log_k1 3.1370 NA NA NA -## log_k2 -1.0880 NA NA NA -## g_ilr -0.2821 NA NA NA -## sigma 1.4140 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 93.9500 9.998e-01 91.5900 96.3100 +## log_k1 3.1370 2.376e+03 -5616.0000 5622.0000 +## 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: -## No covariance matrix +## parent_0 log_k1 log_k2 g_ilr sigma +## parent_0 1.000e+00 5.155e-07 2.371e-09 2.665e-01 -6.849e-09 +## log_k1 5.155e-07 1.000e+00 8.434e-05 -1.659e-04 -7.791e-06 +## log_k2 2.371e-09 8.434e-05 1.000e+00 -7.903e-01 -1.262e-08 +## g_ilr 2.665e-01 -1.659e-04 -7.903e-01 1.000e+00 3.241e-08 +## sigma -6.849e-09 -7.791e-06 -1.262e-08 3.241e-08 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 93.9500 NA NA NA NA -## k1 23.0400 NA NA NA NA -## k2 0.3369 NA NA NA NA -## g 0.4016 NA NA NA NA -## sigma 1.4140 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 93.9500 9.397e+01 2.036e-12 91.5900 96.3100 +## k1 23.0400 4.303e-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 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -454,18 +470,18 @@ <h1 class="hasAnchor"> <a href="#laboratory-data-l3" class="anchor"></a>Laboratory Data L3</h1> <p>The following code defines example dataset L3 from the FOCUS kinetics report, p. 290.</p> -<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1">FOCUS_<span class="dv">2006</span>_L3 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> -<a class="sourceLine" id="cb23-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a> -<a class="sourceLine" id="cb23-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">97.8</span>, <span class="dv">60</span>, <span class="dv">51</span>, <span class="dv">43</span>, <span class="dv">35</span>, <span class="dv">22</span>, <span class="dv">15</span>, <span class="dv">12</span>))</a> -<a class="sourceLine" id="cb23-4" title="4">FOCUS_<span class="dv">2006</span>_L3_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L3)</a></code></pre></div> +<div class="sourceCode" id="cb22"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb22-1" title="1">FOCUS_<span class="dv">2006</span>_L3 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> +<a class="sourceLine" id="cb22-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a> +<a class="sourceLine" id="cb22-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">97.8</span>, <span class="dv">60</span>, <span class="dv">51</span>, <span class="dv">43</span>, <span class="dv">35</span>, <span class="dv">22</span>, <span class="dv">15</span>, <span class="dv">12</span>))</a> +<a class="sourceLine" id="cb22-4" title="4">FOCUS_<span class="dv">2006</span>_L3_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L3)</a></code></pre></div> <div id="fit-multiple-models" class="section level2"> <h2 class="hasAnchor"> <a href="#fit-multiple-models" class="anchor"></a>Fit multiple models</h2> <p>As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function <code>mmkin</code>. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above.</p> -<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb24-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a> -<a class="sourceLine" id="cb24-2" title="2">mm.L3 <-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a> -<a class="sourceLine" id="cb24-3" title="3"> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L3"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L3_mkin), <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> -<a class="sourceLine" id="cb24-4" title="4"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3)</a></code></pre></div> +<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a> +<a class="sourceLine" id="cb23-2" title="2">mm.L3 <-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>, <span class="st">"DFOP"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a> +<a class="sourceLine" id="cb23-3" title="3"> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L3"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L3_mkin), <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> +<a class="sourceLine" id="cb23-4" title="4"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-12-1.png" width="700"></p> <p>The <span class="math inline">\(\chi^2\)</span> error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the <span class="math inline">\(\chi^2\)</span> test passes of 7%. Fitting the four parameter DFOP model further reduces the <span class="math inline">\(\chi^2\)</span> error level considerably.</p> </div> @@ -474,13 +490,11 @@ <a href="#accessing-mmkin-objects" class="anchor"></a>Accessing mmkin objects</h2> <p>The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.</p> <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="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" 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>## Warning in summary.mkinfit(mm.L3[["DFOP", 1]]): Could not calculate -## correlation; no covariance matrix</code></pre> +<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: 3.6.0 -## Date of fit: Tue May 7 08:09:17 2019 -## Date of summary: Tue May 7 08:09:17 2019 +## Date of fit: Tue May 7 08:37:55 2019 +## Date of summary: Tue May 7 08:37:55 2019 ## ## Equations: ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * @@ -489,7 +503,7 @@ ## ## Model predictions using solution type analytical ## -## Fitted using 137 model solutions performed in 0.287 s +## Fitted using 373 model solutions performed in 0.791 s ## ## Error model: ## Constant variance @@ -514,25 +528,31 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 97.7500 NA NA NA -## log_k1 -0.6612 NA NA NA -## log_k2 -4.2860 NA NA NA -## g_ilr -0.1229 NA NA NA -## sigma 1.0170 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 97.7500 1.01900 94.5000 101.000000 +## log_k1 -0.6612 0.10050 -0.9812 -0.341300 +## log_k2 -4.2860 0.04322 -4.4230 -4.148000 +## g_ilr -0.1229 0.03727 -0.2415 -0.004343 +## sigma 1.0170 0.25430 0.2079 1.827000 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_k1 log_k2 g_ilr sigma +## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -6.872e-07 +## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 3.200e-07 +## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 7.673e-07 +## g_ilr 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -8.731e-07 +## sigma -6.872e-07 3.200e-07 7.673e-07 -8.731e-07 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 97.75000 NA NA NA NA -## k1 0.51620 NA NA NA NA -## k2 0.01376 NA NA NA NA -## g 0.45660 NA NA NA NA -## sigma 1.01700 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 97.75000 95.960 1.248e-06 94.50000 101.00000 +## k1 0.51620 9.947 1.081e-03 0.37490 0.71090 +## k2 0.01376 23.140 8.840e-05 0.01199 0.01579 +## g 0.45660 34.920 2.581e-05 0.41540 0.49850 +## sigma 1.01700 4.000 1.400e-02 0.20790 1.82700 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -553,7 +573,7 @@ ## 60 parent 22.0 23.26 -1.25919 ## 91 parent 15.0 15.18 -0.18181 ## 120 parent 12.0 10.19 1.81395</code></pre> -<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]], <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>)</a></code></pre></div> +<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb26-1" title="1"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L3[[<span class="st">"DFOP"</span>, <span class="dv">1</span>]], <span class="dt">show_errmin =</span> <span class="ot">TRUE</span>)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-13-1.png" width="700"></p> <p>Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the <span class="math inline">\(\chi^2\)</span> error level criterion for laboratory data L3.</p> <p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter <code>g</code> is quite narrow.</p> @@ -563,32 +583,30 @@ <h1 class="hasAnchor"> <a href="#laboratory-data-l4" class="anchor"></a>Laboratory Data L4</h1> <p>The following code defines example dataset L4 from the FOCUS kinetics report, p. 293:</p> -<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" title="1">FOCUS_<span class="dv">2006</span>_L4 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> -<a class="sourceLine" id="cb29-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a> -<a class="sourceLine" id="cb29-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span>))</a> -<a class="sourceLine" id="cb29-4" title="4">FOCUS_<span class="dv">2006</span>_L4_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L4)</a></code></pre></div> +<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" title="1">FOCUS_<span class="dv">2006</span>_L4 =<span class="st"> </span><span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/data.frame">data.frame</a></span>(</a> +<a class="sourceLine" id="cb27-2" title="2"> <span class="dt">t =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="dv">0</span>, <span class="dv">3</span>, <span class="dv">7</span>, <span class="dv">14</span>, <span class="dv">30</span>, <span class="dv">60</span>, <span class="dv">91</span>, <span class="dv">120</span>),</a> +<a class="sourceLine" id="cb27-3" title="3"> <span class="dt">parent =</span> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="fl">96.6</span>, <span class="fl">96.3</span>, <span class="fl">94.3</span>, <span class="fl">88.8</span>, <span class="fl">74.9</span>, <span class="fl">59.9</span>, <span class="fl">53.5</span>, <span class="fl">49.0</span>))</a> +<a class="sourceLine" id="cb27-4" title="4">FOCUS_<span class="dv">2006</span>_L4_mkin <-<span class="st"> </span><span class="kw"><a href="../reference/mkin_wide_to_long.html">mkin_wide_to_long</a></span>(FOCUS_<span class="dv">2006</span>_L4)</a></code></pre></div> <p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p> -<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb30-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a> -<a class="sourceLine" id="cb30-2" title="2">mm.L4 <-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a> -<a class="sourceLine" id="cb30-3" title="3"> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L4"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L4_mkin),</a> -<a class="sourceLine" id="cb30-4" title="4"> <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> -<a class="sourceLine" id="cb30-5" title="5"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L4)</a></code></pre></div> +<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" title="1"><span class="co"># Only use one core here, not to offend the CRAN checks</span></a> +<a class="sourceLine" id="cb28-2" title="2">mm.L4 <-<span class="st"> </span><span class="kw"><a href="../reference/mmkin.html">mmkin</a></span>(<span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/c">c</a></span>(<span class="st">"SFO"</span>, <span class="st">"FOMC"</span>), <span class="dt">cores =</span> <span class="dv">1</span>,</a> +<a class="sourceLine" id="cb28-3" title="3"> <span class="kw"><a href="https://www.rdocumentation.org/packages/base/topics/list">list</a></span>(<span class="st">"FOCUS L4"</span> =<span class="st"> </span>FOCUS_<span class="dv">2006</span>_L4_mkin),</a> +<a class="sourceLine" id="cb28-4" title="4"> <span class="dt">quiet =</span> <span class="ot">TRUE</span>)</a> +<a class="sourceLine" id="cb28-5" title="5"><span class="kw"><a href="https://www.rdocumentation.org/packages/graphics/topics/plot">plot</a></span>(mm.L4)</a></code></pre></div> <p><img src="FOCUS_L_files/figure-html/unnamed-chunk-15-1.png" width="700"></p> <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="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">"SFO"</span>, <span class="dv">1</span>]], <span class="dt">data =</span> <span class="ot">FALSE</span>)</a></code></pre></div> -<pre><code>## Warning in summary.mkinfit(mm.L4[["SFO", 1]], data = FALSE): Could not -## calculate correlation; no covariance matrix</code></pre> +<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: 3.6.0 -## Date of fit: Tue May 7 08:09:17 2019 -## Date of summary: Tue May 7 08:09:18 2019 +## Date of fit: Tue May 7 08:37:56 2019 +## Date of summary: Tue May 7 08:37:56 2019 ## ## Equations: ## d_parent/dt = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted using 50 model solutions performed in 0.105 s +## Fitted using 142 model solutions performed in 0.29 s ## ## Error model: ## Constant variance @@ -609,21 +627,25 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 96.440 NA NA NA -## log_k_parent_sink -5.030 NA NA NA -## sigma 3.162 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 96.440 1.69900 92.070 100.800 +## log_k_parent_sink -5.030 0.07059 -5.211 -4.848 +## sigma 3.162 0.79050 1.130 5.194 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_k_parent_sink sigma +## parent_0 1.000e+00 5.938e-01 3.440e-07 +## log_k_parent_sink 5.938e-01 1.000e+00 5.885e-07 +## sigma 3.440e-07 5.885e-07 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 96.440000 NA NA NA NA -## k_parent_sink 0.006541 NA NA NA NA -## sigma 3.162000 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 96.440000 56.77 1.604e-08 92.070000 1.008e+02 +## 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 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df @@ -637,20 +659,18 @@ ## Estimated disappearance times: ## DT50 DT90 ## parent 106 352</code></pre> -<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" 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>## Warning in summary.mkinfit(mm.L4[["FOMC", 1]], data = FALSE): Could not -## calculate correlation; no covariance matrix</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: 3.6.0 -## Date of fit: Tue May 7 08:09:18 2019 -## Date of summary: Tue May 7 08:09:18 2019 +## Date of fit: Tue May 7 08:37:56 2019 +## Date of summary: Tue May 7 08:37:56 2019 ## ## Equations: ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent ## ## Model predictions using solution type analytical ## -## Fitted using 68 model solutions performed in 0.139 s +## Fitted using 224 model solutions performed in 0.453 s ## ## Error model: ## Constant variance @@ -673,23 +693,28 @@ ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 99.1400 NA NA NA -## log_alpha -0.3506 NA NA NA -## log_beta 4.1740 NA NA NA -## sigma 1.8300 NA NA NA +## Estimate Std. Error Lower Upper +## parent_0 99.1400 1.2670 95.6300 102.7000 +## log_alpha -0.3506 0.2616 -1.0770 0.3756 +## log_beta 4.1740 0.3938 3.0810 5.2670 +## sigma 1.8300 0.4575 0.5598 3.1000 ## ## Parameter correlation: -## No covariance matrix +## parent_0 log_alpha log_beta sigma +## parent_0 1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07 +## log_alpha -4.696e-01 1.000e+00 9.889e-01 4.066e-08 +## log_beta -5.543e-01 9.889e-01 1.000e+00 6.818e-08 +## sigma -2.563e-07 4.066e-08 6.818e-08 1.000e+00 +## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. -## Estimate t value Pr(>t) Lower Upper -## parent_0 99.1400 NA NA NA NA -## alpha 0.7042 NA NA NA NA -## beta 64.9800 NA NA NA NA -## sigma 1.8300 NA NA NA NA +## Estimate t value Pr(>t) Lower Upper +## parent_0 99.1400 78.250 7.993e-08 95.6300 102.700 +## alpha 0.7042 3.823 9.365e-03 0.3407 1.456 +## beta 64.9800 2.540 3.201e-02 21.7800 193.900 +## sigma 1.8300 4.000 8.065e-03 0.5598 3.100 ## ## FOCUS Chi2 error levels in percent: ## err.min n.optim df |