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In each step of the optimisation, the +kinetic model is solved using the function mkinpredict(), except +if an analytical solution is implemented, in which case the model is solved +using the degradation function in the mkinmod object. 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In each step of the optimisation, the +kinetic model is solved using the function <code><a href='mkinpredict.html'>mkinpredict()</a></code>, except +if an analytical solution is implemented, in which case the model is solved +using the degradation function in the <a href='mkinmod.html'>mkinmod</a> object. The +parameters of the selected error model are fitted simultaneously with the +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> + + <h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2> + <table class="ref-arguments"> + <colgroup><col class="name" /><col class="desc" /></colgroup> + <tr> + <th>mkinmod</th> + <td><p>A list of class <a href='mkinmod.html'>mkinmod</a>, containing the kinetic +model to be fitted to the data, or one of the shorthand names ("SFO", +"FOMC", "DFOP", "HS", "SFORB", "IORE"). If a shorthand name is given, a +parent only degradation model is generated for the variable with the +highest value in <code>observed</code>.</p></td> + </tr> + <tr> + <th>observed</th> + <td><p>A dataframe with the observed data. The first column called +"name" must contain the name of the observed variable for each data point. +The second column must contain the times of observation, named "time". +The third column must be named "value" and contain the observed values. +Zero values in the "value" column will be removed, with a warning, in +order to avoid problems with fitting the two-component error model. This +is not expected to be a problem, because in general, values of zero are +not observed in degradation data, because there is a lower limit of +detection.</p></td> + </tr> + <tr> + <th>parms.ini</th> + <td><p>A named vector of initial values for the parameters, +including parameters to be optimised and potentially also fixed parameters +as indicated by <code>fixed_parms</code>. If set to "auto", initial values for +rate constants are set to default values. Using parameter names that are +not in the model gives an error.</p> +<p>It is possible to only specify a subset of the parameters that the model +needs. You can use the parameter lists "bparms.ode" from a previously +fitted model, which contains the differential equation parameters from +this model. This works nicely if the models are nested. An example is +given below.</p></td> + </tr> + <tr> + <th>state.ini</th> + <td><p>A named vector of initial values for the state variables of +the model. In case the observed variables are represented by more than one +model variable, the names will differ from the names of the observed +variables (see <code>map</code> component of <a href='mkinmod.html'>mkinmod</a>). The default +is to set the initial value of the first model variable to the mean of the +time zero values for the variable with the maximum observed value, and all +others to 0. If this variable has no time zero observations, its initial +value is set to 100.</p></td> + </tr> + <tr> + <th>err.ini</th> + <td><p>A named vector of initial values for the error model +parameters to be optimised. If set to "auto", initial values are set to +default values. Otherwise, inital values for all error model parameters +must be given.</p></td> + </tr> + <tr> + <th>fixed_parms</th> + <td><p>The names of parameters that should not be optimised but +rather kept at the values specified in <code>parms.ini</code>. Alternatively, +a named numeric vector of parameters to be fixed, regardless of the values +in parms.ini.</p></td> + </tr> + <tr> + <th>fixed_initials</th> + <td><p>The names of model variables for which the initial +state at time 0 should be excluded from the optimisation. Defaults to all +state variables except for the first one.</p></td> + </tr> + <tr> + <th>from_max_mean</th> + <td><p>If this is set to TRUE, and the model has only one +observed variable, then data before the time of the maximum observed value +(after averaging for each sampling time) are discarded, and this time is +subtracted from all remaining time values, so the time of the maximum +observed mean value is the new time zero.</p></td> + </tr> + <tr> + <th>solution_type</th> + <td><p>If set to "eigen", the solution of the system of +differential equations is based on the spectral decomposition of the +coefficient matrix in cases that this is possible. If set to "deSolve", a +numerical <a href='https://rdrr.io/pkg/deSolve/man/ode.html'>ode solver from package deSolve</a> is used. If +set to "analytical", an analytical solution of the model is used. This is +only implemented for relatively simple degradation models. The default is +"auto", which uses "analytical" if possible, otherwise "deSolve" if a +compiler is present, and "eigen" if no compiler is present and the model +can be expressed using eigenvalues and eigenvectors.</p></td> + </tr> + <tr> + <th>method.ode</th> + <td><p>The solution method passed via <code><a href='mkinpredict.html'>mkinpredict()</a></code> +to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code> in case the solution type is "deSolve". The default +"lsoda" is performant, but sometimes fails to converge.</p></td> + </tr> + <tr> + <th>use_compiled</th> + <td><p>If set to <code>FALSE</code>, no compiled version of the +<a href='mkinmod.html'>mkinmod</a> model is used in the calls to <code><a href='mkinpredict.html'>mkinpredict()</a></code> even if a compiled +version is present.</p></td> + </tr> + <tr> + <th>control</th> + <td><p>A list of control arguments passed to <code><a href='https://rdrr.io/r/stats/nlminb.html'>stats::nlminb()</a></code>.</p></td> + </tr> + <tr> + <th>transform_rates</th> + <td><p>Boolean specifying if kinetic rate constants should +be transformed in the model specification used in the fitting for better +compliance with the assumption of normal distribution of the estimator. If +TRUE, also alpha and beta parameters of the FOMC model are +log-transformed, as well as k1 and k2 rate constants for the DFOP and HS +models and the break point tb of the HS model. If FALSE, zero is used as +a lower bound for the rates in the optimisation.</p></td> + </tr> + <tr> + <th>transform_fractions</th> + <td><p>Boolean specifying if formation fractions +constants should be transformed in the model specification used in the +fitting for better compliance with the assumption of normal distribution +of the estimator. The default (TRUE) is to do transformations. If TRUE, +the g parameter of the DFOP and HS models are also transformed, as they +can also be seen as compositional data. The transformation used for these +transformations is the <code><a href='ilr.html'>ilr()</a></code> transformation.</p></td> + </tr> + <tr> + <th>quiet</th> + <td><p>Suppress printing out the current value of the negative +log-likelihood after each improvement?</p></td> + </tr> + <tr> + <th>atol</th> + <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default +is 1e-8, which is lower than the default in the <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code> +function which is used per default.</p></td> + </tr> + <tr> + <th>rtol</th> + <td><p>Absolute error tolerance, passed to <code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>. Default +is 1e-10, much lower than in <code><a href='https://rdrr.io/pkg/deSolve/man/lsoda.html'>deSolve::lsoda()</a></code>.</p></td> + </tr> + <tr> + <th>error_model</th> + <td><p>If the error model is "const", a constant standard +deviation is assumed.</p> +<p>If the error model is "obs", each observed variable is assumed to have its +own variance.</p> +<p>If the error model is "tc" (two-component error model), a two component +error model similar to the one described by Rocke and Lorenzato (1995) is +used for setting up the likelihood function. Note that this model +deviates from the model by Rocke and Lorenzato, as their model implies +that the errors follow a lognormal distribution for large values, not a +normal distribution as assumed by this method.</p></td> + </tr> + <tr> + <th>error_model_algorithm</th> + <td><p>If "auto", the selected algorithm depends on +the error model. If the error model is "const", unweighted nonlinear +least squares fitting ("OLS") is selected. If the error model is "obs", or +"tc", the "d_3" algorithm is selected.</p> +<p>The algorithm "d_3" will directly minimize the negative log-likelihood +and independently also use the three step algorithm described below. +The fit with the higher likelihood is returned.</p> +<p>The algorithm "direct" will directly minimize the negative log-likelihood.</p> +<p>The algorithm "twostep" will minimize the negative log-likelihood after an +initial unweighted least squares optimisation step.</p> +<p>The algorithm "threestep" starts with unweighted least squares, then +optimizes only the error model using the degradation model parameters +found, and then minimizes the negative log-likelihood with free +degradation and error model parameters.</p> +<p>The algorithm "fourstep" starts with unweighted least squares, then +optimizes only the error model using the degradation model parameters +found, then optimizes the degradation model again with fixed error model +parameters, and finally minimizes the negative log-likelihood with free +degradation and error model parameters.</p> +<p>The algorithm "IRLS" (Iteratively Reweighted Least Squares) starts with +unweighted least squares, and then iterates optimization of the error +model parameters and subsequent optimization of the degradation model +using those error model parameters, until the error model parameters +converge.</p></td> + </tr> + <tr> + <th>reweight.tol</th> + <td><p>Tolerance for the convergence criterion calculated from +the error model parameters in IRLS fits.</p></td> + </tr> + <tr> + <th>reweight.max.iter</th> + <td><p>Maximum number of iterations in IRLS fits.</p></td> + </tr> + <tr> + <th>trace_parms</th> + <td><p>Should a trace of the parameter values be listed?</p></td> + </tr> + <tr> + <th>...</th> + <td><p>Further arguments that will be passed on to +<code><a href='https://rdrr.io/pkg/deSolve/man/ode.html'>deSolve::ode()</a></code>.</p></td> + </tr> + </table> + + <h2 class="hasAnchor" id="value"><a class="anchor" href="#value"></a>Value</h2> + + <p>A list with "mkinfit" in the class attribute.</p> + <h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2> + + <p>Per default, parameters in the kinetic models are internally transformed in +order to better satisfy the assumption of a normal distribution of their +estimators.</p> + <h2 class="hasAnchor" id="note"><a class="anchor" href="#note"></a>Note</h2> + + <p>When using the "IORE" submodel for metabolites, fitting with +"transform_rates = TRUE" (the default) often leads to failures of the +numerical ODE solver. In this situation it may help to switch off the +internal rate transformation.</p> + <h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2> + + <p>Rocke DM and Lorenzato S (1995) A two-component model +for measurement error in analytical chemistry. <em>Technometrics</em> 37(2), 176-184.</p> +<p>Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical +Degradation Data. <em>Environments</em> 6(12) 124 +<a href='https://doi.org/10.3390/environments6120124'>doi:10.3390/environments6120124</a>.</p> + <h2 class="hasAnchor" id="see-also"><a class="anchor" href="#see-also"></a>See also</h2> + + <div class='dont-index'><p><a href='summary.mkinfit.html'>summary.mkinfit</a>, <a href='plot.mkinfit.html'>plot.mkinfit</a>, <a href='parms.html'>parms</a> and <a href='https://rdrr.io/pkg/lmtest/man/lrtest.html'>lrtest</a>.</p> +<p>Comparisons of models fitted to the same data can be made using +<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="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'><-</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'>#> mkin version used for fitting: 0.9.50.3 +#> R version used for fitting: 4.0.0 +#> Date of fit: Wed May 27 05:54:13 2020 +#> Date of summary: Wed May 27 05:54:13 2020 +#> +#> Equations: +#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent +#> +#> Model predictions using solution type analytical +#> +#> Fitted using 222 model solutions performed in 0.043 s +#> +#> Error model: Constant variance +#> +#> Error model algorithm: OLS +#> +#> Starting values for parameters to be optimised: +#> value type +#> parent_0 85.1 state +#> alpha 1.0 deparm +#> beta 10.0 deparm +#> +#> Starting values for the transformed parameters actually optimised: +#> value lower upper +#> parent_0 85.100000 -Inf Inf +#> log_alpha 0.000000 -Inf Inf +#> log_beta 2.302585 -Inf Inf +#> +#> Fixed parameter values: +#> None +#> +#> Results: +#> +#> AIC BIC logLik +#> 44.68652 45.47542 -18.34326 +#> +#> Optimised, transformed parameters with symmetric confidence intervals: +#> Estimate Std. Error Lower Upper +#> parent_0 85.87000 1.8070 81.23000 90.5200 +#> log_alpha 0.05192 0.1353 -0.29580 0.3996 +#> log_beta 0.65100 0.2287 0.06315 1.2390 +#> sigma 1.85700 0.4378 0.73200 2.9830 +#> +#> Parameter correlation: +#> parent_0 log_alpha log_beta sigma +#> parent_0 1.000e+00 -1.565e-01 -3.142e-01 4.770e-08 +#> log_alpha -1.565e-01 1.000e+00 9.564e-01 9.974e-08 +#> log_beta -3.142e-01 9.564e-01 1.000e+00 8.468e-08 +#> sigma 4.770e-08 9.974e-08 8.468e-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 85.870 47.530 3.893e-08 81.2300 90.520 +#> alpha 1.053 7.393 3.562e-04 0.7439 1.491 +#> beta 1.917 4.373 3.601e-03 1.0650 3.451 +#> sigma 1.857 4.243 4.074e-03 0.7320 2.983 +#> +#> FOCUS Chi2 error levels in percent: +#> err.min n.optim df +#> All data 6.657 3 6 +#> parent 6.657 3 6 +#> +#> Estimated disappearance times: +#> DT50 DT90 DT50back +#> parent 1.785 15.15 4.56 +#> +#> Data: +#> time variable observed predicted residual +#> 0 parent 85.1 85.875 -0.7749 +#> 1 parent 57.9 55.191 2.7091 +#> 3 parent 29.9 31.845 -1.9452 +#> 7 parent 14.6 17.012 -2.4124 +#> 14 parent 9.7 9.241 0.4590 +#> 28 parent 6.6 4.754 1.8460 +#> 63 parent 4.0 2.102 1.8977 +#> 91 parent 3.9 1.441 2.4590 +#> 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'># Use mkinsub for convenience in model formulation. Pathway to sink included per default.</span> +<span class='no'>SFO_SFO</span> <span class='kw'><-</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'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span> +<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fit</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, + <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"eigen"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)))</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#> user system elapsed +#> 0.414 0.000 0.418 </div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#> parent_0 k_parent k_m1 f_parent_to_m1 sigma +#> 99.598481046 0.098697740 0.005260651 0.514475962 3.125503875 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit</span>)</div><div class='output co'>#> $ff +#> parent_m1 parent_sink +#> 0.514476 0.485524 +#> +#> $distimes +#> DT50 DT90 +#> parent 7.022929 23.32966 +#> m1 131.760724 437.69965 +#> </div><div class='input'><span class='co'># \dontrun{</span> +<span class='co'># deSolve is slower when no C compiler (gcc) was available during model generation</span> +<span class='fu'><a href='https://rdrr.io/r/base/print.html'>print</a></span>(<span class='fu'><a href='https://rdrr.io/r/base/system.time.html'>system.time</a></span>(<span class='no'>fit.deSolve</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO</span>, <span class='no'>FOCUS_2006_D</span>, + <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>)))</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#> <span class='message'>Ordinary least squares optimisation</span></div><div class='output co'>#> Sum of squared residuals at call 1: 15156.12 +#> Sum of squared residuals at call 2: 15156.12 +#> Sum of squared residuals at call 6: 8243.645 +#> Sum of squared residuals at call 12: 6290.712 +#> Sum of squared residuals at call 13: 6290.683 +#> Sum of squared residuals at call 15: 6290.452 +#> Sum of squared residuals at call 18: 1700.749 +#> Sum of squared residuals at call 20: 1700.611 +#> Sum of squared residuals at call 24: 1190.923 +#> Sum of squared residuals at call 26: 1190.922 +#> Sum of squared residuals at call 29: 1017.417 +#> Sum of squared residuals at call 31: 1017.417 +#> Sum of squared residuals at call 33: 1017.416 +#> Sum of squared residuals at call 34: 644.0472 +#> Sum of squared residuals at call 36: 644.047 +#> Sum of squared residuals at call 38: 644.047 +#> Sum of squared residuals at call 39: 590.5025 +#> Sum of squared residuals at call 41: 590.5022 +#> Sum of squared residuals at call 43: 590.5016 +#> Sum of squared residuals at call 44: 543.2196 +#> Sum of squared residuals at call 45: 543.2193 +#> Sum of squared residuals at call 46: 543.2192 +#> Sum of squared residuals at call 50: 391.348 +#> Sum of squared residuals at call 51: 391.3479 +#> Sum of squared residuals at call 56: 386.479 +#> Sum of squared residuals at call 58: 386.479 +#> Sum of squared residuals at call 60: 386.4779 +#> Sum of squared residuals at call 61: 384.0686 +#> Sum of squared residuals at call 63: 384.0686 +#> Sum of squared residuals at call 66: 382.7813 +#> Sum of squared residuals at call 68: 382.7813 +#> Sum of squared residuals at call 70: 382.7813 +#> Sum of squared residuals at call 71: 378.9273 +#> Sum of squared residuals at call 73: 378.9273 +#> Sum of squared residuals at call 75: 378.9272 +#> Sum of squared residuals at call 76: 377.4847 +#> Sum of squared residuals at call 78: 377.4846 +#> Sum of squared residuals at call 81: 375.9738 +#> Sum of squared residuals at call 83: 375.9738 +#> Sum of squared residuals at call 86: 375.3387 +#> Sum of squared residuals at call 88: 375.3387 +#> Sum of squared residuals at call 91: 374.5774 +#> Sum of squared residuals at call 93: 374.5774 +#> Sum of squared residuals at call 95: 374.5774 +#> Sum of squared residuals at call 96: 373.5438 +#> Sum of squared residuals at call 100: 373.5438 +#> Sum of squared residuals at call 102: 373.265 +#> Sum of squared residuals at call 104: 373.265 +#> Sum of squared residuals at call 107: 372.6825 +#> Sum of squared residuals at call 111: 372.6825 +#> Sum of squared residuals at call 114: 372.6356 +#> Sum of squared residuals at call 116: 372.6356 +#> Sum of squared residuals at call 119: 372.6199 +#> Sum of squared residuals at call 121: 372.6199 +#> Sum of squared residuals at call 123: 372.6199 +#> Sum of squared residuals at call 124: 372.5881 +#> Sum of squared residuals at call 126: 372.5881 +#> Sum of squared residuals at call 129: 372.5418 +#> Sum of squared residuals at call 130: 372.4866 +#> Sum of squared residuals at call 131: 372.2242 +#> Sum of squared residuals at call 132: 371.5237 +#> Sum of squared residuals at call 134: 371.5237 +#> Sum of squared residuals at call 137: 371.292 +#> Sum of squared residuals at call 139: 371.292 +#> Sum of squared residuals at call 143: 371.2256 +#> Sum of squared residuals at call 144: 371.2256 +#> Sum of squared residuals at call 146: 371.2256 +#> Sum of squared residuals at call 149: 371.2194 +#> Sum of squared residuals at call 150: 371.2147 +#> Sum of squared residuals at call 153: 371.2147 +#> Sum of squared residuals at call 155: 371.2137 +#> Sum of squared residuals at call 156: 371.2137 +#> Sum of squared residuals at call 157: 371.2137 +#> Sum of squared residuals at call 160: 371.2134 +#> Sum of squared residuals at call 164: 371.2134 +#> Sum of squared residuals at call 165: 371.2134 +#> Sum of squared residuals at call 167: 371.2134 +#> Negative log-likelihood at call 177: 97.22429</div><div class='output co'>#> <span class='message'>Optimisation successfully terminated.</span></div><div class='output co'>#> user system elapsed +#> 0.371 0.001 0.370 </div><div class='input'><span class='fu'><a href='parms.html'>parms</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#> parent_0 k_parent k_m1 f_parent_to_m1 sigma +#> 99.598480300 0.098697739 0.005260651 0.514475968 3.125503874 </div><div class='input'><span class='fu'><a href='endpoints.html'>endpoints</a></span>(<span class='no'>fit.deSolve</span>)</div><div class='output co'>#> $ff +#> parent_m1 parent_sink +#> 0.514476 0.485524 +#> +#> $distimes +#> DT50 DT90 +#> parent 7.022929 23.32966 +#> m1 131.760721 437.69964 +#> </div><div class='input'><span class='co'># }</span> + +<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC</span> +<span class='co'># \dontrun{</span> +<span class='no'>FOMC_SFO</span> <span class='kw'><-</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'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span> +<span class='no'>fit.FOMC_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='co'># Use starting parameters from parent only FOMC fit</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='no'>fit.FOMC_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>FOMC_SFO</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'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.FOMC</span>$<span class='no'>bparms.ode</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'> +<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, SFORB</span> +<span class='no'>SFORB_SFO</span> <span class='kw'><-</span> <span class='fu'><a href='mkinmod.html'>mkinmod</a></span>( + <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFORB"</span>, <span class='kw'>to</span> <span class='kw'>=</span> <span class='st'>"m1"</span>, <span class='kw'>sink</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>), + <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'><a href='https://rdrr.io/r/base/list.html'>list</a></span>(<span class='kw'>type</span> <span class='kw'>=</span> <span class='st'>"SFO"</span>))</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span> +<span class='no'>fit.SFORB_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='no'>fit.SFORB_SFO.deSolve</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>solution_type</span> <span class='kw'>=</span> <span class='st'>"deSolve"</span>, + <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='co'># Use starting parameters from parent only SFORB fit (not really needed in this case)</span> +<span class='no'>fit.SFORB</span> <span class='kw'>=</span> <span class='fu'>mkinfit</span>(<span class='st'>"SFORB"</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>) +<span class='no'>fit.SFORB_SFO</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFORB_SFO</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>parms.ini</span> <span class='kw'>=</span> <span class='no'>fit.SFORB</span>$<span class='no'>bparms.ode</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='output co'>#> <span class='warning'>Warning: Initial parameter(s) k_parent_free_sink not used in the model</span></div><div class='input'><span class='co'># }</span> + +<span class='co'># \dontrun{</span> +<span class='co'># Weighted fits, including IRLS (error_model = "obs")</span> +<span class='no'>SFO_SFO.ff</span> <span class='kw'><-</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>), <span class='kw'>use_of_ff</span> <span class='kw'>=</span> <span class='st'>"max"</span>)</div><div class='output co'>#> <span class='message'>Successfully compiled differential equation model from auto-generated C code.</span></div><div class='input'><span class='no'>f.noweight</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.noweight</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.50.3 +#> R version used for fitting: 4.0.0 +#> Date of fit: Wed May 27 05:54:19 2020 +#> Date of summary: Wed May 27 05:54:19 2020 +#> +#> Equations: +#> d_parent/dt = - k_parent * parent +#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1 +#> +#> Model predictions using solution type analytical +#> +#> Fitted using 421 model solutions performed in 0.126 s +#> +#> Error model: Constant variance +#> +#> Error model algorithm: OLS +#> +#> Starting values for parameters to be optimised: +#> value type +#> parent_0 100.7500 state +#> k_parent 0.1000 deparm +#> k_m1 0.1001 deparm +#> f_parent_to_m1 0.5000 deparm +#> +#> Starting values for the transformed parameters actually optimised: +#> value lower upper +#> parent_0 100.750000 -Inf Inf +#> log_k_parent -2.302585 -Inf Inf +#> log_k_m1 -2.301586 -Inf Inf +#> f_parent_ilr_1 0.000000 -Inf Inf +#> +#> Fixed parameter values: +#> value type +#> m1_0 0 state +#> +#> Results: +#> +#> AIC BIC logLik +#> 204.4486 212.6365 -97.22429 +#> +#> Optimised, transformed parameters with symmetric confidence intervals: +#> Estimate Std. Error Lower Upper +#> parent_0 99.60000 1.57000 96.40000 102.8000 +#> log_k_parent -2.31600 0.04087 -2.39900 -2.2330 +#> log_k_m1 -5.24800 0.13320 -5.51800 -4.9770 +#> f_parent_ilr_1 0.04096 0.06312 -0.08746 0.1694 +#> sigma 3.12600 0.35850 2.39600 3.8550 +#> +#> Parameter correlation: +#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma +#> parent_0 1.000e+00 5.174e-01 -1.688e-01 -5.471e-01 -3.190e-07 +#> log_k_parent 5.174e-01 1.000e+00 -3.263e-01 -5.426e-01 3.168e-07 +#> log_k_m1 -1.688e-01 -3.263e-01 1.000e+00 7.478e-01 -1.406e-07 +#> f_parent_ilr_1 -5.471e-01 -5.426e-01 7.478e-01 1.000e+00 -1.587e-10 +#> sigma -3.190e-07 3.168e-07 -1.406e-07 -1.587e-10 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 99.600000 63.430 2.298e-36 96.400000 1.028e+02 +#> k_parent 0.098700 24.470 4.955e-23 0.090820 1.073e-01 +#> k_m1 0.005261 7.510 6.165e-09 0.004012 6.898e-03 +#> f_parent_to_m1 0.514500 23.070 3.104e-22 0.469100 5.596e-01 +#> sigma 3.126000 8.718 2.235e-10 2.396000 3.855e+00 +#> +#> FOCUS Chi2 error levels in percent: +#> err.min n.optim df +#> All data 6.398 4 15 +#> parent 6.459 2 7 +#> m1 4.690 2 8 +#> +#> Resulting formation fractions: +#> ff +#> parent_m1 0.5145 +#> parent_sink 0.4855 +#> +#> Estimated disappearance times: +#> DT50 DT90 +#> parent 7.023 23.33 +#> m1 131.761 437.70 +#> +#> Data: +#> time variable observed predicted residual +#> 0 parent 99.46 99.59848 -1.385e-01 +#> 0 parent 102.04 99.59848 2.442e+00 +#> 1 parent 93.50 90.23787 3.262e+00 +#> 1 parent 92.50 90.23787 2.262e+00 +#> 3 parent 63.23 74.07319 -1.084e+01 +#> 3 parent 68.99 74.07319 -5.083e+00 +#> 7 parent 52.32 49.91206 2.408e+00 +#> 7 parent 55.13 49.91206 5.218e+00 +#> 14 parent 27.27 25.01257 2.257e+00 +#> 14 parent 26.64 25.01257 1.627e+00 +#> 21 parent 11.50 12.53462 -1.035e+00 +#> 21 parent 11.64 12.53462 -8.946e-01 +#> 35 parent 2.85 3.14787 -2.979e-01 +#> 35 parent 2.91 3.14787 -2.379e-01 +#> 50 parent 0.69 0.71624 -2.624e-02 +#> 50 parent 0.63 0.71624 -8.624e-02 +#> 75 parent 0.05 0.06074 -1.074e-02 +#> 75 parent 0.06 0.06074 -7.381e-04 +#> 1 m1 4.84 4.80296 3.704e-02 +#> 1 m1 5.64 4.80296 8.370e-01 +#> 3 m1 12.91 13.02400 -1.140e-01 +#> 3 m1 12.96 13.02400 -6.400e-02 +#> 7 m1 22.97 25.04476 -2.075e+00 +#> 7 m1 24.47 25.04476 -5.748e-01 +#> 14 m1 41.69 36.69002 5.000e+00 +#> 14 m1 33.21 36.69002 -3.480e+00 +#> 21 m1 44.37 41.65310 2.717e+00 +#> 21 m1 46.44 41.65310 4.787e+00 +#> 35 m1 41.22 43.31312 -2.093e+00 +#> 35 m1 37.95 43.31312 -5.363e+00 +#> 50 m1 41.19 41.21831 -2.831e-02 +#> 50 m1 40.01 41.21831 -1.208e+00 +#> 75 m1 40.09 36.44703 3.643e+00 +#> 75 m1 33.85 36.44703 -2.597e+00 +#> 100 m1 31.04 31.98163 -9.416e-01 +#> 100 m1 33.13 31.98163 1.148e+00 +#> 120 m1 25.15 28.78984 -3.640e+00 +#> 120 m1 33.31 28.78984 4.520e+00</div><div class='input'><span class='no'>f.obs</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"obs"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.obs</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.50.3 +#> R version used for fitting: 4.0.0 +#> Date of fit: Wed May 27 05:54:19 2020 +#> Date of summary: Wed May 27 05:54:19 2020 +#> +#> Equations: +#> d_parent/dt = - k_parent * parent +#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1 +#> +#> Model predictions using solution type analytical +#> +#> Fitted using 978 model solutions performed in 0.33 s +#> +#> Error model: Variance unique to each observed variable +#> +#> Error model algorithm: d_3 +#> Direct fitting and three-step fitting yield approximately the same likelihood +#> +#> Starting values for parameters to be optimised: +#> value type +#> parent_0 100.7500 state +#> k_parent 0.1000 deparm +#> k_m1 0.1001 deparm +#> f_parent_to_m1 0.5000 deparm +#> sigma_parent 3.0000 error +#> sigma_m1 3.0000 error +#> +#> Starting values for the transformed parameters actually optimised: +#> value lower upper +#> parent_0 100.750000 -Inf Inf +#> log_k_parent -2.302585 -Inf Inf +#> log_k_m1 -2.301586 -Inf Inf +#> f_parent_ilr_1 0.000000 -Inf Inf +#> sigma_parent 3.000000 0 Inf +#> sigma_m1 3.000000 0 Inf +#> +#> Fixed parameter values: +#> value type +#> m1_0 0 state +#> +#> Results: +#> +#> AIC BIC logLik +#> 205.8727 215.6982 -96.93634 +#> +#> Optimised, transformed parameters with symmetric confidence intervals: +#> Estimate Std. Error Lower Upper +#> parent_0 99.65000 1.70200 96.19000 103.1000 +#> log_k_parent -2.31300 0.04376 -2.40200 -2.2240 +#> log_k_m1 -5.25000 0.12430 -5.50400 -4.9970 +#> f_parent_ilr_1 0.03861 0.06171 -0.08708 0.1643 +#> sigma_parent 3.40100 0.56820 2.24400 4.5590 +#> sigma_m1 2.85500 0.45240 1.93400 3.7770 +#> +#> Parameter correlation: +#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_parent +#> parent_0 1.00000 0.51078 -0.19133 -0.59997 0.035670 +#> log_k_parent 0.51078 1.00000 -0.37458 -0.59239 0.069833 +#> log_k_m1 -0.19133 -0.37458 1.00000 0.74398 -0.026158 +#> f_parent_ilr_1 -0.59997 -0.59239 0.74398 1.00000 -0.041369 +#> sigma_parent 0.03567 0.06983 -0.02616 -0.04137 1.000000 +#> sigma_m1 -0.03385 -0.06627 0.02482 0.03926 -0.004628 +#> sigma_m1 +#> parent_0 -0.033847 +#> log_k_parent -0.066265 +#> log_k_m1 0.024823 +#> f_parent_ilr_1 0.039256 +#> sigma_parent -0.004628 +#> sigma_m1 1.000000 +#> +#> 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 99.650000 58.560 2.004e-34 96.190000 1.031e+02 +#> k_parent 0.098970 22.850 1.099e-21 0.090530 1.082e-01 +#> k_m1 0.005245 8.046 1.732e-09 0.004072 6.756e-03 +#> f_parent_to_m1 0.513600 23.560 4.352e-22 0.469300 5.578e-01 +#> sigma_parent 3.401000 5.985 5.662e-07 2.244000 4.559e+00 +#> sigma_m1 2.855000 6.311 2.215e-07 1.934000 3.777e+00 +#> +#> FOCUS Chi2 error levels in percent: +#> err.min n.optim df +#> All data 6.398 4 15 +#> parent 6.464 2 7 +#> m1 4.682 2 8 +#> +#> Resulting formation fractions: +#> ff +#> parent_m1 0.5136 +#> parent_sink 0.4864 +#> +#> Estimated disappearance times: +#> DT50 DT90 +#> parent 7.003 23.26 +#> m1 132.154 439.01 +#> +#> Data: +#> time variable observed predicted residual +#> 0 parent 99.46 99.65417 -1.942e-01 +#> 0 parent 102.04 99.65417 2.386e+00 +#> 1 parent 93.50 90.26332 3.237e+00 +#> 1 parent 92.50 90.26332 2.237e+00 +#> 3 parent 63.23 74.05306 -1.082e+01 +#> 3 parent 68.99 74.05306 -5.063e+00 +#> 7 parent 52.32 49.84325 2.477e+00 +#> 7 parent 55.13 49.84325 5.287e+00 +#> 14 parent 27.27 24.92971 2.340e+00 +#> 14 parent 26.64 24.92971 1.710e+00 +#> 21 parent 11.50 12.46890 -9.689e-01 +#> 21 parent 11.64 12.46890 -8.289e-01 +#> 35 parent 2.85 3.11925 -2.692e-01 +#> 35 parent 2.91 3.11925 -2.092e-01 +#> 50 parent 0.69 0.70679 -1.679e-02 +#> 50 parent 0.63 0.70679 -7.679e-02 +#> 75 parent 0.05 0.05952 -9.523e-03 +#> 75 parent 0.06 0.05952 4.772e-04 +#> 1 m1 4.84 4.81075 2.925e-02 +#> 1 m1 5.64 4.81075 8.292e-01 +#> 3 m1 12.91 13.04196 -1.320e-01 +#> 3 m1 12.96 13.04196 -8.196e-02 +#> 7 m1 22.97 25.06847 -2.098e+00 +#> 7 m1 24.47 25.06847 -5.985e-01 +#> 14 m1 41.69 36.70308 4.987e+00 +#> 14 m1 33.21 36.70308 -3.493e+00 +#> 21 m1 44.37 41.65115 2.719e+00 +#> 21 m1 46.44 41.65115 4.789e+00 +#> 35 m1 41.22 43.29465 -2.075e+00 +#> 35 m1 37.95 43.29465 -5.345e+00 +#> 50 m1 41.19 41.19948 -9.479e-03 +#> 50 m1 40.01 41.19948 -1.189e+00 +#> 75 m1 40.09 36.44035 3.650e+00 +#> 75 m1 33.85 36.44035 -2.590e+00 +#> 100 m1 31.04 31.98773 -9.477e-01 +#> 100 m1 33.13 31.98773 1.142e+00 +#> 120 m1 25.15 28.80429 -3.654e+00 +#> 120 m1 33.31 28.80429 4.506e+00</div><div class='input'><span class='no'>f.tc</span> <span class='kw'><-</span> <span class='fu'>mkinfit</span>(<span class='no'>SFO_SFO.ff</span>, <span class='no'>FOCUS_2006_D</span>, <span class='kw'>error_model</span> <span class='kw'>=</span> <span class='st'>"tc"</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>TRUE</span>)</div><div class='output co'>#> <span class='warning'>Warning: Observations with value of zero were removed from the data</span></div><div class='input'><span class='fu'><a href='https://rdrr.io/r/base/summary.html'>summary</a></span>(<span class='no'>f.tc</span>)</div><div class='output co'>#> mkin version used for fitting: 0.9.50.3 +#> R version used for fitting: 4.0.0 +#> Date of fit: Wed May 27 05:54:20 2020 +#> Date of summary: Wed May 27 05:54:20 2020 +#> +#> Equations: +#> d_parent/dt = - k_parent * parent +#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1 +#> +#> Model predictions using solution type analytical +#> +#> Fitted using 2088 model solutions performed in 0.714 s +#> +#> Error model: Two-component variance function +#> +#> Error model algorithm: d_3 +#> Direct fitting and three-step fitting yield approximately the same likelihood +#> +#> Starting values for parameters to be optimised: +#> value type +#> parent_0 100.7500 state +#> k_parent 0.1000 deparm +#> k_m1 0.1001 deparm +#> f_parent_to_m1 0.5000 deparm +#> sigma_low 0.1000 error +#> rsd_high 0.1000 error +#> +#> Starting values for the transformed parameters actually optimised: +#> value lower upper +#> parent_0 100.750000 -Inf Inf +#> log_k_parent -2.302585 -Inf Inf +#> log_k_m1 -2.301586 -Inf Inf +#> f_parent_ilr_1 0.000000 -Inf Inf +#> sigma_low 0.100000 0 Inf +#> rsd_high 0.100000 0 Inf +#> +#> Fixed parameter values: +#> value type +#> m1_0 0 state +#> +#> Results: +#> +#> AIC BIC logLik +#> 141.9656 151.7911 -64.98278 +#> +#> Optimised, transformed parameters with symmetric confidence intervals: +#> Estimate Std. Error Lower Upper +#> parent_0 100.70000 2.621000 95.400000 106.10000 +#> log_k_parent -2.29700 0.008862 -2.315000 -2.27900 +#> log_k_m1 -5.26600 0.091310 -5.452000 -5.08000 +#> f_parent_ilr_1 0.02374 0.055300 -0.088900 0.13640 +#> sigma_low 0.00305 0.004829 -0.006786 0.01289 +#> rsd_high 0.07928 0.009418 0.060100 0.09847 +#> +#> Parameter correlation: +#> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_low rsd_high +#> parent_0 1.00000 0.67644 -0.10215 -0.76822 0.14294 -0.08783 +#> log_k_parent 0.67644 1.00000 -0.15102 -0.59491 0.34611 -0.08125 +#> log_k_m1 -0.10215 -0.15102 1.00000 0.51808 -0.05236 0.01240 +#> f_parent_ilr_1 -0.76822 -0.59491 0.51808 1.00000 -0.13900 0.03248 +#> sigma_low 0.14294 0.34611 -0.05236 -0.13900 1.00000 -0.16546 +#> rsd_high -0.08783 -0.08125 0.01240 0.03248 -0.16546 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 1.007e+02 38.4300 1.180e-28 95.400000 1.061e+02 +#> k_parent 1.006e-01 112.8000 1.718e-43 0.098760 1.024e-01 +#> k_m1 5.167e-03 10.9500 1.171e-12 0.004290 6.223e-03 +#> f_parent_to_m1 5.084e-01 26.0100 2.146e-23 0.468600 5.481e-01 +#> sigma_low 3.050e-03 0.6314 2.661e-01 -0.006786 1.289e-02 +#> rsd_high 7.928e-02 8.4170 6.418e-10 0.060100 9.847e-02 +#> +#> FOCUS Chi2 error levels in percent: +#> err.min n.optim df +#> All data 6.475 4 15 +#> parent 6.573 2 7 +#> m1 4.671 2 8 +#> +#> Resulting formation fractions: +#> ff +#> parent_m1 0.5084 +#> parent_sink 0.4916 +#> +#> Estimated disappearance times: +#> DT50 DT90 +#> parent 6.893 22.9 +#> m1 134.156 445.7 +#> +#> Data: +#> time variable observed predicted residual +#> 0 parent 99.46 100.73434 -1.274340 +#> 0 parent 102.04 100.73434 1.305660 +#> 1 parent 93.50 91.09751 2.402486 +#> 1 parent 92.50 91.09751 1.402486 +#> 3 parent 63.23 74.50141 -11.271410 +#> 3 parent 68.99 74.50141 -5.511410 +#> 7 parent 52.32 49.82880 2.491200 +#> 7 parent 55.13 49.82880 5.301200 +#> 14 parent 27.27 24.64809 2.621908 +#> 14 parent 26.64 24.64809 1.991908 +#> 21 parent 11.50 12.19232 -0.692315 +#> 21 parent 11.64 12.19232 -0.552315 +#> 35 parent 2.85 2.98327 -0.133266 +#> 35 parent 2.91 2.98327 -0.073266 +#> 50 parent 0.69 0.66013 0.029874 +#> 50 parent 0.63 0.66013 -0.030126 +#> 75 parent 0.05 0.05344 -0.003438 +#> 75 parent 0.06 0.05344 0.006562 +#> 1 m1 4.84 4.88645 -0.046451 +#> 1 m1 5.64 4.88645 0.753549 +#> 3 m1 12.91 13.22867 -0.318669 +#> 3 m1 12.96 13.22867 -0.268669 +#> 7 m1 22.97 25.36417 -2.394166 +#> 7 m1 24.47 25.36417 -0.894166 +#> 14 m1 41.69 37.00974 4.680263 +#> 14 m1 33.21 37.00974 -3.799737 +#> 21 m1 44.37 41.90133 2.468669 +#> 21 m1 46.44 41.90133 4.538669 +#> 35 m1 41.22 43.45691 -2.236913 +#> 35 m1 37.95 43.45691 -5.506913 +#> 50 m1 41.19 41.34199 -0.151985 +#> 50 m1 40.01 41.34199 -1.331985 +#> 75 m1 40.09 36.61471 3.475295 +#> 75 m1 33.85 36.61471 -2.764705 +#> 100 m1 31.04 32.20082 -1.160823 +#> 100 m1 33.13 32.20082 0.929177 +#> 120 m1 25.15 29.04130 -3.891304 +#> 120 m1 33.31 29.04130 4.268696</div><div class='input'># } + + +</div></pre> + </div> + <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar"> + <nav id="toc" data-toggle="toc" class="sticky-top"> + <h2 data-toc-skip>Contents</h2> + </nav> + </div> +</div> + + + <footer> + <div class="copyright"> + <p>Developed by Johannes Ranke.</p> +</div> + +<div class="pkgdown"> + <p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.5.1.</p> +</div> + + </footer> + </div> + + + + + </body> +</html> + + |