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This model cost is + then minimised using the Port algorithm <code>nlminb</code>, + using the specified initial or fixed parameters and starting values. + Per default, parameters in the kinetic models are internally transformed in order + to better satisfy the assumption of a normal distribution of their estimators. + In each step of the optimsation, the kinetic model is solved using the + function <code>mkinpredict</code>. The variance of the residuals for each + observed variable can optionally be iteratively reweighted until convergence + using the argument <code>reweight.method = "obs"</code>.</p> + + + <pre><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'>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'>names</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'>c</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'>method.modFit</span> <span class='kw'>=</span> <span class='fu'>c</span>(<span class='st'>"Port"</span>, <span class='st'>"Marq"</span>, <span class='st'>"SANN"</span>, <span class='st'>"Nelder-Mead"</span>, <span class='st'>"BFGS"</span>, <span class='st'>"CG"</span>, <span class='st'>"L-BFGS-B"</span>), + <span class='kw'>maxit.modFit</span> <span class='kw'>=</span> <span class='st'>"auto"</span>, + <span class='kw'>control.modFit</span> <span class='kw'>=</span> <span class='fu'>list</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'>plot</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='kw'>quiet</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, <span class='kw'>err</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, <span class='kw'>weight</span> <span class='kw'>=</span> <span class='st'>"none"</span>, + <span class='kw'>scaleVar</span> <span class='kw'>=</span> <span class='fl'>FALSE</span>, + <span class='kw'>atol</span> <span class='kw'>=</span> <span class='fl'>1e-8</span>, <span class='kw'>rtol</span> <span class='kw'>=</span> <span class='fl'>1e-10</span>, <span class='kw'>n.outtimes</span> <span class='kw'>=</span> <span class='fl'>100</span>, + <span class='kw'>reweight.method</span> <span class='kw'>=</span> <span class='kw'>NULL</span>, + <span class='kw'>reweight.tol</span> <span class='kw'>=</span> <span class='fl'>1e-8</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>Arguments</h2> + <dl class="dl-horizontal"> + <dt>mkinmod</dt> + <dd> + A list of class <code>mkinmod</code>, containing the kinetic model to be + fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP", + "HS", "SFORB"). If a shorthand name is given, a parent only degradation + model is generated for the variable with the highest value in + <code>observed</code>. + </dd> + <dt>observed</dt> + <dd> + The observed data. It has to be in the long format as described in + <code>modFit</code>, i.e. 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. Optionally, a further column + can contain weights for each data point. Its name must be passed as a + further argument named <code>err</code> which is then passed on to + <code>modFit</code>. + </dd> + <dt>parms.ini</dt> + <dd> + 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. + + 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. + </dd> + <dt>state.ini</dt> + <dd> + 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 <code>mkinmod</code>). 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. + </dd> + <dt>fixed_parms</dt> + <dd> + The names of parameters that should not be optimised but rather kept at the + values specified in <code>parms.ini</code>. + </dd> + <dt>fixed_initials</dt> + <dd> + 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. + </dd> + <dt>from_max_mean</dt> + <dd> + 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. + </dd> + <dt>solution_type</dt> + <dd> + 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 ode solver from package + <code>deSolve</code> is used. If set to "analytical", an analytical + solution of the model is used. This is only implemented for simple + degradation experiments with only one state variable, i.e. with no + metabolites. The default is "auto", which uses "analytical" if possible, + otherwise "eigen" if the model can be expressed using eigenvalues and + eigenvectors, and finally "deSolve" for the remaining models (time + dependence of degradation rates and metabolites). This argument is passed + on to the helper function <code>mkinpredict</code>. + </dd> + <dt>method.ode</dt> + <dd> + The solution method passed via <code>mkinpredict</code> to + <code>ode</code> in case the solution type is "deSolve". The default + "lsoda" is performant, but sometimes fails to converge. + </dd> + <dt>use_compiled</dt> + <dd> + If set to <code>FALSE</code>, no compiled version of the <code>mkinmod</code> + model is used, in the calls to <code>mkinpredict</code> even if + a compiled verion is present. + </dd> + <dt>method.modFit</dt> + <dd> + The optimisation method passed to <code>modFit</code>. + + In order to optimally deal with problems where local minima occur, the + "Port" algorithm is now used per default as it is less prone to get trapped + in local minima and depends less on starting values for parameters than + the Levenberg Marquardt variant selected by "Marq". However, "Port" needs + more iterations. + + The former default "Marq" is the Levenberg Marquardt algorithm + <code>nls.lm</code> from the package <code>minpack.lm</code> and usually needs + the least number of iterations. + + The "Pseudo" algorithm is not included because it needs finite parameter bounds + which are currently not supported. + + The "Newton" algorithm is not included because its number of iterations + can not be controlled by <code>control.modFit</code> and it does not appear + to provide advantages over the other algorithms. + </dd> + <dt>maxit.modFit</dt> + <dd> + Maximum number of iterations in the optimisation. If not "auto", this will + be passed to the method called by <code>modFit</code>, overriding + what may be specified in the next argument <code>control.modFit</code>. + </dd> + <dt>control.modFit</dt> + <dd> + Additional arguments passed to the optimisation method used by + <code>modFit</code>. + </dd> + <dt>transform_rates</dt> + <dd> + 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. + </dd> + <dt>transform_fractions</dt> + <dd> + 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>ilr</code> transformation. + </dd> + <dt>plot</dt> + <dd> + Should the observed values and the numerical solutions be plotted at each + stage of the optimisation? + </dd> + <dt>quiet</dt> + <dd> + Suppress printing out the current model cost after each improvement? + </dd> + <dt>err </dt> + <dd>either <code>NULL</code>, or the name of the column with the + <em>error</em> estimates, used to weigh the residuals (see details of + <code>modCost</code>); if <code>NULL</code>, then the residuals are not weighed. + </dd> + <dt>weight</dt> + <dd> + only if <code>err</code>=<code>NULL</code>: how to weight the residuals, one of "none", + "std", "mean", see details of <code>modCost</code>. + </dd> + <dt>scaleVar</dt> + <dd> + Will be passed to <code>modCost</code>. Default is not to scale Variables + according to the number of observations. + </dd> + <dt>atol</dt> + <dd> + Absolute error tolerance, passed to <code>ode</code>. Default is 1e-8, + lower than in <code>lsoda</code>. + </dd> + <dt>rtol</dt> + <dd> + Absolute error tolerance, passed to <code>ode</code>. Default is 1e-10, + much lower than in <code>lsoda</code>. + </dd> + <dt>n.outtimes</dt> + <dd> + The length of the dataseries that is produced by the model prediction + function <code>mkinpredict</code>. This impacts the accuracy of + the numerical solver if that is used (see <code>solution_type</code> argument. + The default value is 100. + </dd> + <dt>reweight.method</dt> + <dd> + The method used for iteratively reweighting residuals, also known + as iteratively reweighted least squares (IRLS). Default is NULL, + the other method implemented is called "obs", meaning that each + observed variable is assumed to have its own variance, this is + estimated from the fit and used for weighting the residuals + in each iteration until convergence of this estimate up to + <code>reweight.tol</code> or up to the maximum number of iterations + specified by <code>reweight.max.iter</code>. + </dd> + <dt>reweight.tol</dt> + <dd> + Tolerance for convergence criterion for the variance components + in IRLS fits. + </dd> + <dt>reweight.max.iter</dt> + <dd> + Maximum iterations in IRLS fits. + </dd> + <dt>trace_parms</dt> + <dd> + Should a trace of the parameter values be listed? + </dd> + <dt>&#8230;</dt> + <dd> + Further arguments that will be passed to <code>modFit</code>. + </dd> + </dl> + + <div class="Value"> + <h2>Value</h2> + + <p>A list with "mkinfit" and "modFit" in the class attribute. + A summary can be obtained by <code>summary.mkinfit</code>.</p> + </div> + + <div class="See also"> + <h2>See also</h2> + + <p>Plotting methods <code>plot.mkinfit</code> and + <code>mkinparplot</code>.</p> + <p>Fitting of several models to several datasets in a single call to + <code>mmkin</code>.</p> + </div> + + <div class="Note"> + <h2>Note</h2> + + <p>The implementation of iteratively reweighted least squares is inspired by the + work of the KinGUII team at Bayer Crop Science (Walter Schmitt and Zhenglei + Gao). A similar implemention can also be found in CAKE 2.0, which is the + other GUI derivative of mkin, sponsored by Syngenta.</p> + </div> + + <div class="Note"> + <h2>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> + </div> + + <h2 id="examples">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'>summary</span>(<span class='no'>fit</span>)</div><div class='output co'>#> mkin version: 0.9.44.9000 +#> R version: 3.3.1 +#> Date of fit: Thu Oct 6 09:17:59 2016 +#> Date of summary: Thu Oct 6 09:17:59 2016 +#> +#> Equations: +#> d_parent = - (alpha/beta) * 1/((time/beta) + 1) * parent +#> +#> Model predictions using solution type analytical +#> +#> Fitted with method Port using 64 model solutions performed in 0.153 s +#> +#> Weighting: none +#> +#> 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 +#> +#> Optimised, transformed parameters with symmetric confidence intervals: +#> Estimate Std. Error Lower Upper +#> parent_0 85.87000 2.2460 80.38000 91.3700 +#> log_alpha 0.05192 0.1605 -0.34080 0.4446 +#> log_beta 0.65100 0.2801 -0.03452 1.3360 +#> +#> Parameter correlation: +#> parent_0 log_alpha log_beta +#> parent_0 1.0000 -0.2033 -0.3624 +#> log_alpha -0.2033 1.0000 0.9547 +#> log_beta -0.3624 0.9547 1.0000 +#> +#> Residual standard error: 2.275 on 6 degrees of freedom +#> +#> 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 38.230 1.069e-08 80.3800 91.370 +#> alpha 1.053 6.231 3.953e-04 0.7112 1.560 +#> beta 1.917 3.570 5.895e-03 0.9661 3.806 +#> +#> 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'>mkinmod</span>( + <span class='kw'>parent</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>, <span class='st'>"m1"</span>), + <span class='kw'>m1</span> <span class='kw'>=</span> <span class='fu'>mkinsub</span>(<span class='st'>"SFO"</span>))</div><div class='output'><strong class='text-info'>Successfully compiled differential equation model from auto-generated C code.</strong></div><div class='input'><span class='co'># Fit the model to the FOCUS example dataset D using defaults</span> +<span class='fu'>print</span>(<span class='fu'>system.time</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'>#> user system elapsed +#> 1.252 1.176 0.914 +#> </div><div class='input'><span class='fu'>coef</span>(<span class='no'>fit</span>)</div><div class='output co'>#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink +#> 99.59848 -3.03822 -2.98030 -5.24750 +#> </div><div class='input'><span class='fu'>endpoints</span>(<span class='no'>fit</span>)</div><div class='output co'>#> $ff +#> parent_sink parent_m1 m1_sink +#> 0.485524 0.514476 1.000000 +#> +#> $SFORB +#> logical(0) +#> +#> $distimes +#> DT50 DT90 +#> parent 7.022929 23.32967 +#> m1 131.760712 437.69961 +#> +#> </div><div class='input'><span class='co'>## Not run: ------------------------------------</span> +<span class='co'># # deSolve is slower when no C compiler (gcc) was available during model generation</span> +<span class='co'># print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D, </span> +<span class='co'># solution_type = "deSolve")))</span> +<span class='co'># coef(fit.deSolve)</span> +<span class='co'># endpoints(fit.deSolve)</span> +<span class='co'>## ---------------------------------------------</span> + +<span class='co'># Use stepwise fitting, using optimised parameters from parent only fit, FOMC</span> +<span class='co'>## Not run: ------------------------------------</span> +<span class='co'># FOMC_SFO <- mkinmod(</span> +<span class='co'># parent = mkinsub("FOMC", "m1"),</span> +<span class='co'># m1 = mkinsub("SFO"))</span> +<span class='co'># # Fit the model to the FOCUS example dataset D using defaults</span> +<span class='co'># fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D)</span> +<span class='co'># # Use starting parameters from parent only FOMC fit</span> +<span class='co'># fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, plot=TRUE)</span> +<span class='co'># fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, </span> +<span class='co'># parms.ini = fit.FOMC$bparms.ode, plot=TRUE)</span> +<span class='co'># </span> +<span class='co'># # Use stepwise fitting, using optimised parameters from parent only fit, SFORB</span> +<span class='co'># SFORB_SFO <- mkinmod(</span> +<span class='co'># parent = list(type = "SFORB", to = "m1", sink = TRUE),</span> +<span class='co'># m1 = list(type = "SFO"))</span> +<span class='co'># # Fit the model to the FOCUS example dataset D using defaults</span> +<span class='co'># fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D)</span> +<span class='co'># fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve")</span> +<span class='co'># # Use starting parameters from parent only SFORB fit (not really needed in this case)</span> +<span class='co'># fit.SFORB = mkinfit("SFORB", FOCUS_2006_D)</span> +<span class='co'># fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode)</span> +<span class='co'>## ---------------------------------------------</span> + +<span class='co'>## Not run: ------------------------------------</span> +<span class='co'># # Weighted fits, including IRLS</span> +<span class='co'># SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"),</span> +<span class='co'># m1 = mkinsub("SFO"), use_of_ff = "max")</span> +<span class='co'># f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D)</span> +<span class='co'># summary(f.noweight)</span> +<span class='co'># f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs")</span> +<span class='co'># summary(f.irls)</span> +<span class='co'># f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean")</span> +<span class='co'># summary(f.w.mean)</span> +<span class='co'># f.w.value <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value")</span> +<span class='co'># summary(f.w.value)</span> +<span class='co'>## ---------------------------------------------</span> + +<span class='co'>## Not run: ------------------------------------</span> +<span class='co'># # Manual weighting</span> +<span class='co'># dw <- FOCUS_2006_D</span> +<span class='co'># errors <- c(parent = 2, m1 = 1)</span> +<span class='co'># dw$err.man <- errors[FOCUS_2006_D$name]</span> +<span class='co'># f.w.man <- mkinfit(SFO_SFO.ff, dw, err = "err.man")</span> +<span class='co'># summary(f.w.man)</span> +<span class='co'># f.w.man.irls <- mkinfit(SFO_SFO.ff, dw, err = "err.man",</span> +<span class='co'># reweight.method = "obs")</span> +<span class='co'># summary(f.w.man.irls)</span> +<span class='co'>## ---------------------------------------------</span></div></pre> + </div> + <div class="col-md-3"> + <h2>Author</h2> + + Johannes Ranke + + </div> +</div> + + <footer> + <p>Built by <a href="http://hadley.github.io/pkgdown/">pkgdown</a>. Styled with <a href="http://getbootstrap.com">Bootstrap 3</a>.</p> + </footer> + </div> + + </body> +</html> |