This function uses the Flexible Modelling Environment package
FME to create a function calculating the model cost, i.e. the
deviation between the kinetic model and the observed data. This model cost is
then minimised using the Port algorithm nlminb,
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 mkinpredict. The variance of the residuals for each
observed variable can optionally be iteratively reweighted until convergence
using the argument reweight.method = "obs".
mkinfit(mkinmod, observed, parms.ini = "auto", state.ini = "auto", fixed_parms = NULL, fixed_initials = names(mkinmod$diffs)[-1], from_max_mean = FALSE, solution_type = c("auto", "analytical", "eigen", "deSolve"), method.ode = "lsoda", use_compiled = "auto", method.modFit = c("Port", "Marq", "SANN", "Nelder-Mead", "BFGS", "CG", "L-BFGS-B"), maxit.modFit = "auto", control.modFit = list(), transform_rates = TRUE, transform_fractions = TRUE, plot = FALSE, quiet = FALSE, err = NULL, weight = "none", scaleVar = FALSE, atol = 1e-8, rtol = 1e-10, n.outtimes = 100, reweight.method = NULL, reweight.tol = 1e-8, reweight.max.iter = 10, trace_parms = FALSE, ...)
mkinmod, 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
observed.
modFit, 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 err which is then passed on to
modFit.
fixed_parms. 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.
map component of mkinmod). 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.
parms.ini.
deSolve 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 mkinpredict.
mkinpredict to
ode in case the solution type is "deSolve". The default
"lsoda" is performant, but sometimes fails to converge.
FALSE, no compiled version of the mkinmod
model is used, in the calls to mkinpredict even if
a compiled verion is present.
modFit.
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
nls.lm from the package minpack.lm 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 control.modFit and it does not appear
to provide advantages over the other algorithms.
modFit, overriding
what may be specified in the next argument control.modFit.
modFit.
ilr transformation.
NULL, or the name of the column with the
error estimates, used to weigh the residuals (see details of
modCost); if NULL, then the residuals are not weighed.
err=NULL: how to weight the residuals, one of "none",
"std", "mean", see details of modCost.
modCost. Default is not to scale Variables
according to the number of observations.
ode. Default is 1e-8,
lower than in lsoda.
ode. Default is 1e-10,
much lower than in lsoda.
mkinpredict. This impacts the accuracy of
the numerical solver if that is used (see solution_type argument.
The default value is 100.
reweight.tol or up to the maximum number of iterations
specified by reweight.max.iter.
modFit.
A list with "mkinfit" and "modFit" in the class attribute.
A summary can be obtained by summary.mkinfit.
Plotting methods plot.mkinfit and
mkinparplot.
Fitting of several models to several datasets in a single call to
mmkin.
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.
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.
# Use shorthand notation for parent only degradation fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE) summary(fit)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:37 2016 #> Date of summary: Fri Nov 18 15:19:37 2016 #> #> Equations: #> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent #> #> Model predictions using solution type analytical #> #> Fitted with method Port using 64 model solutions performed in 0.152 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# One parent compound, one metabolite, both single first order. # Use mkinsub for convenience in model formulation. Pathway to sink included per default. SFO_SFO <- mkinmod( parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"))#># Fit the model to the FOCUS example dataset D using defaults print(system.time(fit <- mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = TRUE)))#> user system elapsed #> 1.220 1.184 0.904coef(fit)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750endpoints(fit)#> $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 #># deSolve is slower when no C compiler (gcc) was available during model generation print(system.time(fit.deSolve <- mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve")))#> Model cost at call 1 : 18915.53 #> Model cost at call 2 : 18915.53 #> Model cost at call 6 : 11424.02 #> Model cost at call 10 : 11424 #> Model cost at call 12 : 4094.396 #> Model cost at call 16 : 4094.396 #> Model cost at call 19 : 1340.595 #> Model cost at call 20 : 1340.593 #> Model cost at call 25 : 1072.239 #> Model cost at call 28 : 1072.236 #> Model cost at call 30 : 874.2614 #> Model cost at call 33 : 874.2611 #> Model cost at call 35 : 616.2379 #> Model cost at call 37 : 616.2374 #> Model cost at call 40 : 467.4388 #> Model cost at call 42 : 467.4382 #> Model cost at call 46 : 398.2914 #> Model cost at call 48 : 398.2914 #> Model cost at call 49 : 398.2913 #> Model cost at call 51 : 395.0712 #> Model cost at call 54 : 395.0711 #> Model cost at call 56 : 378.3298 #> Model cost at call 59 : 378.3298 #> Model cost at call 62 : 376.9812 #> Model cost at call 64 : 376.9811 #> Model cost at call 67 : 375.2085 #> Model cost at call 69 : 375.2085 #> Model cost at call 70 : 375.2085 #> Model cost at call 71 : 375.2085 #> Model cost at call 72 : 374.5723 #> Model cost at call 74 : 374.5723 #> Model cost at call 77 : 374.0075 #> Model cost at call 79 : 374.0075 #> Model cost at call 80 : 374.0075 #> Model cost at call 82 : 373.1711 #> Model cost at call 84 : 373.1711 #> Model cost at call 87 : 372.6445 #> Model cost at call 88 : 372.1614 #> Model cost at call 90 : 372.1614 #> Model cost at call 91 : 372.1614 #> Model cost at call 94 : 371.6464 #> Model cost at call 99 : 371.4299 #> Model cost at call 101 : 371.4299 #> Model cost at call 104 : 371.407 #> Model cost at call 106 : 371.407 #> Model cost at call 107 : 371.407 #> Model cost at call 109 : 371.2524 #> Model cost at call 113 : 371.2524 #> Model cost at call 114 : 371.2136 #> Model cost at call 115 : 371.2136 #> Model cost at call 116 : 371.2136 #> Model cost at call 119 : 371.2134 #> Model cost at call 120 : 371.2134 #> Model cost at call 122 : 371.2134 #> Model cost at call 123 : 371.2134 #> Model cost at call 125 : 371.2134 #> Model cost at call 126 : 371.2134 #> Model cost at call 135 : 371.2134 #> Model cost at call 147 : 371.2134 #> Model cost at call 152 : 371.2134 #> Optimisation by method Port successfully terminated. #> user system elapsed #> 0.712 0.040 0.707coef(fit.deSolve)#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750endpoints(fit.deSolve)#> $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 131.760713 437.69961 #># Use stepwise fitting, using optimised parameters from parent only fit, FOMC FOMC_SFO <- mkinmod( parent = mkinsub("FOMC", "m1"), m1 = mkinsub("SFO"))#># Fit the model to the FOCUS example dataset D using defaults fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D)#> Model cost at call 1 : 18857.28 #> Model cost at call 4 : 18857.28 #> Model cost at call 5 : 18857.28 #> Model cost at call 8 : 15273.94 #> Model cost at call 9 : 15273.93 #> Model cost at call 12 : 15273.67 #> Model cost at call 13 : 15273.64 #> Model cost at call 14 : 12764.42 #> Model cost at call 15 : 8382.7 #> Model cost at call 20 : 8382.696 #> Model cost at call 23 : 2729.177 #> Model cost at call 24 : 2729.175 #> Model cost at call 26 : 2729.164 #> Model cost at call 30 : 2299.383 #> Model cost at call 34 : 2299.379 #> Model cost at call 35 : 2299.373 #> Model cost at call 36 : 1944.782 #> Model cost at call 40 : 1944.782 #> Model cost at call 42 : 1328.087 #> Model cost at call 43 : 908.661 #> Model cost at call 44 : 908.6604 #> Model cost at call 50 : 877.3556 #> Model cost at call 51 : 877.3554 #> Model cost at call 54 : 877.3546 #> Model cost at call 56 : 769.5186 #> Model cost at call 59 : 769.5157 #> Model cost at call 62 : 690.3426 #> Model cost at call 66 : 690.3425 #> Model cost at call 68 : 608.4032 #> Model cost at call 72 : 608.4031 #> Model cost at call 73 : 608.4031 #> Model cost at call 74 : 601.5178 #> Model cost at call 78 : 601.5174 #> Model cost at call 79 : 601.5174 #> Model cost at call 80 : 459.9885 #> Model cost at call 81 : 459.9883 #> Model cost at call 83 : 459.9878 #> Model cost at call 87 : 447.0145 #> Model cost at call 91 : 447.0145 #> Model cost at call 94 : 445.7322 #> Model cost at call 97 : 445.7322 #> Model cost at call 99 : 445.7322 #> Model cost at call 100 : 444.6965 #> Model cost at call 103 : 444.6965 #> Model cost at call 106 : 442.9742 #> Model cost at call 109 : 442.9742 #> Model cost at call 112 : 439.9665 #> Model cost at call 115 : 439.9665 #> Model cost at call 116 : 439.9664 #> Model cost at call 118 : 435.0752 #> Model cost at call 121 : 435.0751 #> Model cost at call 124 : 430.4718 #> Model cost at call 127 : 430.4717 #> Model cost at call 132 : 424.7004 #> Model cost at call 134 : 424.7003 #> Model cost at call 138 : 423.6102 #> Model cost at call 141 : 423.6102 #> Model cost at call 142 : 423.6102 #> Model cost at call 144 : 421.1786 #> Model cost at call 147 : 421.1786 #> Model cost at call 148 : 421.1786 #> Model cost at call 150 : 418.1431 #> Model cost at call 151 : 412.8665 #> Model cost at call 152 : 396.6067 #> Model cost at call 154 : 396.6067 #> Model cost at call 158 : 391.0492 #> Model cost at call 160 : 391.0492 #> Model cost at call 164 : 385.8205 #> Model cost at call 165 : 385.8205 #> Model cost at call 170 : 379.7674 #> Model cost at call 171 : 379.7674 #> Model cost at call 172 : 379.7674 #> Model cost at call 176 : 374.9389 #> Model cost at call 177 : 374.9389 #> Model cost at call 182 : 372.727 #> Model cost at call 185 : 372.727 #> Model cost at call 188 : 371.5297 #> Model cost at call 194 : 370.3738 #> Model cost at call 195 : 370.3738 #> Model cost at call 200 : 370.0182 #> Model cost at call 206 : 369.8634 #> Model cost at call 212 : 369.8188 #> Model cost at call 213 : 369.8188 #> Model cost at call 219 : 369.8114 #> Model cost at call 221 : 369.8114 #> Model cost at call 224 : 369.8114 #> Model cost at call 226 : 369.8114 #> Model cost at call 230 : 369.8105 #> Model cost at call 231 : 369.8105 #> Model cost at call 235 : 369.8105 #> Model cost at call 236 : 369.8105 #> Model cost at call 237 : 369.8105 #> Model cost at call 238 : 369.8105 #> Model cost at call 249 : 369.8105 #> Model cost at call 260 : 369.8105 #> Model cost at call 275 : 369.8105 #> Model cost at call 276 : 369.8105 #> Optimisation by method Port successfully terminated.# Use starting parameters from parent only FOMC fit fit.FOMC = mkinfit("FOMC", FOCUS_2006_D)#> Model cost at call 1 : 3237.008 #> Model cost at call 3 : 3237.007 #> Model cost at call 6 : 671.2571 #> Model cost at call 7 : 671.2559 #> Model cost at call 8 : 671.2301 #> Model cost at call 9 : 671.2249 #> Model cost at call 10 : 468.4899 #> Model cost at call 12 : 468.4899 #> Model cost at call 14 : 371.3486 #> Model cost at call 16 : 371.3485 #> Model cost at call 18 : 346.2972 #> Model cost at call 19 : 346.2971 #> Model cost at call 20 : 346.297 #> Model cost at call 21 : 346.2969 #> Model cost at call 22 : 269.7053 #> Model cost at call 23 : 269.7053 #> Model cost at call 26 : 243.9936 #> Model cost at call 27 : 235.1625 #> Model cost at call 28 : 235.1624 #> Model cost at call 30 : 235.1624 #> Model cost at call 31 : 224.2195 #> Model cost at call 35 : 218.1922 #> Model cost at call 36 : 218.1922 #> Model cost at call 38 : 218.1922 #> Model cost at call 39 : 211.5012 #> Model cost at call 41 : 211.5012 #> Model cost at call 43 : 207.9511 #> Model cost at call 44 : 207.9511 #> Model cost at call 47 : 206.5377 #> Model cost at call 51 : 205.8736 #> Model cost at call 55 : 205.5625 #> Model cost at call 59 : 205.4704 #> Model cost at call 63 : 205.4499 #> Model cost at call 67 : 205.448 #> Model cost at call 69 : 205.448 #> Model cost at call 70 : 205.448 #> Model cost at call 73 : 205.448 #> Model cost at call 74 : 205.4478 #> Model cost at call 75 : 205.4478 #> Model cost at call 77 : 205.4478 #> Model cost at call 79 : 205.4478 #> Model cost at call 84 : 205.4478 #> Model cost at call 95 : 205.4478 #> Model cost at call 98 : 205.4478 #> Optimisation by method Port successfully terminated.fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, parms.ini = fit.FOMC$bparms.ode)#> Model cost at call 1 : 15169.96 #> Model cost at call 2 : 15169.96 #> Model cost at call 7 : 8247.462 #> Model cost at call 14 : 6734.371 #> Model cost at call 15 : 6734.339 #> Model cost at call 16 : 6734.136 #> Model cost at call 20 : 4855.056 #> Model cost at call 24 : 4855.038 #> Model cost at call 27 : 1239.986 #> Model cost at call 29 : 1239.985 #> Model cost at call 34 : 1030.523 #> Model cost at call 38 : 1030.523 #> Model cost at call 40 : 894.2766 #> Model cost at call 43 : 894.275 #> Model cost at call 46 : 750.3629 #> Model cost at call 49 : 750.3623 #> Model cost at call 52 : 627.6819 #> Model cost at call 55 : 627.6818 #> Model cost at call 58 : 546.2947 #> Model cost at call 61 : 546.2944 #> Model cost at call 65 : 502.5529 #> Model cost at call 69 : 502.5525 #> Model cost at call 70 : 502.5525 #> Model cost at call 71 : 475.2423 #> Model cost at call 72 : 465.5298 #> Model cost at call 75 : 465.5298 #> Model cost at call 76 : 465.5297 #> Model cost at call 78 : 464.9476 #> Model cost at call 81 : 464.9476 #> Model cost at call 82 : 464.9473 #> Model cost at call 84 : 426.9626 #> Model cost at call 88 : 426.9626 #> Model cost at call 90 : 414.5235 #> Model cost at call 93 : 414.5234 #> Model cost at call 96 : 412.1478 #> Model cost at call 99 : 412.1477 #> Model cost at call 100 : 412.1477 #> Model cost at call 101 : 412.1477 #> Model cost at call 102 : 394.146 #> Model cost at call 105 : 394.146 #> Model cost at call 106 : 394.146 #> Model cost at call 107 : 394.146 #> Model cost at call 108 : 384.2002 #> Model cost at call 112 : 384.2001 #> Model cost at call 113 : 384.2001 #> Model cost at call 115 : 380.5495 #> Model cost at call 119 : 380.5494 #> Model cost at call 120 : 380.5494 #> Model cost at call 121 : 378.4803 #> Model cost at call 123 : 378.4802 #> Model cost at call 124 : 378.4792 #> Model cost at call 127 : 374.8432 #> Model cost at call 129 : 374.8431 #> Model cost at call 133 : 372.8364 #> Model cost at call 136 : 372.8364 #> Model cost at call 137 : 372.8363 #> Model cost at call 138 : 372.8363 #> Model cost at call 141 : 372.668 #> Model cost at call 145 : 372.6679 #> Model cost at call 147 : 372.5882 #> Model cost at call 150 : 372.5882 #> Model cost at call 153 : 372.4828 #> Model cost at call 156 : 372.4828 #> Model cost at call 159 : 372.3639 #> Model cost at call 162 : 372.3639 #> Model cost at call 163 : 372.3639 #> Model cost at call 164 : 372.3639 #> Model cost at call 165 : 372.1959 #> Model cost at call 168 : 372.1959 #> Model cost at call 171 : 371.9627 #> Model cost at call 172 : 371.7467 #> Model cost at call 173 : 371.1161 #> Model cost at call 174 : 370.3326 #> Model cost at call 177 : 370.3326 #> Model cost at call 178 : 370.3326 #> Model cost at call 180 : 370.3267 #> Model cost at call 186 : 370.0471 #> Model cost at call 187 : 370.0471 #> Model cost at call 193 : 369.9649 #> Model cost at call 194 : 369.9649 #> Model cost at call 196 : 369.9649 #> Model cost at call 199 : 369.8684 #> Model cost at call 200 : 369.8684 #> Model cost at call 204 : 369.8684 #> Model cost at call 206 : 369.8349 #> Model cost at call 207 : 369.8349 #> Model cost at call 209 : 369.8349 #> Model cost at call 210 : 369.8349 #> Model cost at call 211 : 369.8349 #> Model cost at call 212 : 369.8105 #> Model cost at call 214 : 369.8105 #> Model cost at call 218 : 369.8105 #> Model cost at call 220 : 369.8105 #> Model cost at call 225 : 369.8105 #> Model cost at call 229 : 369.8105 #> Model cost at call 231 : 369.8105 #> Model cost at call 232 : 369.8105 #> Model cost at call 236 : 369.8105 #> Model cost at call 239 : 369.8105 #> Model cost at call 240 : 369.8105 #> Model cost at call 255 : 369.8105 #> Model cost at call 258 : 369.8105 #> Optimisation by method Port successfully terminated.# Use stepwise fitting, using optimised parameters from parent only fit, SFORB SFORB_SFO <- mkinmod( parent = list(type = "SFORB", to = "m1", sink = TRUE), m1 = list(type = "SFO"))#># Fit the model to the FOCUS example dataset D using defaults fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D)#> Model cost at call 1 : 19233.21 #> Model cost at call 2 : 19233.21 #> Model cost at call 5 : 19233.21 #> Model cost at call 8 : 14482.65 #> Model cost at call 11 : 14482.51 #> Model cost at call 13 : 14482.17 #> Model cost at call 15 : 6973.814 #> Model cost at call 16 : 5161.041 #> Model cost at call 17 : 5161.029 #> Model cost at call 22 : 5161.026 #> Model cost at call 24 : 3249.595 #> Model cost at call 26 : 3249.595 #> Model cost at call 27 : 3249.519 #> Model cost at call 31 : 2615.891 #> Model cost at call 32 : 2615.888 #> Model cost at call 39 : 989.1788 #> Model cost at call 44 : 989.1772 #> Model cost at call 45 : 989.1771 #> Model cost at call 47 : 647.4307 #> Model cost at call 50 : 647.4302 #> Model cost at call 51 : 647.4261 #> Model cost at call 54 : 626.7937 #> Model cost at call 55 : 626.7935 #> Model cost at call 56 : 626.7931 #> Model cost at call 61 : 527.9042 #> Model cost at call 62 : 527.9041 #> Model cost at call 68 : 505.8828 #> Model cost at call 70 : 505.8828 #> Model cost at call 73 : 505.8827 #> Model cost at call 75 : 452.8932 #> Model cost at call 77 : 452.893 #> Model cost at call 82 : 414.4918 #> Model cost at call 83 : 414.4918 #> Model cost at call 84 : 414.4918 #> Model cost at call 88 : 414.4917 #> Model cost at call 89 : 408.2617 #> Model cost at call 90 : 408.2616 #> Model cost at call 91 : 408.2616 #> Model cost at call 95 : 408.2615 #> Model cost at call 96 : 384.4461 #> Model cost at call 102 : 384.4461 #> Model cost at call 104 : 383.4905 #> Model cost at call 105 : 383.4905 #> Model cost at call 106 : 383.4905 #> Model cost at call 109 : 383.4904 #> Model cost at call 111 : 381.8828 #> Model cost at call 112 : 381.8827 #> Model cost at call 118 : 380.8499 #> Model cost at call 120 : 380.8499 #> Model cost at call 123 : 380.8499 #> Model cost at call 125 : 379.1403 #> Model cost at call 127 : 379.1402 #> Model cost at call 132 : 376.4962 #> Model cost at call 133 : 373.0958 #> Model cost at call 134 : 365.247 #> Model cost at call 137 : 365.2469 #> Model cost at call 142 : 360.8231 #> Model cost at call 143 : 360.8231 #> Model cost at call 146 : 360.8231 #> Model cost at call 148 : 360.8231 #> Model cost at call 149 : 358.3976 #> Model cost at call 152 : 358.3976 #> Model cost at call 154 : 358.3976 #> Model cost at call 156 : 355.9066 #> Model cost at call 157 : 355.9066 #> Model cost at call 163 : 354.3386 #> Model cost at call 164 : 353.6335 #> Model cost at call 172 : 353.2094 #> Model cost at call 173 : 353.2094 #> Model cost at call 174 : 353.2093 #> Model cost at call 177 : 353.2093 #> Model cost at call 178 : 353.2093 #> Model cost at call 179 : 352.6641 #> Model cost at call 182 : 352.6641 #> Model cost at call 183 : 352.6641 #> Model cost at call 186 : 352.4908 #> Model cost at call 187 : 352.4429 #> Model cost at call 195 : 352.3246 #> Model cost at call 203 : 352.2858 #> Model cost at call 204 : 352.2858 #> Model cost at call 205 : 352.2858 #> Model cost at call 206 : 352.2858 #> Model cost at call 207 : 352.2858 #> Model cost at call 210 : 352.2332 #> Model cost at call 211 : 352.2081 #> Model cost at call 214 : 352.2081 #> Model cost at call 216 : 352.2081 #> Model cost at call 218 : 352.2049 #> Model cost at call 219 : 352.2049 #> Model cost at call 220 : 352.2049 #> Model cost at call 226 : 352.2048 #> Model cost at call 228 : 352.2048 #> Model cost at call 231 : 352.2048 #> Model cost at call 232 : 352.2048 #> Model cost at call 238 : 352.2048 #> Model cost at call 239 : 352.2048 #> Model cost at call 251 : 352.2048 #> Model cost at call 264 : 352.2048 #> Model cost at call 283 : 352.2048 #> Model cost at call 284 : 352.2048 #> Model cost at call 285 : 352.2048 #> Model cost at call 286 : 352.2048 #> Optimisation by method Port successfully terminated.fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve")#> Model cost at call 1 : 19233.21 #> Model cost at call 2 : 19233.21 #> Model cost at call 5 : 19233.21 #> Model cost at call 8 : 14482.65 #> Model cost at call 11 : 14482.51 #> Model cost at call 13 : 14482.17 #> Model cost at call 15 : 6973.814 #> Model cost at call 16 : 5161.041 #> Model cost at call 17 : 5161.029 #> Model cost at call 22 : 5161.026 #> Model cost at call 24 : 3249.595 #> Model cost at call 26 : 3249.595 #> Model cost at call 27 : 3249.519 #> Model cost at call 31 : 2615.891 #> Model cost at call 32 : 2615.888 #> Model cost at call 39 : 989.1788 #> Model cost at call 44 : 989.1772 #> Model cost at call 45 : 989.1771 #> Model cost at call 47 : 647.4307 #> Model cost at call 50 : 647.4302 #> Model cost at call 51 : 647.4261 #> Model cost at call 54 : 626.7937 #> Model cost at call 55 : 626.7935 #> Model cost at call 56 : 626.7931 #> Model cost at call 61 : 527.9042 #> Model cost at call 62 : 527.9041 #> Model cost at call 68 : 505.8828 #> Model cost at call 70 : 505.8828 #> Model cost at call 73 : 505.8827 #> Model cost at call 75 : 452.8932 #> Model cost at call 77 : 452.893 #> Model cost at call 82 : 414.4918 #> Model cost at call 83 : 414.4918 #> Model cost at call 84 : 414.4918 #> Model cost at call 88 : 414.4917 #> Model cost at call 89 : 408.2617 #> Model cost at call 90 : 408.2616 #> Model cost at call 91 : 408.2616 #> Model cost at call 95 : 408.2615 #> Model cost at call 96 : 384.4461 #> Model cost at call 102 : 384.4461 #> Model cost at call 104 : 383.4905 #> Model cost at call 105 : 383.4905 #> Model cost at call 106 : 383.4905 #> Model cost at call 109 : 383.4904 #> Model cost at call 111 : 381.8828 #> Model cost at call 112 : 381.8827 #> Model cost at call 118 : 380.8499 #> Model cost at call 120 : 380.8499 #> Model cost at call 123 : 380.8499 #> Model cost at call 125 : 379.1403 #> Model cost at call 127 : 379.1402 #> Model cost at call 132 : 376.4962 #> Model cost at call 133 : 373.0958 #> Model cost at call 134 : 365.247 #> Model cost at call 137 : 365.2469 #> Model cost at call 142 : 360.8231 #> Model cost at call 143 : 360.8231 #> Model cost at call 146 : 360.8231 #> Model cost at call 148 : 360.8231 #> Model cost at call 149 : 358.3976 #> Model cost at call 152 : 358.3976 #> Model cost at call 154 : 358.3976 #> Model cost at call 156 : 355.9066 #> Model cost at call 157 : 355.9066 #> Model cost at call 163 : 354.3386 #> Model cost at call 164 : 353.6335 #> Model cost at call 172 : 353.2094 #> Model cost at call 173 : 353.2094 #> Model cost at call 174 : 353.2093 #> Model cost at call 177 : 353.2093 #> Model cost at call 178 : 353.2093 #> Model cost at call 179 : 352.6641 #> Model cost at call 182 : 352.6641 #> Model cost at call 183 : 352.6641 #> Model cost at call 186 : 352.4908 #> Model cost at call 187 : 352.4429 #> Model cost at call 195 : 352.3246 #> Model cost at call 203 : 352.2858 #> Model cost at call 204 : 352.2858 #> Model cost at call 205 : 352.2858 #> Model cost at call 206 : 352.2858 #> Model cost at call 207 : 352.2858 #> Model cost at call 210 : 352.2332 #> Model cost at call 211 : 352.2081 #> Model cost at call 214 : 352.2081 #> Model cost at call 216 : 352.2081 #> Model cost at call 218 : 352.2049 #> Model cost at call 219 : 352.2049 #> Model cost at call 220 : 352.2049 #> Model cost at call 226 : 352.2048 #> Model cost at call 228 : 352.2048 #> Model cost at call 231 : 352.2048 #> Model cost at call 232 : 352.2048 #> Model cost at call 238 : 352.2048 #> Model cost at call 239 : 352.2048 #> Model cost at call 251 : 352.2048 #> Model cost at call 264 : 352.2048 #> Model cost at call 283 : 352.2048 #> Model cost at call 284 : 352.2048 #> Model cost at call 285 : 352.2048 #> Model cost at call 286 : 352.2048 #> Optimisation by method Port successfully terminated.# Use starting parameters from parent only SFORB fit (not really needed in this case) fit.SFORB = mkinfit("SFORB", FOCUS_2006_D)#> Model cost at call 1 : 10426.65 #> Model cost at call 3 : 10426.65 #> Model cost at call 6 : 1995.326 #> Model cost at call 7 : 1995.322 #> Model cost at call 8 : 1995.14 #> Model cost at call 11 : 718.5568 #> Model cost at call 12 : 718.5566 #> Model cost at call 13 : 718.5563 #> Model cost at call 16 : 408.9208 #> Model cost at call 17 : 408.9204 #> Model cost at call 18 : 408.9204 #> Model cost at call 20 : 408.9203 #> Model cost at call 21 : 402.7935 #> Model cost at call 22 : 402.793 #> Model cost at call 26 : 202.0443 #> Model cost at call 28 : 202.0443 #> Model cost at call 30 : 202.0443 #> Model cost at call 31 : 196.438 #> Model cost at call 36 : 196.1947 #> Model cost at call 37 : 196.1947 #> Model cost at call 41 : 192.9338 #> Model cost at call 43 : 192.9338 #> Model cost at call 45 : 192.9338 #> Model cost at call 46 : 191.6452 #> Model cost at call 47 : 191.6452 #> Model cost at call 51 : 188.9328 #> Model cost at call 54 : 188.9328 #> Model cost at call 55 : 188.9328 #> Model cost at call 56 : 183.6499 #> Model cost at call 59 : 183.6499 #> Model cost at call 62 : 181.9039 #> Model cost at call 67 : 179.0543 #> Model cost at call 68 : 179.0543 #> Model cost at call 69 : 179.0543 #> Model cost at call 70 : 179.0543 #> Model cost at call 72 : 176.749 #> Model cost at call 73 : 176.2321 #> Model cost at call 74 : 176.232 #> Model cost at call 75 : 176.232 #> Model cost at call 76 : 176.232 #> Model cost at call 78 : 175.3914 #> Model cost at call 79 : 175.3914 #> Model cost at call 81 : 175.3913 #> Model cost at call 83 : 174.6257 #> Model cost at call 84 : 174.6257 #> Model cost at call 89 : 174.1476 #> Model cost at call 92 : 174.1476 #> Model cost at call 93 : 174.1476 #> Model cost at call 94 : 173.8512 #> Model cost at call 99 : 173.6987 #> Model cost at call 104 : 173.6813 #> Model cost at call 105 : 173.6813 #> Model cost at call 106 : 173.6813 #> Model cost at call 107 : 173.6813 #> Model cost at call 108 : 173.6813 #> Model cost at call 109 : 173.6802 #> Model cost at call 110 : 173.6802 #> Model cost at call 111 : 173.6802 #> Model cost at call 112 : 173.6802 #> Model cost at call 113 : 173.6802 #> Model cost at call 114 : 173.6799 #> Model cost at call 116 : 173.6799 #> Model cost at call 118 : 173.6799 #> Model cost at call 119 : 173.6799 #> Model cost at call 120 : 173.6799 #> Model cost at call 129 : 173.6799 #> Model cost at call 141 : 173.6799 #> Optimisation by method Port successfully terminated.fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode)#> Model cost at call 1 : 18365.33 #> Model cost at call 2 : 18365.33 #> Model cost at call 8 : 11666.4 #> Model cost at call 9 : 10992.15 #> Model cost at call 10 : 10992.13 #> Model cost at call 11 : 10991.95 #> Model cost at call 12 : 10991.17 #> Model cost at call 14 : 10990.65 #> Model cost at call 17 : 3940.801 #> Model cost at call 20 : 3940.8 #> Model cost at call 22 : 3940.798 #> Model cost at call 24 : 3241.199 #> Model cost at call 27 : 3241.198 #> Model cost at call 30 : 3241.192 #> Model cost at call 31 : 1518.749 #> Model cost at call 37 : 1518.747 #> Model cost at call 39 : 1091.836 #> Model cost at call 42 : 1091.835 #> Model cost at call 43 : 1091.835 #> Model cost at call 44 : 1091.804 #> Model cost at call 46 : 927.8538 #> Model cost at call 49 : 927.8529 #> Model cost at call 53 : 638.102 #> Model cost at call 56 : 638.1019 #> Model cost at call 58 : 638.1018 #> Model cost at call 61 : 560.4352 #> Model cost at call 62 : 560.435 #> Model cost at call 63 : 560.4327 #> Model cost at call 68 : 423.9629 #> Model cost at call 69 : 423.9629 #> Model cost at call 70 : 423.9629 #> Model cost at call 71 : 423.9628 #> Model cost at call 73 : 423.9628 #> Model cost at call 75 : 395.8015 #> Model cost at call 78 : 395.8013 #> Model cost at call 79 : 395.8013 #> Model cost at call 83 : 365.6975 #> Model cost at call 84 : 365.6975 #> Model cost at call 88 : 365.6975 #> Model cost at call 91 : 362.9843 #> Model cost at call 93 : 362.9843 #> Model cost at call 98 : 361.5506 #> Model cost at call 99 : 361.5506 #> Model cost at call 100 : 361.5505 #> Model cost at call 105 : 359.0492 #> Model cost at call 106 : 359.0492 #> Model cost at call 112 : 357.6574 #> Model cost at call 113 : 357.6574 #> Model cost at call 114 : 357.6574 #> Model cost at call 115 : 357.6574 #> Model cost at call 119 : 355.4518 #> Model cost at call 120 : 355.4518 #> Model cost at call 127 : 354.9045 #> Model cost at call 129 : 354.9045 #> Model cost at call 131 : 354.9045 #> Model cost at call 134 : 354.4168 #> Model cost at call 135 : 354.4168 #> Model cost at call 137 : 354.4167 #> Model cost at call 141 : 353.7901 #> Model cost at call 142 : 353.7901 #> Model cost at call 143 : 353.7899 #> Model cost at call 149 : 353.3233 #> Model cost at call 151 : 353.3233 #> Model cost at call 154 : 353.3233 #> Model cost at call 156 : 353.2939 #> Model cost at call 158 : 353.2938 #> Model cost at call 159 : 353.2938 #> Model cost at call 160 : 353.2938 #> Model cost at call 163 : 353.0571 #> Model cost at call 165 : 353.0571 #> Model cost at call 170 : 352.9457 #> Model cost at call 171 : 352.7458 #> Model cost at call 173 : 352.7457 #> Model cost at call 178 : 352.6377 #> Model cost at call 180 : 352.6377 #> Model cost at call 183 : 352.6377 #> Model cost at call 185 : 352.5377 #> Model cost at call 187 : 352.5377 #> Model cost at call 188 : 352.5377 #> Model cost at call 191 : 352.5377 #> Model cost at call 193 : 352.4479 #> Model cost at call 195 : 352.4479 #> Model cost at call 198 : 352.4479 #> Model cost at call 200 : 352.4021 #> Model cost at call 202 : 352.4021 #> Model cost at call 205 : 352.4021 #> Model cost at call 207 : 352.3465 #> Model cost at call 210 : 352.3465 #> Model cost at call 214 : 352.3031 #> Model cost at call 216 : 352.3031 #> Model cost at call 221 : 352.2632 #> Model cost at call 223 : 352.2632 #> Model cost at call 228 : 352.2367 #> Model cost at call 230 : 352.2367 #> Model cost at call 231 : 352.2367 #> Model cost at call 233 : 352.2367 #> Model cost at call 235 : 352.215 #> Model cost at call 238 : 352.215 #> Model cost at call 239 : 352.215 #> Model cost at call 242 : 352.207 #> Model cost at call 245 : 352.207 #> Model cost at call 250 : 352.2053 #> Model cost at call 251 : 352.2053 #> Model cost at call 253 : 352.2053 #> Model cost at call 256 : 352.2053 #> Model cost at call 258 : 352.2053 #> Model cost at call 259 : 352.2052 #> Model cost at call 260 : 352.2052 #> Model cost at call 263 : 352.2052 #> Model cost at call 271 : 352.2048 #> Model cost at call 273 : 352.2048 #> Model cost at call 274 : 352.2048 #> Model cost at call 281 : 352.2048 #> Model cost at call 282 : 352.2048 #> Model cost at call 286 : 352.2048 #> Model cost at call 289 : 352.2048 #> Model cost at call 294 : 352.2048 #> Model cost at call 296 : 352.2048 #> Model cost at call 300 : 352.2048 #> Model cost at call 307 : 352.2048 #> Model cost at call 325 : 352.2048 #> Model cost at call 331 : 352.2048 #> Model cost at call 333 : 352.2048 #> Optimisation by method Port successfully terminated.# Weighted fits, including IRLS SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"), m1 = mkinsub("SFO"), use_of_ff = "max")#>f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D)#> Model cost at call 1 : 15156.12 #> Model cost at call 2 : 15156.12 #> Model cost at call 6 : 8243.644 #> Model cost at call 12 : 6290.714 #> Model cost at call 13 : 6290.684 #> Model cost at call 15 : 6290.453 #> Model cost at call 18 : 1700.75 #> Model cost at call 20 : 1700.612 #> Model cost at call 24 : 1190.923 #> Model cost at call 26 : 1190.922 #> Model cost at call 29 : 1017.417 #> Model cost at call 31 : 1017.417 #> Model cost at call 33 : 1017.416 #> Model cost at call 34 : 644.0471 #> Model cost at call 36 : 644.0469 #> Model cost at call 38 : 644.0468 #> Model cost at call 39 : 590.5024 #> Model cost at call 41 : 590.5021 #> Model cost at call 43 : 590.5015 #> Model cost at call 44 : 543.2187 #> Model cost at call 45 : 543.2183 #> Model cost at call 46 : 543.2182 #> Model cost at call 50 : 391.348 #> Model cost at call 51 : 391.3479 #> Model cost at call 56 : 386.4789 #> Model cost at call 58 : 386.4789 #> Model cost at call 60 : 386.4779 #> Model cost at call 61 : 384.0686 #> Model cost at call 63 : 384.0686 #> Model cost at call 66 : 382.7812 #> Model cost at call 68 : 382.7812 #> Model cost at call 70 : 382.7812 #> Model cost at call 71 : 378.9272 #> Model cost at call 73 : 378.9272 #> Model cost at call 75 : 378.9272 #> Model cost at call 76 : 377.4846 #> Model cost at call 78 : 377.4846 #> Model cost at call 81 : 375.9738 #> Model cost at call 83 : 375.9738 #> Model cost at call 86 : 375.3387 #> Model cost at call 88 : 375.3387 #> Model cost at call 91 : 374.5774 #> Model cost at call 93 : 374.5774 #> Model cost at call 95 : 374.5774 #> Model cost at call 96 : 373.5447 #> Model cost at call 100 : 373.5446 #> Model cost at call 102 : 373.2643 #> Model cost at call 104 : 373.2643 #> Model cost at call 107 : 372.6799 #> Model cost at call 111 : 372.6798 #> Model cost at call 114 : 372.6325 #> Model cost at call 116 : 372.6325 #> Model cost at call 119 : 372.6159 #> Model cost at call 121 : 372.6159 #> Model cost at call 123 : 372.6159 #> Model cost at call 124 : 372.5845 #> Model cost at call 126 : 372.5845 #> Model cost at call 129 : 372.5375 #> Model cost at call 130 : 372.4771 #> Model cost at call 131 : 372.2008 #> Model cost at call 132 : 371.4923 #> Model cost at call 134 : 371.4923 #> Model cost at call 137 : 371.3022 #> Model cost at call 139 : 371.3022 #> Model cost at call 143 : 371.2271 #> Model cost at call 144 : 371.2271 #> Model cost at call 148 : 371.2202 #> Model cost at call 149 : 371.215 #> Model cost at call 152 : 371.215 #> Model cost at call 154 : 371.2136 #> Model cost at call 155 : 371.2136 #> Model cost at call 156 : 371.2136 #> Model cost at call 160 : 371.2134 #> Model cost at call 164 : 371.2134 #> Model cost at call 167 : 371.2134 #> Optimisation by method Port successfully terminated.summary(f.noweight)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:47 2016 #> Date of summary: Fri Nov 18 15:19:47 2016 #> #> 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 deSolve #> #> Fitted with method Port using 185 model solutions performed in 0.748 s #> #> Weighting: none #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.60000 1.61400 96.3300 102.9000 #> log_k_parent -2.31600 0.04187 -2.4010 -2.2310 #> log_k_m1 -5.24800 0.13610 -5.5230 -4.9720 #> f_parent_ilr_1 0.04096 0.06477 -0.0904 0.1723 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.0000 0.5178 -0.1701 -0.5489 #> log_k_parent 0.5178 1.0000 -0.3285 -0.5451 #> log_k_m1 -0.1701 -0.3285 1.0000 0.7466 #> f_parent_ilr_1 -0.5489 -0.5451 0.7466 1.0000 #> #> Residual standard error: 3.211 on 36 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 99.600000 61.720 2.024e-38 96.330000 1.029e+02 #> k_parent 0.098700 23.880 5.701e-24 0.090660 1.074e-01 #> k_m1 0.005261 7.349 5.758e-09 0.003992 6.933e-03 #> f_parent_to_m1 0.514500 22.490 4.374e-23 0.468100 5.606e-01 #> #> 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 9.960e+01 -1.385e-01 #> 0 parent 102.04 9.960e+01 2.442e+00 #> 1 parent 93.50 9.024e+01 3.262e+00 #> 1 parent 92.50 9.024e+01 2.262e+00 #> 3 parent 63.23 7.407e+01 -1.084e+01 #> 3 parent 68.99 7.407e+01 -5.083e+00 #> 7 parent 52.32 4.991e+01 2.408e+00 #> 7 parent 55.13 4.991e+01 5.218e+00 #> 14 parent 27.27 2.501e+01 2.257e+00 #> 14 parent 26.64 2.501e+01 1.627e+00 #> 21 parent 11.50 1.253e+01 -1.035e+00 #> 21 parent 11.64 1.253e+01 -8.946e-01 #> 35 parent 2.85 3.148e+00 -2.979e-01 #> 35 parent 2.91 3.148e+00 -2.379e-01 #> 50 parent 0.69 7.162e-01 -2.624e-02 #> 50 parent 0.63 7.162e-01 -8.624e-02 #> 75 parent 0.05 6.074e-02 -1.074e-02 #> 75 parent 0.06 6.074e-02 -7.381e-04 #> 100 parent NA 5.151e-03 NA #> 100 parent NA 5.151e-03 NA #> 120 parent NA 7.155e-04 NA #> 120 parent NA 7.155e-04 NA #> 0 m1 0.00 0.000e+00 0.000e+00 #> 0 m1 0.00 0.000e+00 0.000e+00 #> 1 m1 4.84 4.803e+00 3.704e-02 #> 1 m1 5.64 4.803e+00 8.370e-01 #> 3 m1 12.91 1.302e+01 -1.140e-01 #> 3 m1 12.96 1.302e+01 -6.400e-02 #> 7 m1 22.97 2.504e+01 -2.075e+00 #> 7 m1 24.47 2.504e+01 -5.748e-01 #> 14 m1 41.69 3.669e+01 5.000e+00 #> 14 m1 33.21 3.669e+01 -3.480e+00 #> 21 m1 44.37 4.165e+01 2.717e+00 #> 21 m1 46.44 4.165e+01 4.787e+00 #> 35 m1 41.22 4.331e+01 -2.093e+00 #> 35 m1 37.95 4.331e+01 -5.363e+00 #> 50 m1 41.19 4.122e+01 -2.831e-02 #> 50 m1 40.01 4.122e+01 -1.208e+00 #> 75 m1 40.09 3.645e+01 3.643e+00 #> 75 m1 33.85 3.645e+01 -2.597e+00 #> 100 m1 31.04 3.198e+01 -9.416e-01 #> 100 m1 33.13 3.198e+01 1.148e+00 #> 120 m1 25.15 2.879e+01 -3.640e+00 #> 120 m1 33.31 2.879e+01 4.520e+00f.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs")#> Model cost at call 1 : 15156.12 #> Model cost at call 2 : 15156.12 #> Model cost at call 6 : 8243.644 #> Model cost at call 12 : 6290.714 #> Model cost at call 13 : 6290.684 #> Model cost at call 15 : 6290.453 #> Model cost at call 18 : 1700.75 #> Model cost at call 20 : 1700.612 #> Model cost at call 24 : 1190.923 #> Model cost at call 26 : 1190.922 #> Model cost at call 29 : 1017.417 #> Model cost at call 31 : 1017.417 #> Model cost at call 33 : 1017.416 #> Model cost at call 34 : 644.0471 #> Model cost at call 36 : 644.0469 #> Model cost at call 38 : 644.0468 #> Model cost at call 39 : 590.5024 #> Model cost at call 41 : 590.5021 #> Model cost at call 43 : 590.5015 #> Model cost at call 44 : 543.2187 #> Model cost at call 45 : 543.2183 #> Model cost at call 46 : 543.2182 #> Model cost at call 50 : 391.348 #> Model cost at call 51 : 391.3479 #> Model cost at call 56 : 386.4789 #> Model cost at call 58 : 386.4789 #> Model cost at call 60 : 386.4779 #> Model cost at call 61 : 384.0686 #> Model cost at call 63 : 384.0686 #> Model cost at call 66 : 382.7812 #> Model cost at call 68 : 382.7812 #> Model cost at call 70 : 382.7812 #> Model cost at call 71 : 378.9272 #> Model cost at call 73 : 378.9272 #> Model cost at call 75 : 378.9272 #> Model cost at call 76 : 377.4846 #> Model cost at call 78 : 377.4846 #> Model cost at call 81 : 375.9738 #> Model cost at call 83 : 375.9738 #> Model cost at call 86 : 375.3387 #> Model cost at call 88 : 375.3387 #> Model cost at call 91 : 374.5774 #> Model cost at call 93 : 374.5774 #> Model cost at call 95 : 374.5774 #> Model cost at call 96 : 373.5447 #> Model cost at call 100 : 373.5446 #> Model cost at call 102 : 373.2643 #> Model cost at call 104 : 373.2643 #> Model cost at call 107 : 372.6799 #> Model cost at call 111 : 372.6798 #> Model cost at call 114 : 372.6325 #> Model cost at call 116 : 372.6325 #> Model cost at call 119 : 372.6159 #> Model cost at call 121 : 372.6159 #> Model cost at call 123 : 372.6159 #> Model cost at call 124 : 372.5845 #> Model cost at call 126 : 372.5845 #> Model cost at call 129 : 372.5375 #> Model cost at call 130 : 372.4771 #> Model cost at call 131 : 372.2008 #> Model cost at call 132 : 371.4923 #> Model cost at call 134 : 371.4923 #> Model cost at call 137 : 371.3022 #> Model cost at call 139 : 371.3022 #> Model cost at call 143 : 371.2271 #> Model cost at call 144 : 371.2271 #> Model cost at call 148 : 371.2202 #> Model cost at call 149 : 371.215 #> Model cost at call 152 : 371.215 #> Model cost at call 154 : 371.2136 #> Model cost at call 155 : 371.2136 #> Model cost at call 156 : 371.2136 #> Model cost at call 160 : 371.2134 #> Model cost at call 164 : 371.2134 #> Model cost at call 167 : 371.2134 #> IRLS based on variance estimates for each observed variable #> Initial variance estimates are: #> parent m1 #> 11.552581 7.421226 #> Model cost at call 186 : 40 #> Model cost at call 188 : 40 #> Model cost at call 194 : 39.99562 #> Model cost at call 195 : 39.99562 #> Model cost at call 201 : 39.9956 #> Model cost at call 203 : 39.99528 #> Model cost at call 205 : 39.99528 #> Model cost at call 207 : 39.99528 #> Model cost at call 209 : 39.99515 #> Model cost at call 211 : 39.99515 #> Model cost at call 214 : 39.99515 #> Model cost at call 215 : 39.99505 #> Model cost at call 217 : 39.99505 #> Model cost at call 219 : 39.99505 #> Model cost at call 220 : 39.99489 #> Model cost at call 222 : 39.99489 #> Model cost at call 224 : 39.99489 #> Model cost at call 225 : 39.99479 #> Model cost at call 227 : 39.99479 #> Model cost at call 231 : 39.99467 #> Model cost at call 234 : 39.99467 #> Model cost at call 235 : 39.99467 #> Model cost at call 236 : 39.99458 #> Model cost at call 238 : 39.99458 #> Model cost at call 239 : 39.99458 #> Model cost at call 241 : 39.99452 #> Model cost at call 242 : 39.99444 #> Model cost at call 243 : 39.99433 #> Model cost at call 245 : 39.99433 #> Model cost at call 248 : 39.99383 #> Model cost at call 250 : 39.99383 #> Model cost at call 251 : 39.99383 #> Model cost at call 252 : 39.99383 #> Model cost at call 253 : 39.9935 #> Model cost at call 254 : 39.99309 #> Model cost at call 256 : 39.99309 #> Model cost at call 261 : 39.99295 #> Model cost at call 264 : 39.99295 #> Model cost at call 267 : 39.99281 #> Model cost at call 272 : 39.99281 #> Model cost at call 273 : 39.99278 #> Model cost at call 276 : 39.99278 #> Model cost at call 278 : 39.99278 #> Model cost at call 279 : 39.99278 #> Model cost at call 281 : 39.99278 #> Model cost at call 283 : 39.99278 #> Model cost at call 286 : 39.99278 #> Model cost at call 289 : 39.99278 #> Model cost at call 290 : 39.99278 #> Iteration 1 yields variance estimates: #> parent m1 #> 11.573172 7.407968 #> Sum of squared differences to last variance estimates: 1.5e-05 #> Iteration 2 yields variance estimates: #> parent m1 #> 11.573405 7.407846 #> Sum of squared differences to last variance estimates: 1.7e-09 #> Optimisation by method Port successfully terminated.summary(f.irls)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:50 2016 #> Date of summary: Fri Nov 18 15:19:50 2016 #> #> 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 deSolve #> #> Fitted with method Port using 486 model solutions performed in 2.052 s #> #> Weighting: none then iterative reweighting method obs #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.67000 1.79200 96.04000 103.300 #> log_k_parent -2.31200 0.04560 -2.40400 -2.220 #> log_k_m1 -5.25100 0.12510 -5.50500 -4.998 #> f_parent_ilr_1 0.03785 0.06318 -0.09027 0.166 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.0000 0.5083 -0.1979 -0.6148 #> log_k_parent 0.5083 1.0000 -0.3894 -0.6062 #> log_k_m1 -0.1979 -0.3894 1.0000 0.7417 #> f_parent_ilr_1 -0.6148 -0.6062 0.7417 1.0000 #> #> Residual standard error: 1.054 on 36 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 99.67000 55.630 8.183e-37 96.040000 1.033e+02 #> k_parent 0.09906 21.930 1.016e-22 0.090310 1.087e-01 #> k_m1 0.00524 7.996 8.487e-10 0.004066 6.753e-03 #> f_parent_to_m1 0.51340 23.000 2.039e-23 0.468100 5.584e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.399 4 15 #> parent 6.466 2 7 #> m1 4.679 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5134 #> parent_sink 0.4866 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 6.997 23.24 #> m1 132.282 439.43 #> #> Data: #> time variable observed predicted residual err #> 0 parent 99.46 9.967e+01 -2.122e-01 3.402 #> 0 parent 102.04 9.967e+01 2.368e+00 3.402 #> 1 parent 93.50 9.027e+01 3.228e+00 3.402 #> 1 parent 92.50 9.027e+01 2.228e+00 3.402 #> 3 parent 63.23 7.405e+01 -1.082e+01 3.402 #> 3 parent 68.99 7.405e+01 -5.056e+00 3.402 #> 7 parent 52.32 4.982e+01 2.499e+00 3.402 #> 7 parent 55.13 4.982e+01 5.309e+00 3.402 #> 14 parent 27.27 2.490e+01 2.367e+00 3.402 #> 14 parent 26.64 2.490e+01 1.737e+00 3.402 #> 21 parent 11.50 1.245e+01 -9.477e-01 3.402 #> 21 parent 11.64 1.245e+01 -8.077e-01 3.402 #> 35 parent 2.85 3.110e+00 -2.600e-01 3.402 #> 35 parent 2.91 3.110e+00 -2.000e-01 3.402 #> 50 parent 0.69 7.037e-01 -1.375e-02 3.402 #> 50 parent 0.63 7.037e-01 -7.375e-02 3.402 #> 75 parent 0.05 5.913e-02 -9.134e-03 3.402 #> 75 parent 0.06 5.913e-02 8.661e-04 3.402 #> 100 parent NA 4.969e-03 NA 3.402 #> 100 parent NA 4.969e-03 NA 3.402 #> 120 parent NA 6.852e-04 NA 3.402 #> 120 parent NA 6.852e-04 NA 3.402 #> 0 m1 0.00 0.000e+00 0.000e+00 2.722 #> 0 m1 0.00 0.000e+00 0.000e+00 2.722 #> 1 m1 4.84 4.813e+00 2.672e-02 2.722 #> 1 m1 5.64 4.813e+00 8.267e-01 2.722 #> 3 m1 12.91 1.305e+01 -1.378e-01 2.722 #> 3 m1 12.96 1.305e+01 -8.779e-02 2.722 #> 7 m1 22.97 2.508e+01 -2.106e+00 2.722 #> 7 m1 24.47 2.508e+01 -6.061e-01 2.722 #> 14 m1 41.69 3.671e+01 4.983e+00 2.722 #> 14 m1 33.21 3.671e+01 -3.497e+00 2.722 #> 21 m1 44.37 4.165e+01 2.719e+00 2.722 #> 21 m1 46.44 4.165e+01 4.789e+00 2.722 #> 35 m1 41.22 4.329e+01 -2.069e+00 2.722 #> 35 m1 37.95 4.329e+01 -5.339e+00 2.722 #> 50 m1 41.19 4.119e+01 -3.388e-03 2.722 #> 50 m1 40.01 4.119e+01 -1.183e+00 2.722 #> 75 m1 40.09 3.644e+01 3.652e+00 2.722 #> 75 m1 33.85 3.644e+01 -2.588e+00 2.722 #> 100 m1 31.04 3.199e+01 -9.497e-01 2.722 #> 100 m1 33.13 3.199e+01 1.140e+00 2.722 #> 120 m1 25.15 2.881e+01 -3.659e+00 2.722 #> 120 m1 33.31 2.881e+01 4.501e+00 2.722f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean")#> Model cost at call 1 : 19.80132 #> Model cost at call 2 : 19.80132 #> Model cost at call 6 : 10.68776 #> Model cost at call 12 : 7.14353 #> Model cost at call 13 : 7.143529 #> Model cost at call 15 : 7.143511 #> Model cost at call 18 : 2.189024 #> Model cost at call 20 : 2.189019 #> Model cost at call 23 : 1.587262 #> Model cost at call 25 : 1.587261 #> Model cost at call 26 : 1.58726 #> Model cost at call 28 : 1.036794 #> Model cost at call 29 : 1.036794 #> Model cost at call 30 : 1.036793 #> Model cost at call 34 : 0.4939937 #> Model cost at call 35 : 0.4939937 #> Model cost at call 38 : 0.4939936 #> Model cost at call 39 : 0.4018506 #> Model cost at call 43 : 0.4018505 #> Model cost at call 45 : 0.3797853 #> Model cost at call 51 : 0.3669779 #> Model cost at call 55 : 0.3669778 #> Model cost at call 56 : 0.3585654 #> Model cost at call 57 : 0.3533252 #> Model cost at call 62 : 0.3502505 #> Model cost at call 64 : 0.3502505 #> Model cost at call 66 : 0.3502505 #> Model cost at call 67 : 0.3501535 #> Model cost at call 72 : 0.3501187 #> Model cost at call 74 : 0.3501187 #> Model cost at call 75 : 0.3501187 #> Model cost at call 77 : 0.3500378 #> Model cost at call 79 : 0.3500378 #> Model cost at call 83 : 0.349831 #> Model cost at call 88 : 0.3494286 #> Model cost at call 93 : 0.3488101 #> Model cost at call 98 : 0.3481444 #> Model cost at call 103 : 0.3478528 #> Model cost at call 108 : 0.3478092 #> Model cost at call 109 : 0.3478092 #> Model cost at call 113 : 0.347807 #> Model cost at call 116 : 0.347807 #> Model cost at call 117 : 0.347807 #> Model cost at call 119 : 0.347807 #> Model cost at call 120 : 0.347807 #> Model cost at call 125 : 0.347807 #> Model cost at call 126 : 0.347807 #> Model cost at call 128 : 0.347807 #> Model cost at call 137 : 0.347807 #> Model cost at call 148 : 0.347807 #> Model cost at call 152 : 0.347807 #> Model cost at call 154 : 0.347807 #> Optimisation by method Port successfully terminated.summary(f.w.mean)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:50 2016 #> Date of summary: Fri Nov 18 15:19:50 2016 #> #> 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 deSolve #> #> Fitted with method Port using 155 model solutions performed in 0.636 s #> #> Weighting: mean #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.7300 1.93200 95.81000 103.6000 #> log_k_parent -2.3090 0.04837 -2.40700 -2.2110 #> log_k_m1 -5.2550 0.12070 -5.49900 -5.0100 #> f_parent_ilr_1 0.0354 0.06344 -0.09327 0.1641 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.0000 0.5004 -0.2143 -0.6514 #> log_k_parent 0.5004 1.0000 -0.4282 -0.6383 #> log_k_m1 -0.2143 -0.4282 1.0000 0.7390 #> f_parent_ilr_1 -0.6514 -0.6383 0.7390 1.0000 #> #> Residual standard error: 0.09829 on 36 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 99.730000 51.630 1.166e-35 95.81000 1.036e+02 #> k_parent 0.099360 20.670 7.304e-22 0.09007 1.096e-01 #> k_m1 0.005224 8.287 3.649e-10 0.00409 6.672e-03 #> f_parent_to_m1 0.512500 22.860 2.497e-23 0.46710 5.578e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.401 4 15 #> parent 6.473 2 7 #> m1 4.671 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5125 #> parent_sink 0.4875 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 6.976 23.18 #> m1 132.696 440.81 #> #> Data: #> time variable observed predicted residual #> 0 parent 99.46 99.730570 -0.270570 #> 0 parent 102.04 99.730570 2.309430 #> 1 parent 93.50 90.298055 3.201945 #> 1 parent 92.50 90.298055 2.201945 #> 3 parent 63.23 74.025028 -10.795028 #> 3 parent 68.99 74.025028 -5.035028 #> 7 parent 52.32 49.748382 2.571618 #> 7 parent 55.13 49.748382 5.381618 #> 14 parent 27.27 24.815876 2.454124 #> 14 parent 26.64 24.815876 1.824124 #> 21 parent 11.50 12.378849 -0.878849 #> 21 parent 11.64 12.378849 -0.738849 #> 35 parent 2.85 3.080219 -0.230219 #> 35 parent 2.91 3.080219 -0.170219 #> 50 parent 0.69 0.693958 -0.003958 #> 50 parent 0.63 0.693958 -0.063958 #> 75 parent 0.05 0.057888 -0.007888 #> 75 parent 0.06 0.057888 0.002112 #> 100 parent NA 0.004829 NA #> 100 parent NA 0.004829 NA #> 120 parent NA 0.000662 NA #> 120 parent NA 0.000662 NA #> 0 m1 0.00 0.000000 0.000000 #> 0 m1 0.00 0.000000 0.000000 #> 1 m1 4.84 4.821488 0.018512 #> 1 m1 5.64 4.821488 0.818512 #> 3 m1 12.91 13.066692 -0.156692 #> 3 m1 12.96 13.066692 -0.106692 #> 7 m1 22.97 25.101058 -2.131058 #> 7 m1 24.47 25.101058 -0.631058 #> 14 m1 41.69 36.720923 4.969077 #> 14 m1 33.21 36.720923 -3.510923 #> 21 m1 44.37 41.648353 2.721647 #> 21 m1 46.44 41.648353 4.791647 #> 35 m1 41.22 43.269225 -2.049225 #> 35 m1 37.95 43.269225 -5.319225 #> 50 m1 41.19 41.173639 0.016361 #> 50 m1 40.01 41.173639 -1.163639 #> 75 m1 40.09 36.431224 3.658776 #> 75 m1 33.85 36.431224 -2.581224 #> 100 m1 31.04 31.996124 -0.956124 #> 100 m1 33.13 31.996124 1.133876 #> 120 m1 25.15 28.824128 -3.674128 #> 120 m1 33.31 28.824128 4.485872f.w.value <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value")#> Model cost at call 1 : 11.21571 #> Model cost at call 2 : 11.21571 #> Model cost at call 3 : 11.21571 #> Model cost at call 8 : 11.12803 #> Model cost at call 10 : 11.128 #> Model cost at call 13 : 10.88016 #> Model cost at call 15 : 10.88016 #> Model cost at call 18 : 10.58819 #> Model cost at call 20 : 10.58819 #> Model cost at call 23 : 9.71699 #> Model cost at call 24 : 7.794026 #> Model cost at call 26 : 7.794026 #> Model cost at call 31 : 6.89734 #> Model cost at call 33 : 6.897337 #> Model cost at call 36 : 5.2239 #> Model cost at call 37 : 3.357735 #> Model cost at call 41 : 3.357733 #> Model cost at call 44 : 2.982323 #> Model cost at call 46 : 2.982322 #> Model cost at call 49 : 2.703946 #> Model cost at call 50 : 2.080395 #> Model cost at call 55 : 0.5307591 #> Model cost at call 56 : 0.5307591 #> Model cost at call 57 : 0.5307591 #> Model cost at call 59 : 0.5307584 #> Model cost at call 60 : 0.3240066 #> Model cost at call 61 : 0.3240066 #> Model cost at call 64 : 0.3240066 #> Model cost at call 65 : 0.2601108 #> Model cost at call 70 : 0.2414055 #> Model cost at call 74 : 0.2414055 #> Model cost at call 75 : 0.2404251 #> Model cost at call 80 : 0.2404087 #> Model cost at call 82 : 0.2404087 #> Model cost at call 85 : 0.2404054 #> Model cost at call 88 : 0.2404054 #> Model cost at call 92 : 0.2403931 #> Model cost at call 93 : 0.2403784 #> Model cost at call 98 : 0.2403784 #> Model cost at call 99 : 0.2403322 #> Model cost at call 104 : 0.2402188 #> Model cost at call 109 : 0.2400275 #> Model cost at call 114 : 0.239844 #> Model cost at call 119 : 0.2397153 #> Model cost at call 120 : 0.2397153 #> Model cost at call 124 : 0.2396978 #> Model cost at call 126 : 0.2396978 #> Model cost at call 130 : 0.239697 #> Model cost at call 131 : 0.2396963 #> Model cost at call 133 : 0.2396963 #> Model cost at call 138 : 0.2396962 #> Model cost at call 139 : 0.2396962 #> Model cost at call 141 : 0.2396962 #> Model cost at call 144 : 0.2396962 #> Model cost at call 147 : 0.2396962 #> Model cost at call 156 : 0.2396962 #> Model cost at call 167 : 0.2396962 #> Model cost at call 169 : 0.2396962 #> Optimisation by method Port successfully terminated.summary(f.w.value)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:51 2016 #> Date of summary: Fri Nov 18 15:19:51 2016 #> #> 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 deSolve #> #> Fitted with method Port using 174 model solutions performed in 0.789 s #> #> Weighting: manual #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.6600 2.712000 94.14000 105.2000 #> log_k_parent -2.2980 0.008118 -2.31500 -2.2820 #> log_k_m1 -5.2410 0.096690 -5.43800 -5.0450 #> f_parent_ilr_1 0.0231 0.057990 -0.09474 0.1409 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.00000 0.6844 -0.08687 -0.7564 #> log_k_parent 0.68435 1.0000 -0.12694 -0.5812 #> log_k_m1 -0.08687 -0.1269 1.00000 0.5195 #> f_parent_ilr_1 -0.75644 -0.5812 0.51951 1.0000 #> #> Residual standard error: 0.08396 on 34 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 99.660000 36.75 2.957e-29 94.14000 1.052e+02 #> k_parent 0.100400 123.20 5.927e-47 0.09878 1.021e-01 #> k_m1 0.005295 10.34 2.447e-12 0.00435 6.444e-03 #> f_parent_to_m1 0.508200 24.79 1.184e-23 0.46660 5.497e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.461 4 15 #> parent 6.520 2 7 #> m1 4.744 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5082 #> parent_sink 0.4918 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 6.902 22.93 #> m1 130.916 434.89 #> #> Data: #> time variable observed predicted residual err #> 0 parent 99.46 99.65571 -0.195714 99.46 #> 0 parent 102.04 99.65571 2.384286 102.04 #> 1 parent 93.50 90.13383 3.366170 93.50 #> 1 parent 92.50 90.13383 2.366170 92.50 #> 3 parent 63.23 73.73252 -10.502518 63.23 #> 3 parent 68.99 73.73252 -4.742518 68.99 #> 7 parent 52.32 49.34027 2.979728 52.32 #> 7 parent 55.13 49.34027 5.789728 55.13 #> 14 parent 27.27 24.42873 2.841271 27.27 #> 14 parent 26.64 24.42873 2.211271 26.64 #> 21 parent 11.50 12.09484 -0.594842 11.50 #> 21 parent 11.64 12.09484 -0.454842 11.64 #> 35 parent 2.85 2.96482 -0.114824 2.85 #> 35 parent 2.91 2.96482 -0.054824 2.91 #> 50 parent 0.69 0.65733 0.032670 0.69 #> 50 parent 0.63 0.65733 -0.027330 0.63 #> 75 parent 0.05 0.05339 -0.003386 0.05 #> 75 parent 0.06 0.05339 0.006614 0.06 #> 1 m1 4.84 4.82570 0.014301 4.84 #> 1 m1 5.64 4.82570 0.814301 5.64 #> 3 m1 12.91 13.06402 -0.154020 12.91 #> 3 m1 12.96 13.06402 -0.104020 12.96 #> 7 m1 22.97 25.04656 -2.076564 22.97 #> 7 m1 24.47 25.04656 -0.576564 24.47 #> 14 m1 41.69 36.53601 5.153988 41.69 #> 14 m1 33.21 36.53601 -3.326012 33.21 #> 21 m1 44.37 41.34639 3.023609 44.37 #> 21 m1 46.44 41.34639 5.093609 46.44 #> 35 m1 41.22 42.82669 -1.606690 41.22 #> 35 m1 37.95 42.82669 -4.876690 37.95 #> 50 m1 41.19 40.67342 0.516578 41.19 #> 50 m1 40.01 40.67342 -0.663422 40.01 #> 75 m1 40.09 35.91105 4.178947 40.09 #> 75 m1 33.85 35.91105 -2.061053 33.85 #> 100 m1 31.04 31.48161 -0.441612 31.04 #> 100 m1 33.13 31.48161 1.648388 33.13 #> 120 m1 25.15 28.32018 -3.170181 25.15 #> 120 m1 33.31 28.32018 4.989819 33.31# Manual weighting dw <- FOCUS_2006_D errors <- c(parent = 2, m1 = 1) dw$err.man <- errors[FOCUS_2006_D$name] f.w.man <- mkinfit(SFO_SFO.ff, dw, err = "err.man")#> Model cost at call 1 : 3949.676 #> Model cost at call 2 : 3949.676 #> Model cost at call 5 : 3949.676 #> Model cost at call 6 : 2252.859 #> Model cost at call 8 : 2252.858 #> Model cost at call 9 : 2252.826 #> Model cost at call 13 : 1567.343 #> Model cost at call 14 : 1567.342 #> Model cost at call 15 : 1567.333 #> Model cost at call 18 : 1041.524 #> Model cost at call 19 : 1041.522 #> Model cost at call 24 : 840.4649 #> Model cost at call 26 : 840.4646 #> Model cost at call 29 : 782.303 #> Model cost at call 31 : 782.3028 #> Model cost at call 34 : 664.539 #> Model cost at call 36 : 664.5389 #> Model cost at call 40 : 615.7908 #> Model cost at call 42 : 615.7907 #> Model cost at call 45 : 569.5971 #> Model cost at call 47 : 569.597 #> Model cost at call 50 : 517.3175 #> Model cost at call 52 : 517.3173 #> Model cost at call 56 : 464.8158 #> Model cost at call 58 : 464.8157 #> Model cost at call 62 : 433.0031 #> Model cost at call 64 : 433.003 #> Model cost at call 67 : 423.7407 #> Model cost at call 69 : 423.7406 #> Model cost at call 70 : 423.7392 #> Model cost at call 72 : 346.2781 #> Model cost at call 74 : 346.278 #> Model cost at call 75 : 346.2779 #> Model cost at call 78 : 334.5399 #> Model cost at call 80 : 334.5398 #> Model cost at call 83 : 324.139 #> Model cost at call 85 : 324.1389 #> Model cost at call 88 : 319.7514 #> Model cost at call 90 : 319.7514 #> Model cost at call 94 : 300.9426 #> Model cost at call 96 : 300.9425 #> Model cost at call 100 : 295.8803 #> Model cost at call 102 : 295.8803 #> Model cost at call 105 : 290.3288 #> Model cost at call 107 : 290.3287 #> Model cost at call 111 : 284.3257 #> Model cost at call 113 : 284.3257 #> Model cost at call 116 : 282.3972 #> Model cost at call 118 : 282.3972 #> Model cost at call 122 : 273.7385 #> Model cost at call 124 : 273.7385 #> Model cost at call 128 : 271.8379 #> Model cost at call 130 : 271.8379 #> Model cost at call 133 : 270.064 #> Model cost at call 135 : 270.064 #> Model cost at call 138 : 268.0107 #> Model cost at call 140 : 268.0107 #> Model cost at call 144 : 265.6194 #> Model cost at call 146 : 265.6194 #> Model cost at call 148 : 265.6194 #> Model cost at call 149 : 263.4825 #> Model cost at call 151 : 263.4825 #> Model cost at call 153 : 263.4824 #> Model cost at call 154 : 262.0988 #> Model cost at call 156 : 262.0988 #> Model cost at call 160 : 260.7078 #> Model cost at call 162 : 260.7078 #> Model cost at call 165 : 259.9453 #> Model cost at call 167 : 259.9453 #> Model cost at call 170 : 258.9623 #> Model cost at call 172 : 258.9623 #> Model cost at call 174 : 258.962 #> Model cost at call 176 : 258.0119 #> Model cost at call 178 : 258.0119 #> Model cost at call 180 : 258.0119 #> Model cost at call 181 : 257.8698 #> Model cost at call 183 : 257.8698 #> Model cost at call 186 : 256.8608 #> Model cost at call 188 : 256.8608 #> Model cost at call 190 : 256.8608 #> Model cost at call 191 : 256.2306 #> Model cost at call 193 : 256.2306 #> Model cost at call 195 : 256.2305 #> Model cost at call 196 : 255.7119 #> Model cost at call 198 : 255.7118 #> Model cost at call 201 : 255.3323 #> Model cost at call 203 : 255.3323 #> Model cost at call 205 : 255.3323 #> Model cost at call 206 : 254.6653 #> Model cost at call 208 : 254.6653 #> Model cost at call 211 : 254.3984 #> Model cost at call 213 : 254.3984 #> Model cost at call 216 : 253.3199 #> Model cost at call 218 : 253.3199 #> Model cost at call 220 : 253.3198 #> Model cost at call 221 : 252.4845 #> Model cost at call 223 : 252.4845 #> Model cost at call 225 : 252.4845 #> Model cost at call 226 : 251.6917 #> Model cost at call 229 : 251.6917 #> Model cost at call 230 : 251.6917 #> Model cost at call 233 : 251.0189 #> Model cost at call 235 : 251.0189 #> Model cost at call 238 : 250.6912 #> Model cost at call 240 : 250.6912 #> Model cost at call 243 : 250.5546 #> Model cost at call 245 : 250.5546 #> Model cost at call 248 : 250.466 #> Model cost at call 249 : 250.3744 #> Model cost at call 250 : 249.9681 #> Model cost at call 251 : 249.2215 #> Model cost at call 260 : 248.919 #> Model cost at call 264 : 248.919 #> Model cost at call 265 : 248.8876 #> Model cost at call 267 : 248.8876 #> Model cost at call 270 : 248.8521 #> Model cost at call 271 : 248.8178 #> Model cost at call 272 : 248.6837 #> Model cost at call 273 : 248.5989 #> Model cost at call 276 : 248.5989 #> Model cost at call 278 : 248.5935 #> Model cost at call 280 : 248.5935 #> Model cost at call 282 : 248.5935 #> Model cost at call 283 : 248.5902 #> Model cost at call 284 : 248.5902 #> Model cost at call 289 : 248.5902 #> Model cost at call 298 : 248.5902 #> Model cost at call 309 : 248.5902 #> Model cost at call 311 : 248.5902 #> Optimisation by method Port successfully terminated.summary(f.w.man)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:53 2016 #> Date of summary: Fri Nov 18 15:19:53 2016 #> #> 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 deSolve #> #> Fitted with method Port using 316 model solutions performed in 1.337 s #> #> Weighting: manual #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.49000 1.33200 96.7800 102.2000 #> log_k_parent -2.32100 0.03550 -2.3930 -2.2490 #> log_k_m1 -5.24100 0.21280 -5.6730 -4.8100 #> f_parent_ilr_1 0.04571 0.08966 -0.1361 0.2275 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.00000 0.5312 -0.09455 -0.3351 #> log_k_parent 0.53123 1.0000 -0.17800 -0.3360 #> log_k_m1 -0.09455 -0.1780 1.00000 0.7616 #> f_parent_ilr_1 -0.33513 -0.3360 0.76156 1.0000 #> #> Residual standard error: 2.628 on 36 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 99.490000 74.69 2.222e-41 96.780000 1.022e+02 #> k_parent 0.098140 28.17 2.012e-26 0.091320 1.055e-01 #> k_m1 0.005292 4.70 1.873e-05 0.003437 8.148e-03 #> f_parent_to_m1 0.516200 16.30 1.686e-18 0.452000 5.798e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.400 4 15 #> parent 6.454 2 7 #> m1 4.708 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5162 #> parent_sink 0.4838 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 7.063 23.46 #> m1 130.971 435.08 #> #> Data: #> time variable observed predicted residual err #> 0 parent 99.46 99.485977 -0.025977 1 #> 0 parent 102.04 99.485977 2.554023 1 #> 1 parent 93.50 90.186118 3.313882 1 #> 1 parent 92.50 90.186118 2.313882 1 #> 3 parent 63.23 74.113162 -10.883162 1 #> 3 parent 68.99 74.113162 -5.123162 1 #> 7 parent 52.32 50.050295 2.269705 1 #> 7 parent 55.13 50.050295 5.079705 1 #> 14 parent 27.27 25.179750 2.090250 1 #> 14 parent 26.64 25.179750 1.460250 1 #> 21 parent 11.50 12.667654 -1.167654 1 #> 21 parent 11.64 12.667654 -1.027654 1 #> 35 parent 2.85 3.206164 -0.356164 1 #> 35 parent 2.91 3.206164 -0.296164 1 #> 50 parent 0.69 0.735619 -0.045619 1 #> 50 parent 0.63 0.735619 -0.105619 1 #> 75 parent 0.05 0.063256 -0.013256 1 #> 75 parent 0.06 0.063256 -0.003256 1 #> 100 parent NA 0.005439 NA 1 #> 100 parent NA 0.005439 NA 1 #> 120 parent NA 0.000764 NA 1 #> 120 parent NA 0.000764 NA 1 #> 0 m1 0.00 0.000000 0.000000 2 #> 0 m1 0.00 0.000000 0.000000 2 #> 1 m1 4.84 4.787287 0.052713 2 #> 1 m1 5.64 4.787287 0.852713 2 #> 3 m1 12.91 12.987848 -0.077848 2 #> 3 m1 12.96 12.987848 -0.027848 2 #> 7 m1 22.97 24.996945 -2.026945 2 #> 7 m1 24.47 24.996945 -0.526945 2 #> 14 m1 41.69 36.663527 5.026473 2 #> 14 m1 33.21 36.663527 -3.453527 2 #> 21 m1 44.37 41.656812 2.713188 2 #> 21 m1 46.44 41.656812 4.783188 2 #> 35 m1 41.22 43.350311 -2.130311 2 #> 35 m1 37.95 43.350311 -5.400311 2 #> 50 m1 41.19 41.256364 -0.066364 2 #> 50 m1 40.01 41.256364 -1.246364 2 #> 75 m1 40.09 36.460566 3.629434 2 #> 75 m1 33.85 36.460566 -2.610566 2 #> 100 m1 31.04 31.969288 -0.929288 2 #> 100 m1 33.13 31.969288 1.160712 2 #> 120 m1 25.15 28.760615 -3.610615 2 #> 120 m1 33.31 28.760615 4.549385 2f.w.man.irls <- mkinfit(SFO_SFO.ff, dw, err = "err.man", reweight.method = "obs")#> Model cost at call 1 : 3949.676 #> Model cost at call 2 : 3949.676 #> Model cost at call 5 : 3949.676 #> Model cost at call 6 : 2252.859 #> Model cost at call 8 : 2252.858 #> Model cost at call 9 : 2252.826 #> Model cost at call 13 : 1567.343 #> Model cost at call 14 : 1567.342 #> Model cost at call 15 : 1567.333 #> Model cost at call 18 : 1041.524 #> Model cost at call 19 : 1041.522 #> Model cost at call 24 : 840.4649 #> Model cost at call 26 : 840.4646 #> Model cost at call 29 : 782.303 #> Model cost at call 31 : 782.3028 #> Model cost at call 34 : 664.539 #> Model cost at call 36 : 664.5389 #> Model cost at call 40 : 615.7908 #> Model cost at call 42 : 615.7907 #> Model cost at call 45 : 569.5971 #> Model cost at call 47 : 569.597 #> Model cost at call 50 : 517.3175 #> Model cost at call 52 : 517.3173 #> Model cost at call 56 : 464.8158 #> Model cost at call 58 : 464.8157 #> Model cost at call 62 : 433.0031 #> Model cost at call 64 : 433.003 #> Model cost at call 67 : 423.7407 #> Model cost at call 69 : 423.7406 #> Model cost at call 70 : 423.7392 #> Model cost at call 72 : 346.2781 #> Model cost at call 74 : 346.278 #> Model cost at call 75 : 346.2779 #> Model cost at call 78 : 334.5399 #> Model cost at call 80 : 334.5398 #> Model cost at call 83 : 324.139 #> Model cost at call 85 : 324.1389 #> Model cost at call 88 : 319.7514 #> Model cost at call 90 : 319.7514 #> Model cost at call 94 : 300.9426 #> Model cost at call 96 : 300.9425 #> Model cost at call 100 : 295.8803 #> Model cost at call 102 : 295.8803 #> Model cost at call 105 : 290.3288 #> Model cost at call 107 : 290.3287 #> Model cost at call 111 : 284.3257 #> Model cost at call 113 : 284.3257 #> Model cost at call 116 : 282.3972 #> Model cost at call 118 : 282.3972 #> Model cost at call 122 : 273.7385 #> Model cost at call 124 : 273.7385 #> Model cost at call 128 : 271.8379 #> Model cost at call 130 : 271.8379 #> Model cost at call 133 : 270.064 #> Model cost at call 135 : 270.064 #> Model cost at call 138 : 268.0107 #> Model cost at call 140 : 268.0107 #> Model cost at call 144 : 265.6194 #> Model cost at call 146 : 265.6194 #> Model cost at call 148 : 265.6194 #> Model cost at call 149 : 263.4825 #> Model cost at call 151 : 263.4825 #> Model cost at call 153 : 263.4824 #> Model cost at call 154 : 262.0988 #> Model cost at call 156 : 262.0988 #> Model cost at call 160 : 260.7078 #> Model cost at call 162 : 260.7078 #> Model cost at call 165 : 259.9453 #> Model cost at call 167 : 259.9453 #> Model cost at call 170 : 258.9623 #> Model cost at call 172 : 258.9623 #> Model cost at call 174 : 258.962 #> Model cost at call 176 : 258.0119 #> Model cost at call 178 : 258.0119 #> Model cost at call 180 : 258.0119 #> Model cost at call 181 : 257.8698 #> Model cost at call 183 : 257.8698 #> Model cost at call 186 : 256.8608 #> Model cost at call 188 : 256.8608 #> Model cost at call 190 : 256.8608 #> Model cost at call 191 : 256.2306 #> Model cost at call 193 : 256.2306 #> Model cost at call 195 : 256.2305 #> Model cost at call 196 : 255.7119 #> Model cost at call 198 : 255.7118 #> Model cost at call 201 : 255.3323 #> Model cost at call 203 : 255.3323 #> Model cost at call 205 : 255.3323 #> Model cost at call 206 : 254.6653 #> Model cost at call 208 : 254.6653 #> Model cost at call 211 : 254.3984 #> Model cost at call 213 : 254.3984 #> Model cost at call 216 : 253.3199 #> Model cost at call 218 : 253.3199 #> Model cost at call 220 : 253.3198 #> Model cost at call 221 : 252.4845 #> Model cost at call 223 : 252.4845 #> Model cost at call 225 : 252.4845 #> Model cost at call 226 : 251.6917 #> Model cost at call 229 : 251.6917 #> Model cost at call 230 : 251.6917 #> Model cost at call 233 : 251.0189 #> Model cost at call 235 : 251.0189 #> Model cost at call 238 : 250.6912 #> Model cost at call 240 : 250.6912 #> Model cost at call 243 : 250.5546 #> Model cost at call 245 : 250.5546 #> Model cost at call 248 : 250.466 #> Model cost at call 249 : 250.3744 #> Model cost at call 250 : 249.9681 #> Model cost at call 251 : 249.2215 #> Model cost at call 260 : 248.919 #> Model cost at call 264 : 248.919 #> Model cost at call 265 : 248.8876 #> Model cost at call 267 : 248.8876 #> Model cost at call 270 : 248.8521 #> Model cost at call 271 : 248.8178 #> Model cost at call 272 : 248.6837 #> Model cost at call 273 : 248.5989 #> Model cost at call 276 : 248.5989 #> Model cost at call 278 : 248.5935 #> Model cost at call 280 : 248.5935 #> Model cost at call 282 : 248.5935 #> Model cost at call 283 : 248.5902 #> Model cost at call 284 : 248.5902 #> Model cost at call 289 : 248.5902 #> Model cost at call 298 : 248.5902 #> Model cost at call 309 : 248.5902 #> Model cost at call 311 : 248.5902 #> IRLS based on variance estimates for each observed variable #> Initial variance estimates are: #> parent m1 #> 11.536305 7.443046 #> Model cost at call 317 : 40 #> Model cost at call 319 : 40 #> Model cost at call 324 : 39.98891 #> Model cost at call 325 : 39.9889 #> Model cost at call 327 : 39.98886 #> Model cost at call 331 : 39.98871 #> Model cost at call 333 : 39.97254 #> Model cost at call 336 : 39.97253 #> Model cost at call 338 : 39.96929 #> Model cost at call 340 : 39.96929 #> Model cost at call 344 : 39.96849 #> Model cost at call 346 : 39.96849 #> Model cost at call 348 : 39.96849 #> Model cost at call 349 : 39.96774 #> Model cost at call 351 : 39.96774 #> Model cost at call 353 : 39.96774 #> Model cost at call 354 : 39.96714 #> Model cost at call 356 : 39.96714 #> Model cost at call 359 : 39.96617 #> Model cost at call 361 : 39.96617 #> Model cost at call 364 : 39.96606 #> Model cost at call 366 : 39.96606 #> Model cost at call 369 : 39.96551 #> Model cost at call 371 : 39.96551 #> Model cost at call 372 : 39.96551 #> Model cost at call 375 : 39.96527 #> Model cost at call 378 : 39.96527 #> Model cost at call 379 : 39.96527 #> Model cost at call 380 : 39.96525 #> Model cost at call 382 : 39.96525 #> Model cost at call 385 : 39.9651 #> Model cost at call 387 : 39.9651 #> Model cost at call 388 : 39.9651 #> Model cost at call 390 : 39.96502 #> Model cost at call 393 : 39.96502 #> Model cost at call 396 : 39.96502 #> Model cost at call 397 : 39.96467 #> Model cost at call 398 : 39.96422 #> Model cost at call 399 : 39.9624 #> Model cost at call 400 : 39.95909 #> Model cost at call 402 : 39.95909 #> Model cost at call 405 : 39.9571 #> Model cost at call 407 : 39.95709 #> Model cost at call 413 : 39.95479 #> Model cost at call 414 : 39.95479 #> Model cost at call 415 : 39.95479 #> Model cost at call 417 : 39.95479 #> Model cost at call 419 : 39.95398 #> Model cost at call 422 : 39.95398 #> Model cost at call 424 : 39.95387 #> Model cost at call 429 : 39.95384 #> Model cost at call 432 : 39.95384 #> Model cost at call 435 : 39.95384 #> Model cost at call 437 : 39.95384 #> Model cost at call 438 : 39.95384 #> Model cost at call 446 : 39.95384 #> Model cost at call 455 : 39.95384 #> Model cost at call 469 : 39.95384 #> Model cost at call 473 : 39.95384 #> Iteration 1 yields variance estimates: #> parent m1 #> 11.572891 7.408116 #> Sum of squared differences to last variance estimates: 7e-05 #> Iteration 2 yields variance estimates: #> parent m1 #> 11.573402 7.407847 #> Sum of squared differences to last variance estimates: 8.1e-09 #> Optimisation by method Port successfully terminated.summary(f.w.man.irls)#> mkin version: 0.9.44.9000 #> R version: 3.3.2 #> Date of fit: Fri Nov 18 15:19:55 2016 #> Date of summary: Fri Nov 18 15:19:55 2016 #> #> 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 deSolve #> #> Fitted with method Port using 648 model solutions performed in 2.716 s #> #> Weighting: manual then iterative reweighting method obs #> #> 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 #> #> Optimised, transformed parameters with symmetric confidence intervals: #> Estimate Std. Error Lower Upper #> parent_0 99.67000 1.79200 96.04000 103.300 #> log_k_parent -2.31200 0.04560 -2.40400 -2.220 #> log_k_m1 -5.25100 0.12510 -5.50500 -4.998 #> f_parent_ilr_1 0.03785 0.06318 -0.09027 0.166 #> #> Parameter correlation: #> parent_0 log_k_parent log_k_m1 f_parent_ilr_1 #> parent_0 1.0000 0.5083 -0.1979 -0.6147 #> log_k_parent 0.5083 1.0000 -0.3894 -0.6062 #> log_k_m1 -0.1979 -0.3894 1.0000 0.7417 #> f_parent_ilr_1 -0.6147 -0.6062 0.7417 1.0000 #> #> Residual standard error: 1.054 on 36 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 99.67000 55.630 8.178e-37 96.040000 1.033e+02 #> k_parent 0.09906 21.930 1.015e-22 0.090310 1.087e-01 #> k_m1 0.00524 7.996 8.488e-10 0.004066 6.753e-03 #> f_parent_to_m1 0.51340 23.000 2.038e-23 0.468100 5.584e-01 #> #> Chi2 error levels in percent: #> err.min n.optim df #> All data 6.399 4 15 #> parent 6.466 2 7 #> m1 4.679 2 8 #> #> Resulting formation fractions: #> ff #> parent_m1 0.5134 #> parent_sink 0.4866 #> #> Estimated disappearance times: #> DT50 DT90 #> parent 6.997 23.24 #> m1 132.281 439.43 #> #> Data: #> time variable observed predicted residual err.ini err #> 0 parent 99.46 9.967e+01 -2.122e-01 1 3.402 #> 0 parent 102.04 9.967e+01 2.368e+00 1 3.402 #> 1 parent 93.50 9.027e+01 3.228e+00 1 3.402 #> 1 parent 92.50 9.027e+01 2.228e+00 1 3.402 #> 3 parent 63.23 7.405e+01 -1.082e+01 1 3.402 #> 3 parent 68.99 7.405e+01 -5.056e+00 1 3.402 #> 7 parent 52.32 4.982e+01 2.499e+00 1 3.402 #> 7 parent 55.13 4.982e+01 5.309e+00 1 3.402 #> 14 parent 27.27 2.490e+01 2.367e+00 1 3.402 #> 14 parent 26.64 2.490e+01 1.737e+00 1 3.402 #> 21 parent 11.50 1.245e+01 -9.477e-01 1 3.402 #> 21 parent 11.64 1.245e+01 -8.077e-01 1 3.402 #> 35 parent 2.85 3.110e+00 -2.600e-01 1 3.402 #> 35 parent 2.91 3.110e+00 -2.000e-01 1 3.402 #> 50 parent 0.69 7.037e-01 -1.375e-02 1 3.402 #> 50 parent 0.63 7.037e-01 -7.375e-02 1 3.402 #> 75 parent 0.05 5.913e-02 -9.134e-03 1 3.402 #> 75 parent 0.06 5.913e-02 8.659e-04 1 3.402 #> 100 parent NA 4.969e-03 NA 1 3.402 #> 100 parent NA 4.969e-03 NA 1 3.402 #> 120 parent NA 6.852e-04 NA 1 3.402 #> 120 parent NA 6.852e-04 NA 1 3.402 #> 0 m1 0.00 0.000e+00 0.000e+00 2 2.722 #> 0 m1 0.00 0.000e+00 0.000e+00 2 2.722 #> 1 m1 4.84 4.813e+00 2.672e-02 2 2.722 #> 1 m1 5.64 4.813e+00 8.267e-01 2 2.722 #> 3 m1 12.91 1.305e+01 -1.378e-01 2 2.722 #> 3 m1 12.96 1.305e+01 -8.778e-02 2 2.722 #> 7 m1 22.97 2.508e+01 -2.106e+00 2 2.722 #> 7 m1 24.47 2.508e+01 -6.061e-01 2 2.722 #> 14 m1 41.69 3.671e+01 4.983e+00 2 2.722 #> 14 m1 33.21 3.671e+01 -3.497e+00 2 2.722 #> 21 m1 44.37 4.165e+01 2.719e+00 2 2.722 #> 21 m1 46.44 4.165e+01 4.789e+00 2 2.722 #> 35 m1 41.22 4.329e+01 -2.069e+00 2 2.722 #> 35 m1 37.95 4.329e+01 -5.339e+00 2 2.722 #> 50 m1 41.19 4.119e+01 -3.394e-03 2 2.722 #> 50 m1 40.01 4.119e+01 -1.183e+00 2 2.722 #> 75 m1 40.09 3.644e+01 3.652e+00 2 2.722 #> 75 m1 33.85 3.644e+01 -2.588e+00 2 2.722 #> 100 m1 31.04 3.199e+01 -9.497e-01 2 2.722 #> 100 m1 33.13 3.199e+01 1.140e+00 2 2.722 #> 120 m1 25.15 2.881e+01 -3.659e+00 2 2.722 #> 120 m1 33.31 2.881e+01 4.501e+00 2 2.722