From af2e1540cdad2fd00bb6216a38a754ff748629ad Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 25 Oct 2019 02:10:08 +0200 Subject: Static documentation rebuilt by pkgdown --- docs/reference/mkinfit.html | 441 ++++++++++++++++++++++---------------------- 1 file changed, 216 insertions(+), 225 deletions(-) (limited to 'docs/reference/mkinfit.html') diff --git a/docs/reference/mkinfit.html b/docs/reference/mkinfit.html index e07d1f13..6c98bc38 100644 --- a/docs/reference/mkinfit.html +++ b/docs/reference/mkinfit.html @@ -8,11 +8,13 @@ Fit a kinetic model to data with one or more state variables — mkinfit • mkin + + @@ -32,21 +34,20 @@ - - + + + @@ -117,7 +118,6 @@ Per default, parameters in the kinetic models are internally transformed in News - @@ -139,135 +139,126 @@ Per default, parameters in the kinetic models are internally transformed in
- -

This function maximises the likelihood of the observed data using - the Port algorithm nlminb, and the specified initial or fixed - parameters and starting values. In each step of the optimsation, the kinetic - model is solved using the function mkinpredict. The parameters - of the selected error model are fitted simultaneously with the degradation - model parameters, as both of them are arguments of the likelihood function.

-

Per default, parameters in the kinetic models are internally transformed in - order to better satisfy the assumption of a normal distribution of their - estimators.

- +

This function maximises the likelihood of the observed data using the Port +algorithm nlminb, and the specified initial or fixed +parameters and starting values. In each step of the optimsation, the +kinetic model is solved using the function mkinpredict. The +parameters of the selected error model are fitted simultaneously with the +degradation model parameters, as both of them are arguments of the +likelihood function.

- 
mkinfit(mkinmod, observed,
-  parms.ini = "auto",
-  state.ini = "auto",
-  err.ini = "auto",
-  fixed_parms = NULL, fixed_initials = names(mkinmod$diffs)[-1],
-  from_max_mean = FALSE,
+    
mkinfit(mkinmod, observed, parms.ini = "auto", state.ini = "auto",
+  err.ini = "auto", fixed_parms = NULL,
+  fixed_initials = names(mkinmod$diffs)[-1], from_max_mean = FALSE,
   solution_type = c("auto", "analytical", "eigen", "deSolve"),
-  method.ode = "lsoda",
-  use_compiled = "auto",
+  method.ode = "lsoda", use_compiled = "auto",
   control = list(eval.max = 300, iter.max = 200),
-  transform_rates = TRUE,
-  transform_fractions = TRUE,
-  quiet = FALSE,
-  atol = 1e-8, rtol = 1e-10, n.outtimes = 100,
+  transform_rates = TRUE, transform_fractions = TRUE, quiet = FALSE,
+  atol = 1e-08, rtol = 1e-10, n.outtimes = 100,
   error_model = c("const", "obs", "tc"),
-  error_model_algorithm = c("auto", "d_3", "direct", "twostep", "threestep",
-    "fourstep", "IRLS", "OLS"),
-  reweight.tol = 1e-8, reweight.max.iter = 10,
-  trace_parms = FALSE, ...)

-    
+  error_model_algorithm = c("auto", "d_3", "direct", "twostep",
+  "threestep", "fourstep", "IRLS", "OLS"), reweight.tol = 1e-08,
+  reweight.max.iter = 10, trace_parms = FALSE, ...)
+

Arguments

- + - + - + 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.

- + - + - + - + - + - + - + - + @@ -275,92 +266,90 @@ Per default, parameters in the kinetic models are internally transformed in - + - + - + - + - + - + - + error model similar to the one described by Rocke and Lorenzato (1995) is + used for setting up the likelihood function. Note that this model + deviates from the model by Rocke and Lorenzato, as their model implies + that the errors follow a lognormal distribution for large values, not a + normal distribution as assumed by this method.

- + unweighted least squares, and then iterates optimization of the error + model parameters and subsequent optimization of the degradation model + using those error model parameters, until the error model parameters + converge.

- + @@ -372,50 +361,54 @@ Per default, parameters in the kinetic models are internally transformed in - +
mkinmod

A list of class mkinmod, containing the kinetic model to be - fitted to the data, or one of the shorthand names ("SFO", "FOMC", "DFOP", - "HS", "SFORB", "IORE"). If a shorthand name is given, a parent only degradation - model is generated for the variable with the highest value in - observed.

A list of class mkinmod, containing the kinetic +model to be fitted to the data, or one of the shorthand names ("SFO", +"FOMC", "DFOP", "HS", "SFORB", "IORE"). If a shorthand name is given, a +parent only degradation model is generated for the variable with the +highest value in observed.
observed

A dataframe with the observed data. The first column called "name" must - contain the name of the observed variable for each data point. The second - column must contain the times of observation, named "time". The third - column must be named "value" and contain the observed values. Zero values - in the "value" column will be removed, with a warning, in order to - avoid problems with fitting the two-component error model. This is not - expected to be a problem, because in general, values of zero are not - observed in degradation data, because there is a lower limit of detection.

A dataframe with the observed data. The first column called +"name" must contain the name of the observed variable for each data point. +The second column must contain the times of observation, named "time". +The third column must be named "value" and contain the observed values. +Zero values in the "value" column will be removed, with a warning, in +order to avoid problems with fitting the two-component error model. This +is not expected to be a problem, because in general, values of zero are +not observed in degradation data, because there is a lower limit of +detection.
parms.ini

A named vector of initial values for the parameters, including parameters - to be optimised and potentially also fixed parameters as indicated by - 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.

+

A named vector of initial values for the parameters, + including parameters to be optimised and potentially also fixed parameters + as indicated by 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.
state.ini

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 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.

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 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.
err.ini

A named vector of initial values for the error model parameters to be - optimised. If set to "auto", initial values are set to default values. - Otherwise, inital values for all error model parameters must be - given.

A named vector of initial values for the error model +parameters to be optimised. If set to "auto", initial values are set to +default values. Otherwise, inital values for all error model parameters +must be given.
fixed_parms

The names of parameters that should not be optimised but rather kept at the - values specified in parms.ini.

The names of parameters that should not be optimised but +rather kept at the values specified in parms.ini.
fixed_initials

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.

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.
from_max_mean

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.

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.
solution_type

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 - 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 "deSolve" if a compiler is present, and "eigen" if no - compiler is present and the model can be expressed using eigenvalues and - eigenvectors. This argument is passed on to the helper function - mkinpredict.

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 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 "deSolve" if a compiler is present, +and "eigen" if no compiler is present and the model can be expressed using +eigenvalues and eigenvectors. This argument is passed on to the helper +function mkinpredict.
method.ode

The solution method passed via mkinpredict to - ode in case the solution type is "deSolve". The default - "lsoda" is performant, but sometimes fails to converge.

The solution method passed via mkinpredict +to ode in case the solution type is "deSolve". The default +"lsoda" is performant, but sometimes fails to converge.
use_compiled

If set to FALSE, no compiled version of the mkinmod - model is used in the calls to mkinpredict even if a compiled - version is present.

If set to FALSE, no compiled version of the +mkinmod model is used in the calls to +mkinpredict even if a compiled version is present.
control
transform_rates

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.

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.
transform_fractions

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 - ilr transformation.

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 ilr transformation.
quiet

Suppress printing out the current value of the negative log-likelihood - after each improvement?

Suppress printing out the current value of the negative +log-likelihood after each improvement?
atol

Absolute error tolerance, passed to ode. Default is 1e-8, - lower than in lsoda.

Absolute error tolerance, passed to ode. Default +is 1e-8, lower than in lsoda.
rtol

Absolute error tolerance, passed to ode. Default is 1e-10, - much lower than in lsoda.

Absolute error tolerance, passed to ode. Default +is 1e-10, much lower than in lsoda.
n.outtimes

The length of the dataseries that is produced by the model prediction - function mkinpredict. This impacts the accuracy of - the numerical solver if that is used (see solution_type argument. - The default value is 100.

The length of the dataseries that is produced by the model +prediction function mkinpredict. This impacts the accuracy +of the numerical solver if that is used (see solution_type +argument. The default value is 100.
error_model

If the error model is "const", a constant standard deviation - is assumed.

+

If the error model is "const", a constant standard + deviation is assumed.

If the error model is "obs", each observed variable is assumed to have its - own variance.

+ own variance.

If the error model is "tc" (two-component error model), a two component - error model similar to the one described by Rocke and Lorenzato (1995) is - used for setting up the likelihood function. Note that this model deviates - from the model by Rocke and Lorenzato, as their model implies that the - errors follow a lognormal distribution for large values, not a normal - distribution as assumed by this method.
error_model_algorithm

If "auto", the selected algorithm depends on the error model. - If the error model is "const", nonlinear least squares fitting ("OLS") is - selected. If the error model is "obs", iteratively reweighted least squares - fitting ("IRLS") is selected. If the error model is "tc", the "d_3" - algorithm is selected.

-

The algorithm "d_3" will directly minimize the negative - log-likelihood and - independently - also use the three step algorithm - described below. The fit with the higher likelihood is returned.

-

The algorithm "direct" will directly minimize the negative - log-likelihood.

-

The algorithm "twostep" will minimize the negative log-likelihood - after an initial unweighted least squares optimisation step.

-

The algorithm "threestep" starts with unweighted least squares, - then optimizes only the error model using the degradation model - parameters found, and then minimizes the negative log-likelihood - with free degradation and error model parameters.

-

The algorithm "fourstep" starts with unweighted least squares, - then optimizes only the error model using the degradation model - parameters found, then optimizes the degradation model again - with fixed error model parameters, and finally minimizes the negative - log-likelihood with free degradation and error model parameters.

+

If "auto", the selected algorithm depends on + the error model. If the error model is "const", unweighted nonlinear + least squares fitting ("OLS") is selected. If the error model is "obs", or + "tc", the "d_3" algorithm is selected.

+

The algorithm "d_3" will directly minimize the negative log-likelihood and + - independently - also use the three step algorithm described below. The + fit with the higher likelihood is returned.

+

The algorithm "direct" will directly minimize the negative log-likelihood.

+

The algorithm "twostep" will minimize the negative log-likelihood after an + initial unweighted least squares optimisation step.

+

The algorithm "threestep" starts with unweighted least squares, then + optimizes only the error model using the degradation model parameters + found, and then minimizes the negative log-likelihood with free + degradation and error model parameters.

+

The algorithm "fourstep" starts with unweighted least squares, then + optimizes only the error model using the degradation model parameters + found, then optimizes the degradation model again with fixed error model + parameters, and finally minimizes the negative log-likelihood with free + degradation and error model parameters.

The algorithm "IRLS" (Iteratively Reweighted Least Squares) starts with - unweighted least squares, and then iterates optimization of the error model - parameters and subsequent - optimization of the degradation model using those error model parameters, - until the error model parameters converge.
reweight.tol

Tolerance for the convergence criterion calculated from the error model - parameters in IRLS fits.

Tolerance for the convergence criterion calculated from +the error model parameters in IRLS fits.
reweight.max.iter
...

Further arguments that will be passed on to deSolve.

Further arguments that will be passed on to +deSolve.
- + +

Source

+ +

Rocke, David M. und Lorenzato, Stefan (1995) A two-component model + for measurement error in analytical chemistry. Technometrics 37(2), 176-184.

Value

-

A list with "mkinfit" in the class attribute. A summary can be obtained by - summary.mkinfit.

- -

See also

+

A list with "mkinfit" in the class attribute. A summary can be + obtained by summary.mkinfit.

+

Details

-

Plotting methods plot.mkinfit and mkinparplot.

-

Comparisons of models fitted to the same data can be made using AIC - by virtue of the method logLik.mkinfit.

-

Fitting of several models to several datasets in a single call to - mmkin.

- +

Per default, parameters in the kinetic models are internally transformed in +order to better satisfy the assumption of a normal distribution of their +estimators.

Note

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.

- -

Source

+

See also

-

Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for - measurement error in analytical chemistry. Technometrics 37(2), 176-184.

- +

Plotting methods plot.mkinfit and + mkinparplot.

+

Comparisons of models fitted to the same data can be made using + AIC by virtue of the method logLik.mkinfit.

+

Fitting of several models to several datasets in a single call to + mmkin.

Examples

- 
# Use shorthand notation for parent only degradation
+    

+# Use shorthand notation for parent only degradation
 fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
 summary(fit)
#> mkin version used for fitting:    0.9.49.6 
 #> R version used for fitting:       3.6.1 
-#> Date of fit:     Mon Oct 21 12:07:39 2019 
-#> Date of summary: Mon Oct 21 12:07:39 2019 
+#> Date of fit:     Fri Oct 25 02:08:07 2019 
+#> Date of summary: Fri Oct 25 02:08:07 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 #> 
 #> Model predictions using solution type analytical 
 #> 
-#> Fitted using 222 model solutions performed in 0.459 s
+#> Fitted using 222 model solutions performed in 0.453 s
 #> 
 #> Error model: Constant variance 
 #> 
@@ -487,7 +480,7 @@ Per default, parameters in the kinetic models are internally transformed in
   m1 = mkinsub("SFO"))
#> Successfully compiled differential equation model from auto-generated C code.
# 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)))
#> Warning: Observations with value of zero were removed from the data
#>        User      System verstrichen 
-#>       1.462       0.000       1.463 
coef(fit)
#> NULL
endpoints(fit)
#> $ff
+#>       1.447       0.000       1.448 
coef(fit)
#> NULL
endpoints(fit)
#> $ff
 #> parent_sink   parent_m1     m1_sink 
 #>    0.485524    0.514476    1.000000 
 #> 
@@ -560,7 +553,7 @@ Per default, parameters in the kinetic models are internally transformed in
 #> Sum of squared residuals at call 126: 371.2134
 #> Sum of squared residuals at call 135: 371.2134
 #> Negative log-likelihood at call 145: 97.22429
#> Optimisation successfully terminated.
#>        User      System verstrichen 
-#>        1.04        0.00        1.04 
coef(fit.deSolve)
#> NULL
endpoints(fit.deSolve)
#> $ff
+#>       1.032       0.000       1.032 
coef(fit.deSolve)
#> NULL
endpoints(fit.deSolve)
#> $ff
 #> parent_sink   parent_m1     m1_sink 
 #>    0.485524    0.514476    1.000000 
 #> 
@@ -596,8 +589,8 @@ Per default, parameters in the kinetic models are internally transformed in
 SFO_SFO.ff <- mkinmod(parent = mkinsub("SFO", "m1"),
                       m1 = mkinsub("SFO"), use_of_ff = "max")
#> Successfully compiled differential equation model from auto-generated C code.
f.noweight <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
summary(f.noweight)
#> mkin version used for fitting:    0.9.49.6 
 #> R version used for fitting:       3.6.1 
-#> Date of fit:     Mon Oct 21 12:07:54 2019 
-#> Date of summary: Mon Oct 21 12:07:54 2019 
+#> Date of fit:     Fri Oct 25 02:08:22 2019 
+#> Date of summary: Fri Oct 25 02:08:22 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
@@ -605,7 +598,7 @@ Per default, parameters in the kinetic models are internally transformed in
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted using 421 model solutions performed in 1.07 s
+#> Fitted using 421 model solutions performed in 1.062 s
 #> 
 #> Error model: Constant variance 
 #> 
@@ -713,8 +706,8 @@ Per default, parameters in the kinetic models are internally transformed in
 #>   120       m1    25.15  28.78984 -3.640e+00
 #>   120       m1    33.31  28.78984  4.520e+00
f.obs <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "obs", quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
summary(f.obs)
#> mkin version used for fitting:    0.9.49.6 
 #> R version used for fitting:       3.6.1 
-#> Date of fit:     Mon Oct 21 12:07:56 2019 
-#> Date of summary: Mon Oct 21 12:07:56 2019 
+#> Date of fit:     Fri Oct 25 02:08:25 2019 
+#> Date of summary: Fri Oct 25 02:08:25 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
@@ -722,11 +715,12 @@ Per default, parameters in the kinetic models are internally transformed in
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted using 897 model solutions performed in 2.363 s
+#> Fitted using 978 model solutions performed in 2.523 s
 #> 
 #> Error model: Variance unique to each observed variable 
 #> 
-#> Error model algorithm: IRLS 
+#> Error model algorithm: d_3 
+#> Direct fitting and three-step fitting yield approximately the same likelihood 
 #> 
 #> Starting values for parameters to be optimised:
 #>                   value   type
@@ -761,16 +755,16 @@ Per default, parameters in the kinetic models are internally transformed in
 #> 
 #> Parameter correlation:
 #>                parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_parent
-#> parent_0        1.00000      0.51078 -0.19132       -0.59997     0.035676
-#> log_k_parent    0.51078      1.00000 -0.37457       -0.59239     0.069834
-#> log_k_m1       -0.19132     -0.37457  1.00000        0.74398    -0.026158
-#> f_parent_ilr_1 -0.59997     -0.59239  0.74398        1.00000    -0.041371
-#> sigma_parent    0.03568      0.06983 -0.02616       -0.04137     1.000000
-#> sigma_m1       -0.03385     -0.06626  0.02482        0.03926    -0.004628
+#> parent_0        1.00000      0.51078 -0.19133       -0.59997     0.035670
+#> log_k_parent    0.51078      1.00000 -0.37458       -0.59239     0.069833
+#> log_k_m1       -0.19133     -0.37458  1.00000        0.74398    -0.026158
+#> f_parent_ilr_1 -0.59997     -0.59239  0.74398        1.00000    -0.041369
+#> sigma_parent    0.03567      0.06983 -0.02616       -0.04137     1.000000
+#> sigma_m1       -0.03385     -0.06627  0.02482        0.03926    -0.004628
 #>                 sigma_m1
 #> parent_0       -0.033847
 #> log_k_parent   -0.066265
-#> log_k_m1        0.024824
+#> log_k_m1        0.024823
 #> f_parent_ilr_1  0.039256
 #> sigma_parent   -0.004628
 #> sigma_m1        1.000000
@@ -784,7 +778,7 @@ Per default, parameters in the kinetic models are internally transformed in
 #> k_parent        0.098970  22.850 1.099e-21  0.090530 1.082e-01
 #> k_m1            0.005245   8.046 1.732e-09  0.004072 6.756e-03
 #> f_parent_to_m1  0.513600  23.560 4.352e-22  0.469300 5.578e-01
-#> sigma_parent    3.401000   5.985 5.661e-07  2.244000 4.559e+00
+#> sigma_parent    3.401000   5.985 5.662e-07  2.244000 4.559e+00
 #> sigma_m1        2.855000   6.311 2.215e-07  1.934000 3.777e+00
 #> 
 #> FOCUS Chi2 error levels in percent:
@@ -805,47 +799,47 @@ Per default, parameters in the kinetic models are internally transformed in
 #> 
 #> Data:
 #>  time variable observed predicted   residual
-#>     0   parent    99.46  99.65420 -1.942e-01
-#>     0   parent   102.04  99.65420  2.386e+00
-#>     1   parent    93.50  90.26335  3.237e+00
-#>     1   parent    92.50  90.26335  2.237e+00
-#>     3   parent    63.23  74.05308 -1.082e+01
-#>     3   parent    68.99  74.05308 -5.063e+00
-#>     7   parent    52.32  49.84326  2.477e+00
-#>     7   parent    55.13  49.84326  5.287e+00
+#>     0   parent    99.46  99.65417 -1.942e-01
+#>     0   parent   102.04  99.65417  2.386e+00
+#>     1   parent    93.50  90.26332  3.237e+00
+#>     1   parent    92.50  90.26332  2.237e+00
+#>     3   parent    63.23  74.05306 -1.082e+01
+#>     3   parent    68.99  74.05306 -5.063e+00
+#>     7   parent    52.32  49.84325  2.477e+00
+#>     7   parent    55.13  49.84325  5.287e+00
 #>    14   parent    27.27  24.92971  2.340e+00
 #>    14   parent    26.64  24.92971  1.710e+00
 #>    21   parent    11.50  12.46890 -9.689e-01
 #>    21   parent    11.64  12.46890 -8.289e-01
 #>    35   parent     2.85   3.11925 -2.692e-01
 #>    35   parent     2.91   3.11925 -2.092e-01
-#>    50   parent     0.69   0.70678 -1.678e-02
-#>    50   parent     0.63   0.70678 -7.678e-02
+#>    50   parent     0.69   0.70679 -1.679e-02
+#>    50   parent     0.63   0.70679 -7.679e-02
 #>    75   parent     0.05   0.05952 -9.523e-03
 #>    75   parent     0.06   0.05952  4.772e-04
 #>     1       m1     4.84   4.81075  2.925e-02
 #>     1       m1     5.64   4.81075  8.292e-01
-#>     3       m1    12.91  13.04197 -1.320e-01
-#>     3       m1    12.96  13.04197 -8.197e-02
-#>     7       m1    22.97  25.06848 -2.098e+00
-#>     7       m1    24.47  25.06848 -5.985e-01
+#>     3       m1    12.91  13.04196 -1.320e-01
+#>     3       m1    12.96  13.04196 -8.196e-02
+#>     7       m1    22.97  25.06847 -2.098e+00
+#>     7       m1    24.47  25.06847 -5.985e-01
 #>    14       m1    41.69  36.70308  4.987e+00
 #>    14       m1    33.21  36.70308 -3.493e+00
 #>    21       m1    44.37  41.65115  2.719e+00
 #>    21       m1    46.44  41.65115  4.789e+00
 #>    35       m1    41.22  43.29465 -2.075e+00
 #>    35       m1    37.95  43.29465 -5.345e+00
-#>    50       m1    41.19  41.19948 -9.477e-03
+#>    50       m1    41.19  41.19948 -9.479e-03
 #>    50       m1    40.01  41.19948 -1.189e+00
 #>    75       m1    40.09  36.44035  3.650e+00
 #>    75       m1    33.85  36.44035 -2.590e+00
-#>   100       m1    31.04  31.98772 -9.477e-01
-#>   100       m1    33.13  31.98772  1.142e+00
-#>   120       m1    25.15  28.80428 -3.654e+00
-#>   120       m1    33.31  28.80428  4.506e+00
f.tc <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "tc", quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
summary(f.tc)
#> mkin version used for fitting:    0.9.49.6 
+#>   100       m1    31.04  31.98773 -9.477e-01
+#>   100       m1    33.13  31.98773  1.142e+00
+#>   120       m1    25.15  28.80429 -3.654e+00
+#>   120       m1    33.31  28.80429  4.506e+00
f.tc <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, error_model = "tc", quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
summary(f.tc)
#> mkin version used for fitting:    0.9.49.6 
 #> R version used for fitting:       3.6.1 
-#> Date of fit:     Mon Oct 21 12:08:06 2019 
-#> Date of summary: Mon Oct 21 12:08:06 2019 
+#> Date of fit:     Fri Oct 25 02:08:34 2019 
+#> Date of summary: Fri Oct 25 02:08:34 2019 
 #> 
 #> Equations:
 #> d_parent/dt = - k_parent * parent
@@ -853,7 +847,7 @@ Per default, parameters in the kinetic models are internally transformed in
 #> 
 #> Model predictions using solution type deSolve 
 #> 
-#> Fitted using 2289 model solutions performed in 9.175 s
+#> Fitted using 2289 model solutions performed in 9.136 s
 #> 
 #> Error model: Two-component variance function 
 #> 
@@ -969,21 +963,18 @@ Per default, parameters in the kinetic models are internally transformed in
 #>   120       m1    25.15  29.04130  -3.891304
 #>   120       m1    33.31  29.04130   4.268696
# }
 
+