From a77a10ea6c607346778ba0700b3b66ac393101a2 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 27 May 2020 06:06:08 +0200 Subject: Create up to date pkgdown docs in development mode --- docs/dev/reference/mkinfit.html | 1054 +++++++++++++++++++++++++++++++++++++++ 1 file changed, 1054 insertions(+) create mode 100644 docs/dev/reference/mkinfit.html (limited to 'docs/dev/reference/mkinfit.html') diff --git a/docs/dev/reference/mkinfit.html b/docs/dev/reference/mkinfit.html new file mode 100644 index 00000000..49e896fc --- /dev/null +++ b/docs/dev/reference/mkinfit.html @@ -0,0 +1,1054 @@ + + + + + + + + +Fit a kinetic model to data with one or more state variables — mkinfit • mkin + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+ +
+
+
+

Fit a kinetic model to data with one or more state variables

+ Source: R/mkinfit.R + +
+ +
+

This function maximises the likelihood of the observed data using the Port +algorithm stats::nlminb(), and the specified initial or fixed +parameters and starting values. In each step of the optimisation, the +kinetic model is solved using the function mkinpredict(), except +if an analytical solution is implemented, in which case the model is solved +using the degradation function in the mkinmod object. 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,
+  solution_type = c("auto", "analytical", "eigen", "deSolve"),
+  method.ode = "lsoda",
+  use_compiled = "auto",
+  control = list(eval.max = 300, iter.max = 200),
+  transform_rates = TRUE,
+  transform_fractions = TRUE,
+  quiet = FALSE,
+  atol = 1e-08,
+  rtol = 1e-10,
+  error_model = c("const", "obs", "tc"),
+  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

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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.

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.

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.

+

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.

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.

fixed_parms

The names of parameters that should not be optimised but +rather kept at the values specified in parms.ini. Alternatively, +a named numeric vector of parameters to be fixed, regardless of the values +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.

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.

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 relatively simple degradation models. The default is +"auto", which uses "analytical" if possible, otherwise "deSolve" if a +compiler is present, and "eigen" if no compiler is present and the model +can be expressed using eigenvalues and eigenvectors.

method.ode

The solution method passed via mkinpredict() +to deSolve::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.

control

A list of control arguments passed to stats::nlminb().

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.

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.

quiet

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

atol

Absolute error tolerance, passed to deSolve::ode(). Default +is 1e-8, which is lower than the default in the deSolve::lsoda() +function which is used per default.

rtol

Absolute error tolerance, passed to deSolve::ode(). Default +is 1e-10, much lower than in deSolve::lsoda().

error_model

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.

+

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", 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.

reweight.max.iter

Maximum number of iterations in IRLS fits.

trace_parms

Should a trace of the parameter values be listed?

...

Further arguments that will be passed on to +deSolve::ode().

+ +

Value

+ +

A list with "mkinfit" in the class attribute.

+

Details

+ +

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.

+

References

+ +

Rocke DM and Lorenzato S (1995) A two-component model +for measurement error in analytical chemistry. Technometrics 37(2), 176-184.

+

Ranke J and Meinecke S (2019) Error Models for the Kinetic Evaluation of Chemical +Degradation Data. Environments 6(12) 124 +doi:10.3390/environments6120124.

+

See also

+ +

summary.mkinfit, plot.mkinfit, parms and lrtest.

+

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
+fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
+summary(fit)
#> mkin version used for fitting:    0.9.50.3 
+#> R version used for fitting:       4.0.0 
+#> Date of fit:     Wed May 27 05:54:13 2020 
+#> Date of summary: Wed May 27 05:54:13 2020 
+#> 
+#> Equations:
+#> d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
+#> 
+#> Model predictions using solution type analytical 
+#> 
+#> Fitted using 222 model solutions performed in 0.043 s
+#> 
+#> Error model: Constant variance 
+#> 
+#> Error model algorithm: OLS 
+#> 
+#> Starting values for parameters to be optimised:
+#>          value   type
+#> parent_0  85.1  state
+#> alpha      1.0 deparm
+#> beta      10.0 deparm
+#> 
+#> Starting values for the transformed parameters actually optimised:
+#>               value lower upper
+#> parent_0  85.100000  -Inf   Inf
+#> log_alpha  0.000000  -Inf   Inf
+#> log_beta   2.302585  -Inf   Inf
+#> 
+#> Fixed parameter values:
+#> None
+#> 
+#> Results:
+#> 
+#>        AIC      BIC    logLik
+#>   44.68652 45.47542 -18.34326
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>           Estimate Std. Error    Lower   Upper
+#> parent_0  85.87000     1.8070 81.23000 90.5200
+#> log_alpha  0.05192     0.1353 -0.29580  0.3996
+#> log_beta   0.65100     0.2287  0.06315  1.2390
+#> sigma      1.85700     0.4378  0.73200  2.9830
+#> 
+#> Parameter correlation:
+#>             parent_0  log_alpha   log_beta     sigma
+#> parent_0   1.000e+00 -1.565e-01 -3.142e-01 4.770e-08
+#> log_alpha -1.565e-01  1.000e+00  9.564e-01 9.974e-08
+#> log_beta  -3.142e-01  9.564e-01  1.000e+00 8.468e-08
+#> sigma      4.770e-08  9.974e-08  8.468e-08 1.000e+00
+#> 
+#> Backtransformed parameters:
+#> Confidence intervals for internally transformed parameters are asymmetric.
+#> t-test (unrealistically) based on the assumption of normal distribution
+#> for estimators of untransformed parameters.
+#>          Estimate t value    Pr(>t)   Lower  Upper
+#> parent_0   85.870  47.530 3.893e-08 81.2300 90.520
+#> alpha       1.053   7.393 3.562e-04  0.7439  1.491
+#> beta        1.917   4.373 3.601e-03  1.0650  3.451
+#> sigma       1.857   4.243 4.074e-03  0.7320  2.983
+#> 
+#> FOCUS Chi2 error levels in percent:
+#>          err.min n.optim df
+#> All data   6.657       3  6
+#> parent     6.657       3  6
+#> 
+#> Estimated disappearance times:
+#>         DT50  DT90 DT50back
+#> parent 1.785 15.15     4.56
+#> 
+#> Data:
+#>  time variable observed predicted residual
+#>     0   parent     85.1    85.875  -0.7749
+#>     1   parent     57.9    55.191   2.7091
+#>     3   parent     29.9    31.845  -1.9452
+#>     7   parent     14.6    17.012  -2.4124
+#>    14   parent      9.7     9.241   0.4590
+#>    28   parent      6.6     4.754   1.8460
+#>    63   parent      4.0     2.102   1.8977
+#>    91   parent      3.9     1.441   2.4590
+#>   119   parent      0.6     1.092  -0.4919

+# 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"))
#> 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 elapsed 
+#>   0.414   0.000   0.418 
parms(fit)
#>       parent_0       k_parent           k_m1 f_parent_to_m1          sigma 
+#>   99.598481046    0.098697740    0.005260651    0.514475962    3.125503875 
endpoints(fit)
#> $ff
+#>   parent_m1 parent_sink 
+#>    0.514476    0.485524 
+#> 
+#> $distimes
+#>              DT50      DT90
+#> parent   7.022929  23.32966
+#> m1     131.760724 437.69965
+#> 
# \dontrun{
+# 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")))
#> Warning: Observations with value of zero were removed from the data
#> Ordinary least squares optimisation
#> Sum of squared residuals at call 1: 15156.12
+#> Sum of squared residuals at call 2: 15156.12
+#> Sum of squared residuals at call 6: 8243.645
+#> Sum of squared residuals at call 12: 6290.712
+#> Sum of squared residuals at call 13: 6290.683
+#> Sum of squared residuals at call 15: 6290.452
+#> Sum of squared residuals at call 18: 1700.749
+#> Sum of squared residuals at call 20: 1700.611
+#> Sum of squared residuals at call 24: 1190.923
+#> Sum of squared residuals at call 26: 1190.922
+#> Sum of squared residuals at call 29: 1017.417
+#> Sum of squared residuals at call 31: 1017.417
+#> Sum of squared residuals at call 33: 1017.416
+#> Sum of squared residuals at call 34: 644.0472
+#> Sum of squared residuals at call 36: 644.047
+#> Sum of squared residuals at call 38: 644.047
+#> Sum of squared residuals at call 39: 590.5025
+#> Sum of squared residuals at call 41: 590.5022
+#> Sum of squared residuals at call 43: 590.5016
+#> Sum of squared residuals at call 44: 543.2196
+#> Sum of squared residuals at call 45: 543.2193
+#> Sum of squared residuals at call 46: 543.2192
+#> Sum of squared residuals at call 50: 391.348
+#> Sum of squared residuals at call 51: 391.3479
+#> Sum of squared residuals at call 56: 386.479
+#> Sum of squared residuals at call 58: 386.479
+#> Sum of squared residuals at call 60: 386.4779
+#> Sum of squared residuals at call 61: 384.0686
+#> Sum of squared residuals at call 63: 384.0686
+#> Sum of squared residuals at call 66: 382.7813
+#> Sum of squared residuals at call 68: 382.7813
+#> Sum of squared residuals at call 70: 382.7813
+#> Sum of squared residuals at call 71: 378.9273
+#> Sum of squared residuals at call 73: 378.9273
+#> Sum of squared residuals at call 75: 378.9272
+#> Sum of squared residuals at call 76: 377.4847
+#> Sum of squared residuals at call 78: 377.4846
+#> Sum of squared residuals at call 81: 375.9738
+#> Sum of squared residuals at call 83: 375.9738
+#> Sum of squared residuals at call 86: 375.3387
+#> Sum of squared residuals at call 88: 375.3387
+#> Sum of squared residuals at call 91: 374.5774
+#> Sum of squared residuals at call 93: 374.5774
+#> Sum of squared residuals at call 95: 374.5774
+#> Sum of squared residuals at call 96: 373.5438
+#> Sum of squared residuals at call 100: 373.5438
+#> Sum of squared residuals at call 102: 373.265
+#> Sum of squared residuals at call 104: 373.265
+#> Sum of squared residuals at call 107: 372.6825
+#> Sum of squared residuals at call 111: 372.6825
+#> Sum of squared residuals at call 114: 372.6356
+#> Sum of squared residuals at call 116: 372.6356
+#> Sum of squared residuals at call 119: 372.6199
+#> Sum of squared residuals at call 121: 372.6199
+#> Sum of squared residuals at call 123: 372.6199
+#> Sum of squared residuals at call 124: 372.5881
+#> Sum of squared residuals at call 126: 372.5881
+#> Sum of squared residuals at call 129: 372.5418
+#> Sum of squared residuals at call 130: 372.4866
+#> Sum of squared residuals at call 131: 372.2242
+#> Sum of squared residuals at call 132: 371.5237
+#> Sum of squared residuals at call 134: 371.5237
+#> Sum of squared residuals at call 137: 371.292
+#> Sum of squared residuals at call 139: 371.292
+#> Sum of squared residuals at call 143: 371.2256
+#> Sum of squared residuals at call 144: 371.2256
+#> Sum of squared residuals at call 146: 371.2256
+#> Sum of squared residuals at call 149: 371.2194
+#> Sum of squared residuals at call 150: 371.2147
+#> Sum of squared residuals at call 153: 371.2147
+#> Sum of squared residuals at call 155: 371.2137
+#> Sum of squared residuals at call 156: 371.2137
+#> Sum of squared residuals at call 157: 371.2137
+#> Sum of squared residuals at call 160: 371.2134
+#> Sum of squared residuals at call 164: 371.2134
+#> Sum of squared residuals at call 165: 371.2134
+#> Sum of squared residuals at call 167: 371.2134
+#> Negative log-likelihood at call 177: 97.22429
#> Optimisation successfully terminated.
#>    user  system elapsed 
+#>   0.371   0.001   0.370 
parms(fit.deSolve)
#>       parent_0       k_parent           k_m1 f_parent_to_m1          sigma 
+#>   99.598480300    0.098697739    0.005260651    0.514475968    3.125503874 
endpoints(fit.deSolve)
#> $ff
+#>   parent_m1 parent_sink 
+#>    0.514476    0.485524 
+#> 
+#> $distimes
+#>              DT50      DT90
+#> parent   7.022929  23.32966
+#> m1     131.760721 437.69964
+#> 
# }
+
+# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
+# \dontrun{
+FOMC_SFO <- mkinmod(
+  parent = mkinsub("FOMC", "m1"),
+  m1 = mkinsub("SFO"))
#> Successfully compiled differential equation model from auto-generated C code.
# Fit the model to the FOCUS example dataset D using defaults
+fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
# Use starting parameters from parent only FOMC fit
+fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE)
+fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE,
+  parms.ini = fit.FOMC$bparms.ode)
#> Warning: Observations with value of zero were removed from the data

+# 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"))
#> Successfully compiled differential equation model from auto-generated C code.
# Fit the model to the FOCUS example dataset D using defaults
+fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve",
+                                 quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
# Use starting parameters from parent only SFORB fit (not really needed in this case)
+fit.SFORB = mkinfit("SFORB", FOCUS_2006_D, quiet = TRUE)
+fit.SFORB_SFO <- mkinfit(SFORB_SFO, FOCUS_2006_D, parms.ini = fit.SFORB$bparms.ode, quiet = TRUE)
#> Warning: Observations with value of zero were removed from the data
#> Warning: Initial parameter(s) k_parent_free_sink not used in the model
# }
+
+# \dontrun{
+# Weighted fits, including IRLS (error_model = "obs")
+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:    0.9.50.3 
+#> R version used for fitting:       4.0.0 
+#> Date of fit:     Wed May 27 05:54:19 2020 
+#> Date of summary: Wed May 27 05:54:19 2020 
+#> 
+#> Equations:
+#> d_parent/dt = - k_parent * parent
+#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+#> 
+#> Model predictions using solution type analytical 
+#> 
+#> Fitted using 421 model solutions performed in 0.126 s
+#> 
+#> Error model: Constant variance 
+#> 
+#> Error model algorithm: OLS 
+#> 
+#> Starting values for parameters to be optimised:
+#>                   value   type
+#> parent_0       100.7500  state
+#> k_parent         0.1000 deparm
+#> k_m1             0.1001 deparm
+#> f_parent_to_m1   0.5000 deparm
+#> 
+#> Starting values for the transformed parameters actually optimised:
+#>                     value lower upper
+#> parent_0       100.750000  -Inf   Inf
+#> log_k_parent    -2.302585  -Inf   Inf
+#> log_k_m1        -2.301586  -Inf   Inf
+#> f_parent_ilr_1   0.000000  -Inf   Inf
+#> 
+#> Fixed parameter values:
+#>      value  type
+#> m1_0     0 state
+#> 
+#> Results:
+#> 
+#>        AIC      BIC    logLik
+#>   204.4486 212.6365 -97.22429
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>                Estimate Std. Error    Lower    Upper
+#> parent_0       99.60000    1.57000 96.40000 102.8000
+#> log_k_parent   -2.31600    0.04087 -2.39900  -2.2330
+#> log_k_m1       -5.24800    0.13320 -5.51800  -4.9770
+#> f_parent_ilr_1  0.04096    0.06312 -0.08746   0.1694
+#> sigma           3.12600    0.35850  2.39600   3.8550
+#> 
+#> Parameter correlation:
+#>                  parent_0 log_k_parent   log_k_m1 f_parent_ilr_1      sigma
+#> parent_0        1.000e+00    5.174e-01 -1.688e-01     -5.471e-01 -3.190e-07
+#> log_k_parent    5.174e-01    1.000e+00 -3.263e-01     -5.426e-01  3.168e-07
+#> log_k_m1       -1.688e-01   -3.263e-01  1.000e+00      7.478e-01 -1.406e-07
+#> f_parent_ilr_1 -5.471e-01   -5.426e-01  7.478e-01      1.000e+00 -1.587e-10
+#> sigma          -3.190e-07    3.168e-07 -1.406e-07     -1.587e-10  1.000e+00
+#> 
+#> Backtransformed parameters:
+#> Confidence intervals for internally transformed parameters are asymmetric.
+#> t-test (unrealistically) based on the assumption of normal distribution
+#> for estimators of untransformed parameters.
+#>                 Estimate t value    Pr(>t)     Lower     Upper
+#> parent_0       99.600000  63.430 2.298e-36 96.400000 1.028e+02
+#> k_parent        0.098700  24.470 4.955e-23  0.090820 1.073e-01
+#> k_m1            0.005261   7.510 6.165e-09  0.004012 6.898e-03
+#> f_parent_to_m1  0.514500  23.070 3.104e-22  0.469100 5.596e-01
+#> sigma           3.126000   8.718 2.235e-10  2.396000 3.855e+00
+#> 
+#> FOCUS Chi2 error levels in percent:
+#>          err.min n.optim df
+#> All data   6.398       4 15
+#> parent     6.459       2  7
+#> m1         4.690       2  8
+#> 
+#> Resulting formation fractions:
+#>                 ff
+#> parent_m1   0.5145
+#> parent_sink 0.4855
+#> 
+#> Estimated disappearance times:
+#>           DT50   DT90
+#> parent   7.023  23.33
+#> m1     131.761 437.70
+#> 
+#> Data:
+#>  time variable observed predicted   residual
+#>     0   parent    99.46  99.59848 -1.385e-01
+#>     0   parent   102.04  99.59848  2.442e+00
+#>     1   parent    93.50  90.23787  3.262e+00
+#>     1   parent    92.50  90.23787  2.262e+00
+#>     3   parent    63.23  74.07319 -1.084e+01
+#>     3   parent    68.99  74.07319 -5.083e+00
+#>     7   parent    52.32  49.91206  2.408e+00
+#>     7   parent    55.13  49.91206  5.218e+00
+#>    14   parent    27.27  25.01257  2.257e+00
+#>    14   parent    26.64  25.01257  1.627e+00
+#>    21   parent    11.50  12.53462 -1.035e+00
+#>    21   parent    11.64  12.53462 -8.946e-01
+#>    35   parent     2.85   3.14787 -2.979e-01
+#>    35   parent     2.91   3.14787 -2.379e-01
+#>    50   parent     0.69   0.71624 -2.624e-02
+#>    50   parent     0.63   0.71624 -8.624e-02
+#>    75   parent     0.05   0.06074 -1.074e-02
+#>    75   parent     0.06   0.06074 -7.381e-04
+#>     1       m1     4.84   4.80296  3.704e-02
+#>     1       m1     5.64   4.80296  8.370e-01
+#>     3       m1    12.91  13.02400 -1.140e-01
+#>     3       m1    12.96  13.02400 -6.400e-02
+#>     7       m1    22.97  25.04476 -2.075e+00
+#>     7       m1    24.47  25.04476 -5.748e-01
+#>    14       m1    41.69  36.69002  5.000e+00
+#>    14       m1    33.21  36.69002 -3.480e+00
+#>    21       m1    44.37  41.65310  2.717e+00
+#>    21       m1    46.44  41.65310  4.787e+00
+#>    35       m1    41.22  43.31312 -2.093e+00
+#>    35       m1    37.95  43.31312 -5.363e+00
+#>    50       m1    41.19  41.21831 -2.831e-02
+#>    50       m1    40.01  41.21831 -1.208e+00
+#>    75       m1    40.09  36.44703  3.643e+00
+#>    75       m1    33.85  36.44703 -2.597e+00
+#>   100       m1    31.04  31.98163 -9.416e-01
+#>   100       m1    33.13  31.98163  1.148e+00
+#>   120       m1    25.15  28.78984 -3.640e+00
+#>   120       m1    33.31  28.78984  4.520e+00
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:    0.9.50.3 
+#> R version used for fitting:       4.0.0 
+#> Date of fit:     Wed May 27 05:54:19 2020 
+#> Date of summary: Wed May 27 05:54:19 2020 
+#> 
+#> Equations:
+#> d_parent/dt = - k_parent * parent
+#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+#> 
+#> Model predictions using solution type analytical 
+#> 
+#> Fitted using 978 model solutions performed in 0.33 s
+#> 
+#> Error model: Variance unique to each observed variable 
+#> 
+#> Error model algorithm: d_3 
+#> Direct fitting and three-step fitting yield approximately the same likelihood 
+#> 
+#> Starting values for parameters to be optimised:
+#>                   value   type
+#> parent_0       100.7500  state
+#> k_parent         0.1000 deparm
+#> k_m1             0.1001 deparm
+#> f_parent_to_m1   0.5000 deparm
+#> sigma_parent     3.0000  error
+#> sigma_m1         3.0000  error
+#> 
+#> Starting values for the transformed parameters actually optimised:
+#>                     value lower upper
+#> parent_0       100.750000  -Inf   Inf
+#> log_k_parent    -2.302585  -Inf   Inf
+#> log_k_m1        -2.301586  -Inf   Inf
+#> f_parent_ilr_1   0.000000  -Inf   Inf
+#> sigma_parent     3.000000     0   Inf
+#> sigma_m1         3.000000     0   Inf
+#> 
+#> Fixed parameter values:
+#>      value  type
+#> m1_0     0 state
+#> 
+#> Results:
+#> 
+#>        AIC      BIC    logLik
+#>   205.8727 215.6982 -96.93634
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>                Estimate Std. Error    Lower    Upper
+#> parent_0       99.65000    1.70200 96.19000 103.1000
+#> log_k_parent   -2.31300    0.04376 -2.40200  -2.2240
+#> log_k_m1       -5.25000    0.12430 -5.50400  -4.9970
+#> f_parent_ilr_1  0.03861    0.06171 -0.08708   0.1643
+#> sigma_parent    3.40100    0.56820  2.24400   4.5590
+#> sigma_m1        2.85500    0.45240  1.93400   3.7770
+#> 
+#> Parameter correlation:
+#>                parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_parent
+#> parent_0        1.00000      0.51078 -0.19133       -0.59997     0.035670
+#> log_k_parent    0.51078      1.00000 -0.37458       -0.59239     0.069833
+#> log_k_m1       -0.19133     -0.37458  1.00000        0.74398    -0.026158
+#> f_parent_ilr_1 -0.59997     -0.59239  0.74398        1.00000    -0.041369
+#> sigma_parent    0.03567      0.06983 -0.02616       -0.04137     1.000000
+#> sigma_m1       -0.03385     -0.06627  0.02482        0.03926    -0.004628
+#>                 sigma_m1
+#> parent_0       -0.033847
+#> log_k_parent   -0.066265
+#> log_k_m1        0.024823
+#> f_parent_ilr_1  0.039256
+#> sigma_parent   -0.004628
+#> sigma_m1        1.000000
+#> 
+#> Backtransformed parameters:
+#> Confidence intervals for internally transformed parameters are asymmetric.
+#> t-test (unrealistically) based on the assumption of normal distribution
+#> for estimators of untransformed parameters.
+#>                 Estimate t value    Pr(>t)     Lower     Upper
+#> parent_0       99.650000  58.560 2.004e-34 96.190000 1.031e+02
+#> k_parent        0.098970  22.850 1.099e-21  0.090530 1.082e-01
+#> k_m1            0.005245   8.046 1.732e-09  0.004072 6.756e-03
+#> f_parent_to_m1  0.513600  23.560 4.352e-22  0.469300 5.578e-01
+#> sigma_parent    3.401000   5.985 5.662e-07  2.244000 4.559e+00
+#> sigma_m1        2.855000   6.311 2.215e-07  1.934000 3.777e+00
+#> 
+#> FOCUS Chi2 error levels in percent:
+#>          err.min n.optim df
+#> All data   6.398       4 15
+#> parent     6.464       2  7
+#> m1         4.682       2  8
+#> 
+#> Resulting formation fractions:
+#>                 ff
+#> parent_m1   0.5136
+#> parent_sink 0.4864
+#> 
+#> Estimated disappearance times:
+#>           DT50   DT90
+#> parent   7.003  23.26
+#> m1     132.154 439.01
+#> 
+#> Data:
+#>  time variable observed predicted   residual
+#>     0   parent    99.46  99.65417 -1.942e-01
+#>     0   parent   102.04  99.65417  2.386e+00
+#>     1   parent    93.50  90.26332  3.237e+00
+#>     1   parent    92.50  90.26332  2.237e+00
+#>     3   parent    63.23  74.05306 -1.082e+01
+#>     3   parent    68.99  74.05306 -5.063e+00
+#>     7   parent    52.32  49.84325  2.477e+00
+#>     7   parent    55.13  49.84325  5.287e+00
+#>    14   parent    27.27  24.92971  2.340e+00
+#>    14   parent    26.64  24.92971  1.710e+00
+#>    21   parent    11.50  12.46890 -9.689e-01
+#>    21   parent    11.64  12.46890 -8.289e-01
+#>    35   parent     2.85   3.11925 -2.692e-01
+#>    35   parent     2.91   3.11925 -2.092e-01
+#>    50   parent     0.69   0.70679 -1.679e-02
+#>    50   parent     0.63   0.70679 -7.679e-02
+#>    75   parent     0.05   0.05952 -9.523e-03
+#>    75   parent     0.06   0.05952  4.772e-04
+#>     1       m1     4.84   4.81075  2.925e-02
+#>     1       m1     5.64   4.81075  8.292e-01
+#>     3       m1    12.91  13.04196 -1.320e-01
+#>     3       m1    12.96  13.04196 -8.196e-02
+#>     7       m1    22.97  25.06847 -2.098e+00
+#>     7       m1    24.47  25.06847 -5.985e-01
+#>    14       m1    41.69  36.70308  4.987e+00
+#>    14       m1    33.21  36.70308 -3.493e+00
+#>    21       m1    44.37  41.65115  2.719e+00
+#>    21       m1    46.44  41.65115  4.789e+00
+#>    35       m1    41.22  43.29465 -2.075e+00
+#>    35       m1    37.95  43.29465 -5.345e+00
+#>    50       m1    41.19  41.19948 -9.479e-03
+#>    50       m1    40.01  41.19948 -1.189e+00
+#>    75       m1    40.09  36.44035  3.650e+00
+#>    75       m1    33.85  36.44035 -2.590e+00
+#>   100       m1    31.04  31.98773 -9.477e-01
+#>   100       m1    33.13  31.98773  1.142e+00
+#>   120       m1    25.15  28.80429 -3.654e+00
+#>   120       m1    33.31  28.80429  4.506e+00
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:    0.9.50.3 
+#> R version used for fitting:       4.0.0 
+#> Date of fit:     Wed May 27 05:54:20 2020 
+#> Date of summary: Wed May 27 05:54:20 2020 
+#> 
+#> Equations:
+#> d_parent/dt = - k_parent * parent
+#> d_m1/dt = + f_parent_to_m1 * k_parent * parent - k_m1 * m1
+#> 
+#> Model predictions using solution type analytical 
+#> 
+#> Fitted using 2088 model solutions performed in 0.714 s
+#> 
+#> Error model: Two-component variance function 
+#> 
+#> Error model algorithm: d_3 
+#> Direct fitting and three-step fitting yield approximately the same likelihood 
+#> 
+#> Starting values for parameters to be optimised:
+#>                   value   type
+#> parent_0       100.7500  state
+#> k_parent         0.1000 deparm
+#> k_m1             0.1001 deparm
+#> f_parent_to_m1   0.5000 deparm
+#> sigma_low        0.1000  error
+#> rsd_high         0.1000  error
+#> 
+#> Starting values for the transformed parameters actually optimised:
+#>                     value lower upper
+#> parent_0       100.750000  -Inf   Inf
+#> log_k_parent    -2.302585  -Inf   Inf
+#> log_k_m1        -2.301586  -Inf   Inf
+#> f_parent_ilr_1   0.000000  -Inf   Inf
+#> sigma_low        0.100000     0   Inf
+#> rsd_high         0.100000     0   Inf
+#> 
+#> Fixed parameter values:
+#>      value  type
+#> m1_0     0 state
+#> 
+#> Results:
+#> 
+#>        AIC      BIC    logLik
+#>   141.9656 151.7911 -64.98278
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>                 Estimate Std. Error     Lower     Upper
+#> parent_0       100.70000   2.621000 95.400000 106.10000
+#> log_k_parent    -2.29700   0.008862 -2.315000  -2.27900
+#> log_k_m1        -5.26600   0.091310 -5.452000  -5.08000
+#> f_parent_ilr_1   0.02374   0.055300 -0.088900   0.13640
+#> sigma_low        0.00305   0.004829 -0.006786   0.01289
+#> rsd_high         0.07928   0.009418  0.060100   0.09847
+#> 
+#> Parameter correlation:
+#>                parent_0 log_k_parent log_k_m1 f_parent_ilr_1 sigma_low rsd_high
+#> parent_0        1.00000      0.67644 -0.10215       -0.76822   0.14294 -0.08783
+#> log_k_parent    0.67644      1.00000 -0.15102       -0.59491   0.34611 -0.08125
+#> log_k_m1       -0.10215     -0.15102  1.00000        0.51808  -0.05236  0.01240
+#> f_parent_ilr_1 -0.76822     -0.59491  0.51808        1.00000  -0.13900  0.03248
+#> sigma_low       0.14294      0.34611 -0.05236       -0.13900   1.00000 -0.16546
+#> rsd_high       -0.08783     -0.08125  0.01240        0.03248  -0.16546  1.00000
+#> 
+#> Backtransformed parameters:
+#> Confidence intervals for internally transformed parameters are asymmetric.
+#> t-test (unrealistically) based on the assumption of normal distribution
+#> for estimators of untransformed parameters.
+#>                 Estimate  t value    Pr(>t)     Lower     Upper
+#> parent_0       1.007e+02  38.4300 1.180e-28 95.400000 1.061e+02
+#> k_parent       1.006e-01 112.8000 1.718e-43  0.098760 1.024e-01
+#> k_m1           5.167e-03  10.9500 1.171e-12  0.004290 6.223e-03
+#> f_parent_to_m1 5.084e-01  26.0100 2.146e-23  0.468600 5.481e-01
+#> sigma_low      3.050e-03   0.6314 2.661e-01 -0.006786 1.289e-02
+#> rsd_high       7.928e-02   8.4170 6.418e-10  0.060100 9.847e-02
+#> 
+#> FOCUS Chi2 error levels in percent:
+#>          err.min n.optim df
+#> All data   6.475       4 15
+#> parent     6.573       2  7
+#> m1         4.671       2  8
+#> 
+#> Resulting formation fractions:
+#>                 ff
+#> parent_m1   0.5084
+#> parent_sink 0.4916
+#> 
+#> Estimated disappearance times:
+#>           DT50  DT90
+#> parent   6.893  22.9
+#> m1     134.156 445.7
+#> 
+#> Data:
+#>  time variable observed predicted   residual
+#>     0   parent    99.46 100.73434  -1.274340
+#>     0   parent   102.04 100.73434   1.305660
+#>     1   parent    93.50  91.09751   2.402486
+#>     1   parent    92.50  91.09751   1.402486
+#>     3   parent    63.23  74.50141 -11.271410
+#>     3   parent    68.99  74.50141  -5.511410
+#>     7   parent    52.32  49.82880   2.491200
+#>     7   parent    55.13  49.82880   5.301200
+#>    14   parent    27.27  24.64809   2.621908
+#>    14   parent    26.64  24.64809   1.991908
+#>    21   parent    11.50  12.19232  -0.692315
+#>    21   parent    11.64  12.19232  -0.552315
+#>    35   parent     2.85   2.98327  -0.133266
+#>    35   parent     2.91   2.98327  -0.073266
+#>    50   parent     0.69   0.66013   0.029874
+#>    50   parent     0.63   0.66013  -0.030126
+#>    75   parent     0.05   0.05344  -0.003438
+#>    75   parent     0.06   0.05344   0.006562
+#>     1       m1     4.84   4.88645  -0.046451
+#>     1       m1     5.64   4.88645   0.753549
+#>     3       m1    12.91  13.22867  -0.318669
+#>     3       m1    12.96  13.22867  -0.268669
+#>     7       m1    22.97  25.36417  -2.394166
+#>     7       m1    24.47  25.36417  -0.894166
+#>    14       m1    41.69  37.00974   4.680263
+#>    14       m1    33.21  37.00974  -3.799737
+#>    21       m1    44.37  41.90133   2.468669
+#>    21       m1    46.44  41.90133   4.538669
+#>    35       m1    41.22  43.45691  -2.236913
+#>    35       m1    37.95  43.45691  -5.506913
+#>    50       m1    41.19  41.34199  -0.151985
+#>    50       m1    40.01  41.34199  -1.331985
+#>    75       m1    40.09  36.61471   3.475295
+#>    75       m1    33.85  36.61471  -2.764705
+#>   100       m1    31.04  32.20082  -1.160823
+#>   100       m1    33.13  32.20082   0.929177
+#>   120       m1    25.15  29.04130  -3.891304
+#>   120       m1    33.31  29.04130   4.268696
# }
+
+
+
+
+ +
+ + + +
+ + + + + + + + -- cgit v1.2.1