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 = c("none", "manual", "std", "mean", "tc"),
  tc = c(sigma_low = 0.5, rsd_high = 0.07),
  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, ...)

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"). If a shorthand name is given, a parent only degradation model is generated for the variable with the highest value in observed.

observed

The observed data. It has to be in the long format as described in 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.

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.

fixed_parms

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.

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 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.

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.

use_compiled

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

method.modFit

The optimisation method passed to 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.

maxit.modFit

Maximum number of iterations in the optimisation. If not "auto", this will be passed to the method called by modFit, overriding what may be specified in the next argument control.modFit.

control.modFit

Additional arguments passed to the optimisation method used by modFit.

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.

plot

Should the observed values and the numerical solutions be plotted at each stage of the optimisation?

quiet

Suppress printing out the current model cost after each improvement?

err

either 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.

weight

only if err=NULL: how to weight the residuals, one of "none", "std", "mean", see details of modCost, or "tc" for the two component error model. The option "manual" is available for the case that err!=NULL, but it is not necessary to specify it.

tc

The two components of the error model as used for (initial) weighting

scaleVar

Will be passed to modCost. Default is not to scale Variables according to the number of observations.

atol

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.

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.

reweight.method

The method used for iteratively reweighting residuals, also known as iteratively reweighted least squares (IRLS). Default is NULL, i.e. no iterative weighting. The first reweighting method is called "obs", meaning that each observed variable is assumed to have its own variance. This variance is estimated from the fit (mean squared residuals) and used for weighting the residuals in each iteration until convergence of this estimate up to reweight.tol or up to the maximum number of iterations specified by reweight.max.iter. The second reweighting method is called "tc" (two-component error model). When using this method, the two components of an error model similar to the one described by Rocke and Lorenzato (1995) are estimated from the fit and the resulting variances are used for weighting the residuals in each iteration until convergence of these components or up to the maximum number of iterations specified. Note that this method 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.

reweight.tol

Tolerance for convergence criterion for the variance components in IRLS fits.

reweight.max.iter

Maximum iterations in IRLS fits.

trace_parms

Should a trace of the parameter values be listed?

Further arguments that will be passed to modFit.

Value

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

See also

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.

Note

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.

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

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

Examples

# Use shorthand notation for parent only degradation fit <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE) summary(fit)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:36 2019 #> Date of summary: Tue Feb 26 09:27:36 2019 #> #> 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 0.163 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"))
#> 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)))
#> User System verstrichen #> 1.008 0.000 1.008
coef(fit)
#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750
#> $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 : 874.2615 #> Model cost at call 33 : 874.2611 #> Model cost at call 35 : 616.2377 #> Model cost at call 37 : 616.2372 #> Model cost at call 40 : 467.4386 #> Model cost at call 42 : 467.4381 #> 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 : 371.4071 #> Model cost at call 106 : 371.4071 #> Model cost at call 107 : 371.4071 #> 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 146 : 371.2134 #> Optimisation by method Port successfully terminated. #> User System verstrichen #> 0.812 0.000 0.813
coef(fit.deSolve)
#> parent_0 log_k_parent_sink log_k_parent_m1 log_k_m1_sink #> 99.59848 -3.03822 -2.98030 -5.24750
endpoints(fit.deSolve)
#> $ff #> parent_sink parent_m1 m1_sink #> 0.485524 0.514476 1.000000 #> #> $SFORB #> logical(0) #> #> $distimes #> DT50 DT90 #> parent 7.022929 23.32967 #> m1 131.760711 437.69961 #>
# Use stepwise fitting, using optimised parameters from parent only fit, FOMC
FOMC_SFO <- mkinmod( parent = mkinsub("FOMC", "m1"), m1 = mkinsub("SFO"))
#> Successfully compiled differential equation model from auto-generated C code.
# Fit the model to the FOCUS example dataset D using defaults fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE) # Use starting parameters from parent only FOMC fit fit.FOMC = mkinfit("FOMC", FOCUS_2006_D, quiet = TRUE) fit.FOMC_SFO <- mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE, parms.ini = fit.FOMC$bparms.ode) # 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) fit.SFORB_SFO.deSolve <- mkinfit(SFORB_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet = TRUE) # 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)
# Weighted fits, including IRLS 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) summary(f.noweight)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:48 2019 #> Date of summary: Tue Feb 26 09:27:48 2019 #> #> 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 186 model solutions performed in 0.845 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 5.700e-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 4.375e-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 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 #> 0 m1 0.00 0.00000 0.000e+00 #> 0 m1 0.00 0.00000 0.000e+00 #> 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.irls <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, reweight.method = "obs", quiet = TRUE) summary(f.irls)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:50 2019 #> Date of summary: Tue Feb 26 09:27:50 2019 #> #> 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 551 model solutions performed in 2.523 s #> #> Weighting: none #> #> Iterative reweighting with method obs #> Final mean squared residuals of observed variables: #> parent m1 #> 11.573407 7.407845 #> #> 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 -2.219 #> 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 8.185e-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 8.486e-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 132.282 439.43 #> #> Data: #> time variable observed predicted residual err #> 0 parent 99.46 99.67218 -2.122e-01 3.402 #> 0 parent 102.04 99.67218 2.368e+00 3.402 #> 1 parent 93.50 90.27153 3.228e+00 3.402 #> 1 parent 92.50 90.27153 2.228e+00 3.402 #> 3 parent 63.23 74.04648 -1.082e+01 3.402 #> 3 parent 68.99 74.04648 -5.056e+00 3.402 #> 7 parent 52.32 49.82092 2.499e+00 3.402 #> 7 parent 55.13 49.82092 5.309e+00 3.402 #> 14 parent 27.27 24.90288 2.367e+00 3.402 #> 14 parent 26.64 24.90288 1.737e+00 3.402 #> 21 parent 11.50 12.44765 -9.476e-01 3.402 #> 21 parent 11.64 12.44765 -8.076e-01 3.402 #> 35 parent 2.85 3.11002 -2.600e-01 3.402 #> 35 parent 2.91 3.11002 -2.000e-01 3.402 #> 50 parent 0.69 0.70374 -1.374e-02 3.402 #> 50 parent 0.63 0.70374 -7.374e-02 3.402 #> 75 parent 0.05 0.05913 -9.134e-03 3.402 #> 75 parent 0.06 0.05913 8.662e-04 3.402 #> 0 m1 0.00 0.00000 0.000e+00 2.722 #> 0 m1 0.00 0.00000 0.000e+00 2.722 #> 1 m1 4.84 4.81328 2.672e-02 2.722 #> 1 m1 5.64 4.81328 8.267e-01 2.722 #> 3 m1 12.91 13.04779 -1.378e-01 2.722 #> 3 m1 12.96 13.04779 -8.779e-02 2.722 #> 7 m1 22.97 25.07615 -2.106e+00 2.722 #> 7 m1 24.47 25.07615 -6.062e-01 2.722 #> 14 m1 41.69 36.70729 4.983e+00 2.722 #> 14 m1 33.21 36.70729 -3.497e+00 2.722 #> 21 m1 44.37 41.65050 2.720e+00 2.722 #> 21 m1 46.44 41.65050 4.790e+00 2.722 #> 35 m1 41.22 43.28866 -2.069e+00 2.722 #> 35 m1 37.95 43.28866 -5.339e+00 2.722 #> 50 m1 41.19 41.19339 -3.386e-03 2.722 #> 50 m1 40.01 41.19339 -1.183e+00 2.722 #> 75 m1 40.09 36.43820 3.652e+00 2.722 #> 75 m1 33.85 36.43820 -2.588e+00 2.722 #> 100 m1 31.04 31.98971 -9.497e-01 2.722 #> 100 m1 33.13 31.98971 1.140e+00 2.722 #> 120 m1 25.15 28.80898 -3.659e+00 2.722 #> 120 m1 33.31 28.80898 4.501e+00 2.722
f.w.mean <- mkinfit(SFO_SFO.ff, FOCUS_2006_D, weight = "mean", quiet = TRUE) summary(f.w.mean)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:51 2019 #> Date of summary: Tue Feb 26 09:27:51 2019 #> #> 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 0.705 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 99.73057 -0.270570 #> 0 parent 102.04 99.73057 2.309430 #> 1 parent 93.50 90.29805 3.201945 #> 1 parent 92.50 90.29805 2.201945 #> 3 parent 63.23 74.02503 -10.795028 #> 3 parent 68.99 74.02503 -5.035028 #> 7 parent 52.32 49.74838 2.571618 #> 7 parent 55.13 49.74838 5.381618 #> 14 parent 27.27 24.81588 2.454124 #> 14 parent 26.64 24.81588 1.824124 #> 21 parent 11.50 12.37885 -0.878849 #> 21 parent 11.64 12.37885 -0.738849 #> 35 parent 2.85 3.08022 -0.230219 #> 35 parent 2.91 3.08022 -0.170219 #> 50 parent 0.69 0.69396 -0.003958 #> 50 parent 0.63 0.69396 -0.063958 #> 75 parent 0.05 0.05789 -0.007888 #> 75 parent 0.06 0.05789 0.002112 #> 0 m1 0.00 0.00000 0.000000 #> 0 m1 0.00 0.00000 0.000000 #> 1 m1 4.84 4.82149 0.018512 #> 1 m1 5.64 4.82149 0.818512 #> 3 m1 12.91 13.06669 -0.156692 #> 3 m1 12.96 13.06669 -0.106692 #> 7 m1 22.97 25.10106 -2.131058 #> 7 m1 24.47 25.10106 -0.631058 #> 14 m1 41.69 36.72092 4.969077 #> 14 m1 33.21 36.72092 -3.510923 #> 21 m1 44.37 41.64835 2.721647 #> 21 m1 46.44 41.64835 4.791647 #> 35 m1 41.22 43.26923 -2.049225 #> 35 m1 37.95 43.26923 -5.319225 #> 50 m1 41.19 41.17364 0.016361 #> 50 m1 40.01 41.17364 -1.163639 #> 75 m1 40.09 36.43122 3.658776 #> 75 m1 33.85 36.43122 -2.581224 #> 100 m1 31.04 31.99612 -0.956124 #> 100 m1 33.13 31.99612 1.133876 #> 120 m1 25.15 28.82413 -3.674128 #> 120 m1 33.31 28.82413 4.485872
f.w.value <- mkinfit(SFO_SFO.ff, subset(FOCUS_2006_D, value != 0), err = "value", quiet = TRUE) summary(f.w.value)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:52 2019 #> Date of summary: Tue Feb 26 09:27:52 2019 #> #> 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 0.8 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 0.6843 -0.08687 -0.7564 #> log_k_parent 0.68435 1.0000 -0.12695 -0.5812 #> log_k_m1 -0.08687 -0.1269 1.00000 0.5195 #> f_parent_ilr_1 -0.75644 -0.5812 0.51952 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 -0.195715 99.46 #> 0 parent 102.04 99.65571 2.384285 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", quiet = TRUE) summary(f.w.man)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:54 2019 #> Date of summary: Tue Feb 26 09:27:54 2019 #> #> 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 270 model solutions performed in 1.238 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 -0.09456 -0.3351 #> log_k_parent 0.53123 1.0000 -0.17800 -0.3360 #> log_k_m1 -0.09456 -0.1780 1.00000 0.7616 #> f_parent_ilr_1 -0.33514 -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 2.221e-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 99.48598 -0.025979 1 #> 0 parent 102.04 99.48598 2.554021 1 #> 1 parent 93.50 90.18612 3.313880 1 #> 1 parent 92.50 90.18612 2.313880 1 #> 3 parent 63.23 74.11316 -10.883163 1 #> 3 parent 68.99 74.11316 -5.123163 1 #> 7 parent 52.32 50.05030 2.269705 1 #> 7 parent 55.13 50.05030 5.079705 1 #> 14 parent 27.27 25.17975 2.090250 1 #> 14 parent 26.64 25.17975 1.460250 1 #> 21 parent 11.50 12.66765 -1.167654 1 #> 21 parent 11.64 12.66765 -1.027654 1 #> 35 parent 2.85 3.20616 -0.356164 1 #> 35 parent 2.91 3.20616 -0.296164 1 #> 50 parent 0.69 0.73562 -0.045619 1 #> 50 parent 0.63 0.73562 -0.105619 1 #> 75 parent 0.05 0.06326 -0.013256 1 #> 75 parent 0.06 0.06326 -0.003256 1 #> 0 m1 0.00 0.00000 0.000000 2 #> 0 m1 0.00 0.00000 0.000000 2 #> 1 m1 4.84 4.78729 0.052713 2 #> 1 m1 5.64 4.78729 0.852713 2 #> 3 m1 12.91 12.98785 -0.077848 2 #> 3 m1 12.96 12.98785 -0.027848 2 #> 7 m1 22.97 24.99695 -2.026946 2 #> 7 m1 24.47 24.99695 -0.526946 2 #> 14 m1 41.69 36.66353 5.026472 2 #> 14 m1 33.21 36.66353 -3.453528 2 #> 21 m1 44.37 41.65681 2.713186 2 #> 21 m1 46.44 41.65681 4.783186 2 #> 35 m1 41.22 43.35031 -2.130314 2 #> 35 m1 37.95 43.35031 -5.400314 2 #> 50 m1 41.19 41.25637 -0.066368 2 #> 50 m1 40.01 41.25637 -1.246368 2 #> 75 m1 40.09 36.46057 3.629429 2 #> 75 m1 33.85 36.46057 -2.610571 2 #> 100 m1 31.04 31.96929 -0.929293 2 #> 100 m1 33.13 31.96929 1.160707 2 #> 120 m1 25.15 28.76062 -3.610621 2 #> 120 m1 33.31 28.76062 4.549379 2
f.w.man.irls <- mkinfit(SFO_SFO.ff, dw, err = "err.man", quiet = TRUE, reweight.method = "obs") summary(f.w.man.irls)
#> mkin version used for fitting: 0.9.48.1 #> R version used for fitting: 3.5.2 #> Date of fit: Tue Feb 26 09:27:57 2019 #> Date of summary: Tue Feb 26 09:27:57 2019 #> #> 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 692 model solutions performed in 3.246 s #> #> Weighting: manual #> #> Iterative reweighting with method obs #> Final mean squared residuals of observed variables: #> parent m1 #> 11.573406 7.407846 #> #> 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 8.185e-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 8.486e-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.ini err #> 0 parent 99.46 99.67217 -2.122e-01 1 3.402 #> 0 parent 102.04 99.67217 2.368e+00 1 3.402 #> 1 parent 93.50 90.27152 3.228e+00 1 3.402 #> 1 parent 92.50 90.27152 2.228e+00 1 3.402 #> 3 parent 63.23 74.04648 -1.082e+01 1 3.402 #> 3 parent 68.99 74.04648 -5.056e+00 1 3.402 #> 7 parent 52.32 49.82092 2.499e+00 1 3.402 #> 7 parent 55.13 49.82092 5.309e+00 1 3.402 #> 14 parent 27.27 24.90288 2.367e+00 1 3.402 #> 14 parent 26.64 24.90288 1.737e+00 1 3.402 #> 21 parent 11.50 12.44765 -9.477e-01 1 3.402 #> 21 parent 11.64 12.44765 -8.077e-01 1 3.402 #> 35 parent 2.85 3.11002 -2.600e-01 1 3.402 #> 35 parent 2.91 3.11002 -2.000e-01 1 3.402 #> 50 parent 0.69 0.70375 -1.375e-02 1 3.402 #> 50 parent 0.63 0.70375 -7.375e-02 1 3.402 #> 75 parent 0.05 0.05913 -9.134e-03 1 3.402 #> 75 parent 0.06 0.05913 8.661e-04 1 3.402 #> 0 m1 0.00 0.00000 0.000e+00 2 2.722 #> 0 m1 0.00 0.00000 0.000e+00 2 2.722 #> 1 m1 4.84 4.81328 2.672e-02 2 2.722 #> 1 m1 5.64 4.81328 8.267e-01 2 2.722 #> 3 m1 12.91 13.04779 -1.378e-01 2 2.722 #> 3 m1 12.96 13.04779 -8.779e-02 2 2.722 #> 7 m1 22.97 25.07615 -2.106e+00 2 2.722 #> 7 m1 24.47 25.07615 -6.062e-01 2 2.722 #> 14 m1 41.69 36.70729 4.983e+00 2 2.722 #> 14 m1 33.21 36.70729 -3.497e+00 2 2.722 #> 21 m1 44.37 41.65050 2.719e+00 2 2.722 #> 21 m1 46.44 41.65050 4.789e+00 2 2.722 #> 35 m1 41.22 43.28866 -2.069e+00 2 2.722 #> 35 m1 37.95 43.28866 -5.339e+00 2 2.722 #> 50 m1 41.19 41.19339 -3.387e-03 2 2.722 #> 50 m1 40.01 41.19339 -1.183e+00 2 2.722 #> 75 m1 40.09 36.43820 3.652e+00 2 2.722 #> 75 m1 33.85 36.43820 -2.588e+00 2 2.722 #> 100 m1 31.04 31.98971 -9.497e-01 2 2.722 #> 100 m1 33.13 31.98971 1.140e+00 2 2.722 #> 120 m1 25.15 28.80897 -3.659e+00 2 2.722 #> 120 m1 33.31 28.80897 4.501e+00 2 2.722