Synthetic datasets for one parent compound with two metabolites

synthetic_data_for_UBA_2014

synthetic_data_for_UBA_2014

Format

A list containing twelve datasets as an R6 class defined by mkinds, + each containing, among others, the following components

title: The name of the dataset, e.g. SFO_lin_a
data: A data frame with the data in the form expected by mkinfit

Source

Ranke (2014) Prüfung und Validierung von Modellierungssoftware als Alternative zu ModelMaker 4.0, Umweltbundesamt Projektnummer 27452

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

Examples

# \dontrun{
-# The data have been generated using the following kinetic models
-m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
-                           M1 = list(type = "SFO", to = "M2"),
-                           M2 = list(type = "SFO"), use_of_ff = "max")
-
#> Temporary DLL for differentials generated and loaded

-
-m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2"),
-                                         sink = FALSE),
-                           M1 = list(type = "SFO"),
-                           M2 = list(type = "SFO"), use_of_ff = "max")
-
#> Temporary DLL for differentials generated and loaded

-m_synth_DFOP_lin <- mkinmod(parent = list(type = "DFOP", to = "M1"),
-                            M1 = list(type = "SFO", to = "M2"),
-                            M2 = list(type = "SFO"), use_of_ff = "max")
-
#> Temporary DLL for differentials generated and loaded

-m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2"),
-                                          sink = FALSE),
-                            M1 = list(type = "SFO"),
-                            M2 = list(type = "SFO"), use_of_ff = "max")
-
#> Temporary DLL for differentials generated and loaded

-# The model predictions without intentional error were generated as follows
-sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-
-d_synth_SFO_lin <- mkinpredict(m_synth_SFO_lin,
-                               c(k_parent = 0.7, f_parent_to_M1 = 0.8,
-                                 k_M1 = 0.3, f_M1_to_M2 = 0.7,
-                                 k_M2 = 0.02),
-                               c(parent = 100, M1 = 0, M2 = 0),
-                               sampling_times)
-
-d_synth_DFOP_lin <- mkinpredict(m_synth_DFOP_lin,
-                                c(k1 = 0.2, k2 = 0.02, g = 0.5,
-                                  f_parent_to_M1 = 0.5, k_M1 = 0.3,
-                                  f_M1_to_M2 = 0.7, k_M2 = 0.02),
-                                 c(parent = 100, M1 = 0, M2 = 0),
-                                 sampling_times)
-
-d_synth_SFO_par <- mkinpredict(m_synth_SFO_par,
-                               c(k_parent = 0.2,
-                                 f_parent_to_M1 = 0.8, k_M1 = 0.01,
-                                 f_parent_to_M2 = 0.2, k_M2 = 0.02),
-                                 c(parent = 100, M1 = 0, M2 = 0),
-                                 sampling_times)
-
-d_synth_DFOP_par <- mkinpredict(m_synth_DFOP_par,
-                               c(k1 = 0.3, k2 = 0.02, g = 0.7,
-                                 f_parent_to_M1 = 0.6, k_M1 = 0.04,
-                                 f_parent_to_M2 = 0.4, k_M2 = 0.01),
-                                 c(parent = 100, M1 = 0, M2 = 0),
-                                 sampling_times)
-
-# Construct names for datasets with errors
-d_synth_names = paste0("d_synth_", c("SFO_lin", "SFO_par",
-                                     "DFOP_lin", "DFOP_par"))
-
-# Original function used or adding errors. The add_err function now published
-# with this package is a slightly generalised version where the names of
-# secondary compartments that should have an initial value of zero (M1 and M2
-# in this case) are not hardcoded any more.
-# add_err = function(d, sdfunc, LOD = 0.1, reps = 2, seed = 123456789)
-# {
-#   set.seed(seed)
-#   d_long = mkin_wide_to_long(d, time = "time")
-#   d_rep = data.frame(lapply(d_long, rep, each = 2))
-#   d_rep$value = rnorm(length(d_rep$value), d_rep$value, sdfunc(d_rep$value))
-#
-#   d_rep[d_rep$time == 0 & d_rep$name %in% c("M1", "M2"), "value"] <- 0
-#   d_NA <- transform(d_rep, value = ifelse(value < LOD, NA, value))
-#   d_NA$value <- round(d_NA$value, 1)
-#   return(d_NA)
-# }
-
-# The following is the simplified version of the two-component model of Rocke
-# and Lorenzato (1995)
-sdfunc_twocomp = function(value, sd_low, rsd_high) {
-  sqrt(sd_low^2 + value^2 * rsd_high^2)
-}
-
-# Add the errors.
-for (d_synth_name in d_synth_names)
-{
-  d_synth = get(d_synth_name)
-  assign(paste0(d_synth_name, "_a"), add_err(d_synth, function(value) 3))
-  assign(paste0(d_synth_name, "_b"), add_err(d_synth, function(value) 7))
-  assign(paste0(d_synth_name, "_c"), add_err(d_synth,
-                           function(value) sdfunc_twocomp(value, 0.5, 0.07)))
-
-}
-
-d_synth_err_names = c(
-  paste(rep(d_synth_names, each = 3), letters[1:3], sep = "_")
-)
-
-# This is just one example of an evaluation using the kinetic model used for
-# the generation of the data
-  fit <- mkinfit(m_synth_SFO_lin, synthetic_data_for_UBA_2014[[1]]$data,
-                 quiet = TRUE)
-  plot_sep(fit)
-
  summary(fit)
-
#> mkin version used for fitting:    1.0.3.9000 
-#> R version used for fitting:       4.0.3 
-#> Date of fit:     Mon Feb 15 17:13:29 2021 
-#> Date of summary: Mon Feb 15 17:13:29 2021 
-#> 
-#> Equations:
-#> d_parent/dt = - k_parent * parent
-#> d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
-#> d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
-#> 
-#> Model predictions using solution type deSolve 
-#> 
-#> Fitted using 833 model solutions performed in 0.649 s
-#> 
-#> Error model: Constant variance 
-#> 
-#> Error model algorithm: OLS 
-#> 
-#> Starting values for parameters to be optimised:
-#>                   value   type
-#> parent_0       101.3500  state
-#> k_parent         0.1000 deparm
-#> k_M1             0.1001 deparm
-#> k_M2             0.1002 deparm
-#> f_parent_to_M1   0.5000 deparm
-#> f_M1_to_M2       0.5000 deparm
-#> 
-#> Starting values for the transformed parameters actually optimised:
-#>                      value lower upper
-#> parent_0        101.350000  -Inf   Inf
-#> log_k_parent     -2.302585  -Inf   Inf
-#> log_k_M1         -2.301586  -Inf   Inf
-#> log_k_M2         -2.300587  -Inf   Inf
-#> f_parent_qlogis   0.000000  -Inf   Inf
-#> f_M1_qlogis       0.000000  -Inf   Inf
-#> 
-#> Fixed parameter values:
-#>      value  type
-#> M1_0     0 state
-#> M2_0     0 state
-#> 
-#> Results:
-#> 
-#>        AIC      BIC    logLik
-#>   188.7274 200.3723 -87.36368
-#> 
-#> Optimised, transformed parameters with symmetric confidence intervals:
-#>                 Estimate Std. Error   Lower    Upper
-#> parent_0        102.1000    1.57000 98.8600 105.3000
-#> log_k_parent     -0.3020    0.03885 -0.3812  -0.2229
-#> log_k_M1         -1.2070    0.07123 -1.3520  -1.0620
-#> log_k_M2         -3.9010    0.06571 -4.0350  -3.7670
-#> f_parent_qlogis   1.2010    0.23530  0.7216   1.6800
-#> f_M1_qlogis       0.9589    0.24890  0.4520   1.4660
-#> sigma             2.2730    0.25740  1.7490   2.7970
-#> 
-#> Parameter correlation:
-#>                   parent_0 log_k_parent   log_k_M1   log_k_M2 f_parent_qlogis
-#> parent_0         1.000e+00    3.933e-01 -1.605e-01  2.819e-02      -4.624e-01
-#> log_k_parent     3.933e-01    1.000e+00 -4.082e-01  7.166e-02      -5.682e-01
-#> log_k_M1        -1.605e-01   -4.082e-01  1.000e+00 -3.929e-01       7.478e-01
-#> log_k_M2         2.819e-02    7.166e-02 -3.929e-01  1.000e+00      -2.658e-01
-#> f_parent_qlogis -4.624e-01   -5.682e-01  7.478e-01 -2.658e-01       1.000e+00
-#> f_M1_qlogis      1.614e-01    4.102e-01 -8.109e-01  5.419e-01      -8.605e-01
-#> sigma           -2.900e-08   -8.030e-09 -2.741e-08  3.938e-08      -2.681e-08
-#>                 f_M1_qlogis      sigma
-#> parent_0          1.614e-01 -2.900e-08
-#> log_k_parent      4.102e-01 -8.030e-09
-#> log_k_M1         -8.109e-01 -2.741e-08
-#> log_k_M2          5.419e-01  3.938e-08
-#> f_parent_qlogis  -8.605e-01 -2.681e-08
-#> f_M1_qlogis       1.000e+00  4.971e-08
-#> sigma             4.971e-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       102.10000  65.000 7.281e-36 98.86000 105.30000
-#> k_parent         0.73930  25.740 2.948e-23  0.68310   0.80020
-#> k_M1             0.29920  14.040 1.577e-15  0.25880   0.34590
-#> k_M2             0.02023  15.220 1.653e-16  0.01769   0.02312
-#> f_parent_to_M1   0.76870  18.370 7.295e-19  0.67300   0.84290
-#> f_M1_to_M2       0.72290  14.500 6.418e-16  0.61110   0.81240
-#> sigma            2.27300   8.832 2.161e-10  1.74900   2.79700
-#> 
-#> FOCUS Chi2 error levels in percent:
-#>          err.min n.optim df
-#> All data   8.454       6 17
-#> parent     8.660       2  6
-#> M1        10.583       2  5
-#> M2         3.586       2  6
-#> 
-#> Resulting formation fractions:
-#>                 ff
-#> parent_M1   0.7687
-#> parent_sink 0.2313
-#> M1_M2       0.7229
-#> M1_sink     0.2771
-#> 
-#> Estimated disappearance times:
-#>           DT50    DT90
-#> parent  0.9376   3.114
-#> M1      2.3170   7.697
-#> M2     34.2689 113.839
-#> 
-#> Data:
-#>  time variable observed  predicted residual
-#>     0   parent    101.5  1.021e+02 -0.56248
-#>     0   parent    101.2  1.021e+02 -0.86248
-#>     1   parent     53.9  4.873e+01  5.17118
-#>     1   parent     47.5  4.873e+01 -1.22882
-#>     3   parent     10.4  1.111e+01 -0.70773
-#>     3   parent      7.6  1.111e+01 -3.50773
-#>     7   parent      1.1  5.772e-01  0.52283
-#>     7   parent      0.3  5.772e-01 -0.27717
-#>    14   parent      3.5  3.264e-03  3.49674
-#>    28   parent      3.2  1.045e-07  3.20000
-#>    90   parent      0.6  9.530e-10  0.60000
-#>   120   parent      3.5 -5.940e-10  3.50000
-#>     1       M1     36.4  3.479e+01  1.61088
-#>     1       M1     37.4  3.479e+01  2.61088
-#>     3       M1     34.3  3.937e+01 -5.07027
-#>     3       M1     39.8  3.937e+01  0.42973
-#>     7       M1     15.1  1.549e+01 -0.38715
-#>     7       M1     17.8  1.549e+01  2.31285
-#>    14       M1      5.8  1.995e+00  3.80469
-#>    14       M1      1.2  1.995e+00 -0.79531
-#>    60       M1      0.5  2.111e-06  0.50000
-#>    90       M1      3.2 -9.670e-10  3.20000
-#>   120       M1      1.5  7.670e-10  1.50000
-#>   120       M1      0.6  7.670e-10  0.60000
-#>     1       M2      4.8  4.455e+00  0.34517
-#>     3       M2     20.9  2.153e+01 -0.62527
-#>     3       M2     19.3  2.153e+01 -2.22527
-#>     7       M2     42.0  4.192e+01  0.07941
-#>     7       M2     43.1  4.192e+01  1.17941
-#>    14       M2     49.4  4.557e+01  3.83353
-#>    14       M2     44.3  4.557e+01 -1.26647
-#>    28       M2     34.6  3.547e+01 -0.87275
-#>    28       M2     33.0  3.547e+01 -2.47275
-#>    60       M2     18.8  1.858e+01  0.21837
-#>    60       M2     17.6  1.858e+01 -0.98163
-#>    90       M2     10.6  1.013e+01  0.47130
-#>    90       M2     10.8  1.013e+01  0.67130
-#>   120       M2      9.8  5.521e+00  4.27893
-#>   120       M2      3.3  5.521e+00 -2.22107
# }
-

Examples

# \dontrun{
+# The data have been generated using the following kinetic models
+m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
+                           M1 = list(type = "SFO", to = "M2"),
+                           M2 = list(type = "SFO"), use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+
+m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2"),
+                                         sink = FALSE),
+                           M1 = list(type = "SFO"),
+                           M2 = list(type = "SFO"), use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+m_synth_DFOP_lin <- mkinmod(parent = list(type = "DFOP", to = "M1"),
+                            M1 = list(type = "SFO", to = "M2"),
+                            M2 = list(type = "SFO"), use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2"),
+                                          sink = FALSE),
+                            M1 = list(type = "SFO"),
+                            M2 = list(type = "SFO"), use_of_ff = "max")
+#> Temporary DLL for differentials generated and loaded
+
+# The model predictions without intentional error were generated as follows
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+
+d_synth_SFO_lin <- mkinpredict(m_synth_SFO_lin,
+                               c(k_parent = 0.7, f_parent_to_M1 = 0.8,
+                                 k_M1 = 0.3, f_M1_to_M2 = 0.7,
+                                 k_M2 = 0.02),
+                               c(parent = 100, M1 = 0, M2 = 0),
+                               sampling_times)
+
+d_synth_DFOP_lin <- mkinpredict(m_synth_DFOP_lin,
+                                c(k1 = 0.2, k2 = 0.02, g = 0.5,
+                                  f_parent_to_M1 = 0.5, k_M1 = 0.3,
+                                  f_M1_to_M2 = 0.7, k_M2 = 0.02),
+                                 c(parent = 100, M1 = 0, M2 = 0),
+                                 sampling_times)
+
+d_synth_SFO_par <- mkinpredict(m_synth_SFO_par,
+                               c(k_parent = 0.2,
+                                 f_parent_to_M1 = 0.8, k_M1 = 0.01,
+                                 f_parent_to_M2 = 0.2, k_M2 = 0.02),
+                                 c(parent = 100, M1 = 0, M2 = 0),
+                                 sampling_times)
+
+d_synth_DFOP_par <- mkinpredict(m_synth_DFOP_par,
+                               c(k1 = 0.3, k2 = 0.02, g = 0.7,
+                                 f_parent_to_M1 = 0.6, k_M1 = 0.04,
+                                 f_parent_to_M2 = 0.4, k_M2 = 0.01),
+                                 c(parent = 100, M1 = 0, M2 = 0),
+                                 sampling_times)
+
+# Construct names for datasets with errors
+d_synth_names = paste0("d_synth_", c("SFO_lin", "SFO_par",
+                                     "DFOP_lin", "DFOP_par"))
+
+# Original function used or adding errors. The add_err function now published
+# with this package is a slightly generalised version where the names of
+# secondary compartments that should have an initial value of zero (M1 and M2
+# in this case) are not hardcoded any more.
+# add_err = function(d, sdfunc, LOD = 0.1, reps = 2, seed = 123456789)
+# {
+#   set.seed(seed)
+#   d_long = mkin_wide_to_long(d, time = "time")
+#   d_rep = data.frame(lapply(d_long, rep, each = 2))
+#   d_rep$value = rnorm(length(d_rep$value), d_rep$value, sdfunc(d_rep$value))
+#
+#   d_rep[d_rep$time == 0 & d_rep$name %in% c("M1", "M2"), "value"] <- 0
+#   d_NA <- transform(d_rep, value = ifelse(value < LOD, NA, value))
+#   d_NA$value <- round(d_NA$value, 1)
+#   return(d_NA)
+# }
+
+# The following is the simplified version of the two-component model of Rocke
+# and Lorenzato (1995)
+sdfunc_twocomp = function(value, sd_low, rsd_high) {
+  sqrt(sd_low^2 + value^2 * rsd_high^2)
+}
+
+# Add the errors.
+for (d_synth_name in d_synth_names)
+{
+  d_synth = get(d_synth_name)
+  assign(paste0(d_synth_name, "_a"), add_err(d_synth, function(value) 3))
+  assign(paste0(d_synth_name, "_b"), add_err(d_synth, function(value) 7))
+  assign(paste0(d_synth_name, "_c"), add_err(d_synth,
+                           function(value) sdfunc_twocomp(value, 0.5, 0.07)))
+
+}
+
+d_synth_err_names = c(
+  paste(rep(d_synth_names, each = 3), letters[1:3], sep = "_")
+)
+
+# This is just one example of an evaluation using the kinetic model used for
+# the generation of the data
+  fit <- mkinfit(m_synth_SFO_lin, synthetic_data_for_UBA_2014[[1]]$data,
+                 quiet = TRUE)
+  plot_sep(fit)
+
+  summary(fit)
+#> mkin version used for fitting:    1.2.2 
+#> R version used for fitting:       4.2.2 
+#> Date of fit:     Thu Nov 24 08:11:54 2022 
+#> Date of summary: Thu Nov 24 08:11:54 2022 
+#> 
+#> Equations:
+#> d_parent/dt = - k_parent * parent
+#> d_M1/dt = + f_parent_to_M1 * k_parent * parent - k_M1 * M1
+#> d_M2/dt = + f_M1_to_M2 * k_M1 * M1 - k_M2 * M2
+#> 
+#> Model predictions using solution type deSolve 
+#> 
+#> Fitted using 833 model solutions performed in 0.574 s
+#> 
+#> Error model: Constant variance 
+#> 
+#> Error model algorithm: OLS 
+#> 
+#> Starting values for parameters to be optimised:
+#>                   value   type
+#> parent_0       101.3500  state
+#> k_parent         0.1000 deparm
+#> k_M1             0.1001 deparm
+#> k_M2             0.1002 deparm
+#> f_parent_to_M1   0.5000 deparm
+#> f_M1_to_M2       0.5000 deparm
+#> 
+#> Starting values for the transformed parameters actually optimised:
+#>                      value lower upper
+#> parent_0        101.350000  -Inf   Inf
+#> log_k_parent     -2.302585  -Inf   Inf
+#> log_k_M1         -2.301586  -Inf   Inf
+#> log_k_M2         -2.300587  -Inf   Inf
+#> f_parent_qlogis   0.000000  -Inf   Inf
+#> f_M1_qlogis       0.000000  -Inf   Inf
+#> 
+#> Fixed parameter values:
+#>      value  type
+#> M1_0     0 state
+#> M2_0     0 state
+#> 
+#> Results:
+#> 
+#>        AIC      BIC    logLik
+#>   188.7274 200.3723 -87.36368
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>                 Estimate Std. Error   Lower    Upper
+#> parent_0        102.1000    1.57000 98.8600 105.3000
+#> log_k_parent     -0.3020    0.03885 -0.3812  -0.2229
+#> log_k_M1         -1.2070    0.07123 -1.3520  -1.0620
+#> log_k_M2         -3.9010    0.06571 -4.0350  -3.7670
+#> f_parent_qlogis   1.2010    0.23530  0.7216   1.6800
+#> f_M1_qlogis       0.9589    0.24890  0.4520   1.4660
+#> sigma             2.2730    0.25740  1.7490   2.7970
+#> 
+#> Parameter correlation:
+#>                   parent_0 log_k_parent   log_k_M1   log_k_M2 f_parent_qlogis
+#> parent_0         1.000e+00    3.933e-01 -1.605e-01  2.819e-02      -4.624e-01
+#> log_k_parent     3.933e-01    1.000e+00 -4.082e-01  7.166e-02      -5.682e-01
+#> log_k_M1        -1.605e-01   -4.082e-01  1.000e+00 -3.929e-01       7.478e-01
+#> log_k_M2         2.819e-02    7.166e-02 -3.929e-01  1.000e+00      -2.658e-01
+#> f_parent_qlogis -4.624e-01   -5.682e-01  7.478e-01 -2.658e-01       1.000e+00
+#> f_M1_qlogis      1.614e-01    4.102e-01 -8.109e-01  5.419e-01      -8.605e-01
+#> sigma           -2.900e-08   -8.030e-09 -2.741e-08  3.938e-08      -2.681e-08
+#>                 f_M1_qlogis      sigma
+#> parent_0          1.614e-01 -2.900e-08
+#> log_k_parent      4.102e-01 -8.030e-09
+#> log_k_M1         -8.109e-01 -2.741e-08
+#> log_k_M2          5.419e-01  3.938e-08
+#> f_parent_qlogis  -8.605e-01 -2.681e-08
+#> f_M1_qlogis       1.000e+00  4.971e-08
+#> sigma             4.971e-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       102.10000  65.000 7.281e-36 98.86000 105.30000
+#> k_parent         0.73930  25.740 2.948e-23  0.68310   0.80020
+#> k_M1             0.29920  14.040 1.577e-15  0.25880   0.34590
+#> k_M2             0.02023  15.220 1.653e-16  0.01769   0.02312
+#> f_parent_to_M1   0.76870  18.370 7.295e-19  0.67300   0.84290
+#> f_M1_to_M2       0.72290  14.500 6.418e-16  0.61110   0.81240
+#> sigma            2.27300   8.832 2.161e-10  1.74900   2.79700
+#> 
+#> FOCUS Chi2 error levels in percent:
+#>          err.min n.optim df
+#> All data   8.454       6 17
+#> parent     8.660       2  6
+#> M1        10.583       2  5
+#> M2         3.586       2  6
+#> 
+#> Resulting formation fractions:
+#>                 ff
+#> parent_M1   0.7687
+#> parent_sink 0.2313
+#> M1_M2       0.7229
+#> M1_sink     0.2771
+#> 
+#> Estimated disappearance times:
+#>           DT50    DT90
+#> parent  0.9376   3.114
+#> M1      2.3170   7.697
+#> M2     34.2689 113.839
+#> 
+#> Data:
+#>  time variable observed  predicted residual
+#>     0   parent    101.5  1.021e+02 -0.56248
+#>     0   parent    101.2  1.021e+02 -0.86248
+#>     1   parent     53.9  4.873e+01  5.17118
+#>     1   parent     47.5  4.873e+01 -1.22882
+#>     3   parent     10.4  1.111e+01 -0.70773
+#>     3   parent      7.6  1.111e+01 -3.50773
+#>     7   parent      1.1  5.772e-01  0.52283
+#>     7   parent      0.3  5.772e-01 -0.27717
+#>    14   parent      3.5  3.264e-03  3.49674
+#>    28   parent      3.2  1.045e-07  3.20000
+#>    90   parent      0.6  9.530e-10  0.60000
+#>   120   parent      3.5 -5.940e-10  3.50000
+#>     1       M1     36.4  3.479e+01  1.61088
+#>     1       M1     37.4  3.479e+01  2.61088
+#>     3       M1     34.3  3.937e+01 -5.07027
+#>     3       M1     39.8  3.937e+01  0.42973
+#>     7       M1     15.1  1.549e+01 -0.38715
+#>     7       M1     17.8  1.549e+01  2.31285
+#>    14       M1      5.8  1.995e+00  3.80469
+#>    14       M1      1.2  1.995e+00 -0.79531
+#>    60       M1      0.5  2.111e-06  0.50000
+#>    90       M1      3.2 -9.670e-10  3.20000
+#>   120       M1      1.5  7.670e-10  1.50000
+#>   120       M1      0.6  7.670e-10  0.60000
+#>     1       M2      4.8  4.455e+00  0.34517
+#>     3       M2     20.9  2.153e+01 -0.62527
+#>     3       M2     19.3  2.153e+01 -2.22527
+#>     7       M2     42.0  4.192e+01  0.07941
+#>     7       M2     43.1  4.192e+01  1.17941
+#>    14       M2     49.4  4.557e+01  3.83353
+#>    14       M2     44.3  4.557e+01 -1.26647
+#>    28       M2     34.6  3.547e+01 -0.87275
+#>    28       M2     33.0  3.547e+01 -2.47275
+#>    60       M2     18.8  1.858e+01  0.21837
+#>    60       M2     17.6  1.858e+01 -0.98163
+#>    90       M2     10.6  1.013e+01  0.47130
+#>    90       M2     10.8  1.013e+01  0.67130
+#>   120       M2      9.8  5.521e+00  4.27893
+#>   120       M2      3.3  5.521e+00 -2.22107
+# }
+