Lists model equations, initial parameter values, optimised parameters for fixed effects (population), random effects (deviations from the population mean) and residual error model, as well as the resulting endpoints such as formation fractions and DT50 values. Optionally (default is FALSE), the data are listed in full.
Arguments
- object
an object of class nlme.mmkin
- data
logical, indicating whether the full data should be included in the summary.
- verbose
Should the summary be verbose?
- distimes
logical, indicating whether DT50 and DT90 values should be included.
- alpha
error level for confidence interval estimation from the t distribution
- ...
optional arguments passed to methods like
print.- x
an object of class summary.nlme.mmkin
- digits
Number of digits to use for printing
Value
The summary function returns a list based on the nlme object obtained in the fit, with at least the following additional components
- nlmeversion, mkinversion, Rversion
The nlme, mkin and R versions used
- date.fit, date.summary
The dates where the fit and the summary were produced
- diffs
The differential equations used in the degradation model
- use_of_ff
Was maximum or minimum use made of formation fractions
- data
The data
- confint_trans
Transformed parameters as used in the optimisation, with confidence intervals
- confint_back
Backtransformed parameters, with confidence intervals if available
- ff
The estimated formation fractions derived from the fitted model.
- distimes
The DT50 and DT90 values for each observed variable.
- SFORB
If applicable, eigenvalues of SFORB components of the model.
The print method is called for its side effect, i.e. printing the summary.
Author
Johannes Ranke for the mkin specific parts José Pinheiro and Douglas Bates for the components inherited from nlme
Examples
# Generate five datasets following SFO kinetics
sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
dt50_sfo_in_pop <- 50
k_in_pop <- log(2) / dt50_sfo_in_pop
set.seed(1234)
k_in <- rlnorm(5, log(k_in_pop), 0.5)
SFO <- mkinmod(parent = mkinsub("SFO"))
pred_sfo <- function(k) {
mkinpredict(SFO,
c(k_parent = k),
c(parent = 100),
sampling_times)
}
ds_sfo_mean <- lapply(k_in, pred_sfo)
names(ds_sfo_mean) <- paste("ds", 1:5)
set.seed(12345)
ds_sfo_syn <- lapply(ds_sfo_mean, function(ds) {
add_err(ds,
sdfunc = function(value) sqrt(1^2 + value^2 * 0.07^2),
n = 1)[[1]]
})
# \dontrun{
# Evaluate using mmkin and nlme
library(nlme)
f_mmkin <- mmkin("SFO", ds_sfo_syn, quiet = TRUE, error_model = "tc", cores = 1)
#> Warning: Optimisation did not converge:
#> iteration limit reached without convergence (10)
f_nlme <- nlme(f_mmkin)
summary(f_nlme, data = TRUE)
#> nlme version used for fitting: 3.1.166
#> mkin version used for pre-fitting: 1.2.10
#> R version used for fitting: 4.4.2
#> Date of fit: Sun Feb 16 17:03:13 2025
#> Date of summary: Sun Feb 16 17:03:13 2025
#>
#> Equations:
#> d_parent/dt = - k_parent * parent
#>
#> Data:
#> 90 observations of 1 variable(s) grouped in 5 datasets
#>
#> Model predictions using solution type analytical
#>
#> Fitted in 0.189 s using 4 iterations
#>
#> Variance model: Two-component variance function
#>
#> Mean of starting values for individual parameters:
#> parent_0 log_k_parent
#> 101.569 -4.454
#>
#> Fixed degradation parameter values:
#> None
#>
#> Results:
#>
#> AIC BIC logLik
#> 584.5 599.5 -286.2
#>
#> Optimised, transformed parameters with symmetric confidence intervals:
#> lower est. upper
#> parent_0 99.371 101.592 103.814
#> log_k_parent -4.973 -4.449 -3.926
#>
#> Correlation:
#> parnt_0
#> log_k_parent 0.0507
#>
#> Random effects:
#> Formula: list(parent_0 ~ 1, log_k_parent ~ 1)
#> Level: ds
#> Structure: Diagonal
#> parent_0 log_k_parent Residual
#> StdDev: 6.921e-05 0.5863 1
#>
#> Variance function:
#> Structure: Constant plus proportion of variance covariate
#> Formula: ~fitted(.)
#> Parameter estimates:
#> const prop
#> 0.0001208313 0.0789967985
#>
#> Backtransformed parameters with asymmetric confidence intervals:
#> lower est. upper
#> parent_0 99.370882 101.59243 103.81398
#> k_parent 0.006923 0.01168 0.01972
#>
#> Estimated disappearance times:
#> DT50 DT90
#> parent 59.32 197.1
#>
#> Data:
#> ds name time observed predicted residual std standardized
#> ds 1 parent 0 104.1 101.592 2.50757 8.0255 0.312451
#> ds 1 parent 0 105.0 101.592 3.40757 8.0255 0.424594
#> ds 1 parent 1 98.5 100.796 -2.29571 7.9625 -0.288313
#> ds 1 parent 1 96.1 100.796 -4.69571 7.9625 -0.589725
#> ds 1 parent 3 101.9 99.221 2.67904 7.8381 0.341796
#> ds 1 parent 3 85.2 99.221 -14.02096 7.8381 -1.788812
#> ds 1 parent 7 99.1 96.145 2.95512 7.5951 0.389081
#> ds 1 parent 7 93.0 96.145 -3.14488 7.5951 -0.414065
#> ds 1 parent 14 88.1 90.989 -2.88944 7.1879 -0.401987
#> ds 1 parent 14 84.1 90.989 -6.88944 7.1879 -0.958480
#> ds 1 parent 28 80.2 81.493 -1.29305 6.4377 -0.200857
#> ds 1 parent 28 91.3 81.493 9.80695 6.4377 1.523364
#> ds 1 parent 60 65.1 63.344 1.75642 5.0039 0.351008
#> ds 1 parent 60 65.8 63.344 2.45642 5.0039 0.490898
#> ds 1 parent 90 47.8 50.018 -2.21764 3.9512 -0.561252
#> ds 1 parent 90 53.5 50.018 3.48236 3.9512 0.881335
#> ds 1 parent 120 37.6 39.495 -1.89515 3.1200 -0.607423
#> ds 1 parent 120 39.3 39.495 -0.19515 3.1200 -0.062549
#> ds 2 parent 0 107.9 101.592 6.30757 8.0255 0.785943
#> ds 2 parent 0 102.1 101.592 0.50757 8.0255 0.063245
#> ds 2 parent 1 103.8 100.058 3.74159 7.9043 0.473361
#> ds 2 parent 1 108.6 100.058 8.54159 7.9043 1.080626
#> ds 2 parent 3 91.0 97.060 -6.05952 7.6674 -0.790297
#> ds 2 parent 3 84.9 97.060 -12.15952 7.6674 -1.585874
#> ds 2 parent 7 79.3 91.329 -12.02867 7.2147 -1.667251
#> ds 2 parent 7 100.9 91.329 9.57133 7.2147 1.326647
#> ds 2 parent 14 77.3 82.102 -4.80185 6.4858 -0.740366
#> ds 2 parent 14 83.5 82.102 1.39815 6.4858 0.215571
#> ds 2 parent 28 66.8 66.351 0.44945 5.2415 0.085748
#> ds 2 parent 28 63.3 66.351 -3.05055 5.2415 -0.582002
#> ds 2 parent 60 40.8 40.775 0.02474 3.2211 0.007679
#> ds 2 parent 60 44.8 40.775 4.02474 3.2211 1.249485
#> ds 2 parent 90 27.8 25.832 1.96762 2.0407 0.964198
#> ds 2 parent 90 27.0 25.832 1.16762 2.0407 0.572171
#> ds 2 parent 120 15.2 16.366 -1.16561 1.2928 -0.901595
#> ds 2 parent 120 15.5 16.366 -0.86561 1.2928 -0.669547
#> ds 3 parent 0 97.7 101.592 -3.89243 8.0255 -0.485009
#> ds 3 parent 0 88.2 101.592 -13.39243 8.0255 -1.668740
#> ds 3 parent 1 109.9 99.218 10.68196 7.8379 1.362858
#> ds 3 parent 1 97.8 99.218 -1.41804 7.8379 -0.180921
#> ds 3 parent 3 100.5 94.634 5.86555 7.4758 0.784603
#> ds 3 parent 3 77.4 94.634 -17.23445 7.4758 -2.305360
#> ds 3 parent 7 78.3 86.093 -7.79273 6.8011 -1.145813
#> ds 3 parent 7 90.3 86.093 4.20727 6.8011 0.618620
#> ds 3 parent 14 76.0 72.958 3.04222 5.7634 0.527848
#> ds 3 parent 14 79.1 72.958 6.14222 5.7634 1.065722
#> ds 3 parent 28 46.0 52.394 -6.39404 4.1390 -1.544842
#> ds 3 parent 28 53.4 52.394 1.00596 4.1390 0.243046
#> ds 3 parent 60 25.1 24.582 0.51786 1.9419 0.266676
#> ds 3 parent 60 21.4 24.582 -3.18214 1.9419 -1.638664
#> ds 3 parent 90 11.0 12.092 -1.09202 0.9552 -1.143199
#> ds 3 parent 90 14.2 12.092 2.10798 0.9552 2.206777
#> ds 3 parent 120 5.8 5.948 -0.14810 0.4699 -0.315178
#> ds 3 parent 120 6.1 5.948 0.15190 0.4699 0.323282
#> ds 4 parent 0 95.3 101.592 -6.29243 8.0255 -0.784057
#> ds 4 parent 0 102.0 101.592 0.40757 8.0255 0.050784
#> ds 4 parent 1 104.4 101.125 3.27549 7.9885 0.410025
#> ds 4 parent 1 105.4 101.125 4.27549 7.9885 0.535205
#> ds 4 parent 3 113.7 100.195 13.50487 7.9151 1.706218
#> ds 4 parent 3 82.3 100.195 -17.89513 7.9151 -2.260886
#> ds 4 parent 7 98.1 98.362 -0.26190 7.7703 -0.033706
#> ds 4 parent 7 87.8 98.362 -10.56190 7.7703 -1.359270
#> ds 4 parent 14 97.9 95.234 2.66590 7.5232 0.354357
#> ds 4 parent 14 104.8 95.234 9.56590 7.5232 1.271521
#> ds 4 parent 28 85.0 89.274 -4.27372 7.0523 -0.606001
#> ds 4 parent 28 77.2 89.274 -12.07372 7.0523 -1.712017
#> ds 4 parent 60 82.2 77.013 5.18661 6.0838 0.852526
#> ds 4 parent 60 86.1 77.013 9.08661 6.0838 1.493571
#> ds 4 parent 90 70.5 67.053 3.44692 5.2970 0.650733
#> ds 4 parent 90 61.7 67.053 -5.35308 5.2970 -1.010591
#> ds 4 parent 120 60.0 58.381 1.61905 4.6119 0.351058
#> ds 4 parent 120 56.4 58.381 -1.98095 4.6119 -0.429530
#> ds 5 parent 0 92.6 101.592 -8.99243 8.0255 -1.120485
#> ds 5 parent 0 116.5 101.592 14.90757 8.0255 1.857531
#> ds 5 parent 1 108.0 99.914 8.08560 7.8929 1.024413
#> ds 5 parent 1 104.9 99.914 4.98560 7.8929 0.631655
#> ds 5 parent 3 100.5 96.641 3.85898 7.6343 0.505477
#> ds 5 parent 3 89.5 96.641 -7.14102 7.6343 -0.935383
#> ds 5 parent 7 91.7 90.412 1.28752 7.1423 0.180267
#> ds 5 parent 7 95.1 90.412 4.68752 7.1423 0.656304
#> ds 5 parent 14 82.2 80.463 1.73715 6.3563 0.273295
#> ds 5 parent 14 84.5 80.463 4.03715 6.3563 0.635141
#> ds 5 parent 28 60.5 63.728 -3.22788 5.0343 -0.641178
#> ds 5 parent 28 72.8 63.728 9.07212 5.0343 1.802062
#> ds 5 parent 60 38.3 37.399 0.90061 2.9544 0.304835
#> ds 5 parent 60 40.7 37.399 3.30061 2.9544 1.117174
#> ds 5 parent 90 22.5 22.692 -0.19165 1.7926 -0.106913
#> ds 5 parent 90 20.8 22.692 -1.89165 1.7926 -1.055273
#> ds 5 parent 120 13.4 13.768 -0.36790 1.0876 -0.338259
#> ds 5 parent 120 13.8 13.768 0.03210 1.0876 0.029517
# }