Summary method for class

+ + +

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.

+ +

# S3 method for nlme.mmkin
+summary(
+  object,
+  data = FALSE,
+  verbose = FALSE,
+  distimes = TRUE,
+  alpha = 0.05,
+  ...
+)
+
+# S3 method for summary.nlme.mmkin
+print(x, digits = max(3, getOption("digits") - 3), verbose = x$verbose, ...)

+ +

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

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)
+
+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]]
+})
+
+# Evaluate using mmkin and nlme
+library(nlme)
+f_mmkin <- mmkin("SFO", ds_sfo_syn, quiet = TRUE, error_model = "tc", cores = 1)
+
#> Warning: Shapiro-Wilk test for standardized residuals: p =  0.00371
f_nlme <- nlme(f_mmkin)
+
#> Warning: Iteration 3, LME step: nlminb() did not converge (code = 1). PORT message: false convergence (8)
summary(f_nlme, data = TRUE)
+
#> nlme version used for fitting:      3.1.150.1 
+#> mkin version used for pre-fitting:  0.9.50.4 
+#> R version used for fitting:         4.0.3 
+#> Date of fit:     Tue Oct 27 15:25:23 2020 
+#> Date of summary: Tue Oct 27 15:25:23 2020 
+#> 
+#> 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 0.581 s using 5 iterations
+#> 
+#> Variance model: Two-component variance function 
+#> 
+#> Mean of starting values for individual parameters:
+#>     parent_0 log_k_parent 
+#>    97.849556    -4.455036 
+#> 
+#> Fixed degradation parameter values:
+#> None
+#> 
+#> Results:
+#> 
+#>       AIC      BIC   logLik
+#>   555.792 570.7908 -271.896
+#> 
+#> Optimised, transformed parameters with symmetric confidence intervals:
+#>                  lower      est.     upper
+#> parent_0     94.701336 97.763446 100.82556
+#> log_k_parent -5.007574 -4.461767  -3.91596
+#> 
+#> Correlation: 
+#>              prnt_0
+#> log_k_parent 0.024 
+#> 
+#> Backtransformed parameters with asymmetric confidence intervals:
+#>                 lower        est.        upper
+#> parent_0 94.701335804 97.76344625 100.82555670
+#> k_parent  0.006687109  0.01154195   0.01992142
+#> Random effects:
+#>  Formula: list(parent_0 ~ 1, log_k_parent ~ 1)
+#>  Level: ds
+#>  Structure: Diagonal
+#>         parent_0 log_k_parent Residual
+#> StdDev: 16.65969     3.516961 5.709013
+#> 
+#> Variance function:
+#>  Structure: Constant plus proportion of variance covariate
+#>  Formula: ~fitted(.) 
+#>  Parameter estimates:
+#>      const       prop 
+#> 1.55075176 0.05680853 
+#> 
+#> Estimated disappearance times:
+#>         DT50  DT90
+#> parent 60.05 199.5
+#> 
+#> Data:
+#>    ds   name time observed predicted residual   std standardized
+#>  ds 1 parent    0    103.6     97.42  6.17540 5.748     1.074413
+#>  ds 1 parent    0     95.9     97.42 -1.52460 5.748    -0.265253
+#>  ds 1 parent    1     95.4     96.72 -1.31719 5.709    -0.230721
+#>  ds 1 parent    1     95.3     96.72 -1.41719 5.709    -0.248237
+#>  ds 1 parent    3     91.6     95.32 -3.71774 5.633    -0.660046
+#>  ds 1 parent    3     94.5     95.32 -0.81774 5.633    -0.145181
+#>  ds 1 parent    7     88.1     92.58 -4.47930 5.483    -0.816920
+#>  ds 1 parent    7     89.6     92.58 -2.97930 5.483    -0.543355
+#>  ds 1 parent   14     90.3     87.97  2.32502 5.233     0.444318
+#>  ds 1 parent   14     96.0     87.97  8.02502 5.233     1.533602
+#>  ds 1 parent   28     80.2     79.44  0.75809 4.772     0.158862
+#>  ds 1 parent   28     77.9     79.44 -1.54191 4.772    -0.323118
+#>  ds 1 parent   60     59.3     62.92 -3.61742 3.896    -0.928458
+#>  ds 1 parent   60     59.6     62.92 -3.31742 3.896    -0.851459
+#>  ds 1 parent   90     59.4     50.56  8.83825 3.264     2.707613
+#>  ds 1 parent   90     51.0     50.56  0.43825 3.264     0.134260
+#>  ds 1 parent  120     38.8     40.63 -1.83247 2.781    -0.658968
+#>  ds 1 parent  120     38.9     40.63 -1.73247 2.781    -0.623007
+#>  ds 2 parent    0    103.2     97.17  6.02995 5.734     1.051655
+#>  ds 2 parent    0     95.1     97.17 -2.07005 5.734    -0.361027
+#>  ds 2 parent    1     88.3     95.59 -7.28901 5.647    -1.290694
+#>  ds 2 parent    1    102.4     95.59  6.81099 5.647     1.206048
+#>  ds 2 parent    3     88.4     92.50 -4.10371 5.479    -0.748984
+#>  ds 2 parent    3     95.2     92.50  2.69629 5.479     0.492110
+#>  ds 2 parent    7     83.5     86.63 -3.12863 5.160    -0.606349
+#>  ds 2 parent    7     96.4     86.63  9.77137 5.160     1.893751
+#>  ds 2 parent   14     77.3     77.23  0.06920 4.653     0.014871
+#>  ds 2 parent   14     76.0     77.23 -1.23080 4.653    -0.264497
+#>  ds 2 parent   28     61.7     61.38  0.31692 3.816     0.083043
+#>  ds 2 parent   28     56.5     61.38 -4.88308 3.816    -1.279513
+#>  ds 2 parent   60     35.1     36.31 -1.21343 2.581    -0.470178
+#>  ds 2 parent   60     32.2     36.31 -4.11343 2.581    -1.593868
+#>  ds 2 parent   90     21.2     22.20 -0.99906 1.999    -0.499832
+#>  ds 2 parent   90     23.3     22.20  1.10094 1.999     0.550800
+#>  ds 2 parent  120     14.1     13.57  0.52931 1.732     0.305638
+#>  ds 2 parent  120     16.9     13.57  3.32931 1.732     1.922443
+#>  ds 3 parent    0     92.4     94.12 -1.71979 5.567    -0.308917
+#>  ds 3 parent    0     94.0     94.12 -0.11979 5.567    -0.021517
+#>  ds 3 parent    1     95.7     91.97  3.72634 5.450     0.683712
+#>  ds 3 parent    1     90.8     91.97 -1.17366 5.450    -0.215343
+#>  ds 3 parent    3     86.7     87.83 -1.12709 5.225    -0.215720
+#>  ds 3 parent    3     85.8     87.83 -2.02709 5.225    -0.387976
+#>  ds 3 parent    7     77.1     80.09 -2.98635 4.807    -0.621300
+#>  ds 3 parent    7     81.5     80.09  1.41365 4.807     0.294104
+#>  ds 3 parent   14     69.1     68.15  0.95467 4.170     0.228922
+#>  ds 3 parent   14     62.4     68.15 -5.74533 4.170    -1.377682
+#>  ds 3 parent   28     49.1     49.34 -0.23911 3.203    -0.074644
+#>  ds 3 parent   28     47.2     49.34 -2.13911 3.203    -0.667787
+#>  ds 3 parent   60     21.9     23.58 -1.68477 2.049    -0.822090
+#>  ds 3 parent   60     23.6     23.58  0.01523 2.049     0.007431
+#>  ds 3 parent   90     12.4     11.81  0.59388 1.690     0.351500
+#>  ds 3 parent   90     13.8     11.81  1.99388 1.690     1.180112
+#>  ds 3 parent  120      4.9      5.91 -1.00993 1.587    -0.636506
+#>  ds 3 parent  120      7.5      5.91  1.59007 1.587     1.002137
+#>  ds 4 parent    0     91.8    101.72 -9.92097 5.983    -1.658171
+#>  ds 4 parent    0    104.6    101.72  2.87903 5.983     0.481194
+#>  ds 4 parent    1    117.5    101.27 16.23017 5.958     2.723944
+#>  ds 4 parent    1     99.3    101.27 -1.96983 5.958    -0.330602
+#>  ds 4 parent    3     94.0    100.37 -6.37355 5.909    -1.078583
+#>  ds 4 parent    3     98.7    100.37 -1.67355 5.909    -0.283212
+#>  ds 4 parent    7    109.2     98.60 10.59529 5.812     1.822915
+#>  ds 4 parent    7     89.2     98.60 -9.40471 5.812    -1.618075
+#>  ds 4 parent   14    103.3     95.58  7.71609 5.647     1.366386
+#>  ds 4 parent   14    103.0     95.58  7.41609 5.647     1.313261
+#>  ds 4 parent   28     90.8     89.82  0.98290 5.333     0.184310
+#>  ds 4 parent   28     88.7     89.82 -1.11710 5.333    -0.209477
+#>  ds 4 parent   60     74.8     77.91 -3.10870 4.690    -0.662879
+#>  ds 4 parent   60     75.3     77.91 -2.60870 4.690    -0.556262
+#>  ds 4 parent   90     71.1     68.18  2.91738 4.172     0.699234
+#>  ds 4 parent   90     78.0     68.18  9.81738 4.172     2.353017
+#>  ds 4 parent  120     59.1     59.67 -0.57073 3.728    -0.153107
+#>  ds 4 parent  120     53.8     59.67 -5.87073 3.728    -1.574902
+#>  ds 5 parent    0     94.9     98.38 -3.48183 5.800    -0.600307
+#>  ds 5 parent    0    101.8     98.38  3.41817 5.800     0.589332
+#>  ds 5 parent    1     96.1     96.75 -0.65141 5.711    -0.114065
+#>  ds 5 parent    1     97.1     96.75  0.34859 5.711     0.061040
+#>  ds 5 parent    3     93.8     93.57  0.22881 5.537     0.041323
+#>  ds 5 parent    3     85.8     93.57 -7.77119 5.537    -1.403444
+#>  ds 5 parent    7     87.6     87.52  0.07909 5.208     0.015186
+#>  ds 5 parent    7     94.0     87.52  6.47909 5.208     1.244026
+#>  ds 5 parent   14     82.5     77.86  4.64101 4.687     0.990182
+#>  ds 5 parent   14     81.7     77.86  3.84101 4.687     0.819498
+#>  ds 5 parent   28     60.0     61.62 -1.61729 3.829    -0.422433
+#>  ds 5 parent   28     61.0     61.62 -0.61729 3.829    -0.161236
+#>  ds 5 parent   60     32.5     36.10 -3.59608 2.571    -1.398750
+#>  ds 5 parent   60     35.5     36.10 -0.59608 2.571    -0.231854
+#>  ds 5 parent   90     21.8     21.86 -0.06415 1.987    -0.032287
+#>  ds 5 parent   90     24.4     21.86  2.53585 1.987     1.276317
+#>  ds 5 parent  120     14.1     13.24  0.85643 1.724     0.496877
+#>  ds 5 parent  120     12.1     13.24 -1.14357 1.724    -0.663473

+

+ +

Summary method for class "nlme.mmkin"

Arguments

Value

Author

Examples