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.

+ +

Usage

# S3 method for class 'saem.mmkin'
+summary(
+  object,
+  data = FALSE,
+  verbose = FALSE,
+  covariates = NULL,
+  covariate_quantile = 0.5,
+  distimes = TRUE,
+  ...
+)
+
+# S3 method for class 'summary.saem.mmkin'
+print(x, digits = max(3, getOption("digits") - 3), verbose = x$verbose, ...)

+ +

Arguments

+ + +

object: an object of class saem.mmkin
data: logical, indicating whether the full data should be included in +the summary.
verbose: Should the summary be verbose?
covariates: Numeric vector with covariate values for all variables in +any covariate models in the object. If given, it overrides 'covariate_quantile'.
covariate_quantile: This argument only has an effect if the fitted +object has covariate models. If so, the default is to show endpoints +for the median of the covariate values (50th percentile).
distimes: logical, indicating whether DT50 and DT90 values should be +included.
...: optional arguments passed to methods like print.
x: an object of class summary.saem.mmkin
digits: Number of digits to use for printing

Value

The summary function returns a list based on the saemix::SaemixObject +obtained in the fit, with at least the following additional components

saemixversion, mkinversion, Rversion: The saemix, 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
confint_errmod: Error model parameters with confidence intervals
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 +saemix authors for the parts inherited from saemix.

+ +

Examples

# Generate five datasets following DFOP-SFO kinetics
+sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
+dfop_sfo <- mkinmod(parent = mkinsub("DFOP", "m1"),
+ m1 = mkinsub("SFO"), quiet = TRUE)
+set.seed(1234)
+k1_in <- rlnorm(5, log(0.1), 0.3)
+k2_in <- rlnorm(5, log(0.02), 0.3)
+g_in <- plogis(rnorm(5, qlogis(0.5), 0.3))
+f_parent_to_m1_in <- plogis(rnorm(5, qlogis(0.3), 0.3))
+k_m1_in <- rlnorm(5, log(0.02), 0.3)
+
+pred_dfop_sfo <- function(k1, k2, g, f_parent_to_m1, k_m1) {
+  mkinpredict(dfop_sfo,
+    c(k1 = k1, k2 = k2, g = g, f_parent_to_m1 = f_parent_to_m1, k_m1 = k_m1),
+    c(parent = 100, m1 = 0),
+    sampling_times)
+}
+
+ds_mean_dfop_sfo <- lapply(1:5, function(i) {
+  mkinpredict(dfop_sfo,
+    c(k1 = k1_in[i], k2 = k2_in[i], g = g_in[i],
+      f_parent_to_m1 = f_parent_to_m1_in[i], k_m1 = k_m1_in[i]),
+    c(parent = 100, m1 = 0),
+    sampling_times)
+})
+names(ds_mean_dfop_sfo) <- paste("ds", 1:5)
+
+ds_syn_dfop_sfo <- lapply(ds_mean_dfop_sfo, function(ds) {
+  add_err(ds,
+    sdfunc = function(value) sqrt(1^2 + value^2 * 0.07^2),
+    n = 1)[[1]]
+})
+
+# \dontrun{
+# Evaluate using mmkin and saem
+f_mmkin_dfop_sfo <- mmkin(list(dfop_sfo), ds_syn_dfop_sfo,
+  quiet = TRUE, error_model = "tc", cores = 5)
+f_saem_dfop_sfo <- saem(f_mmkin_dfop_sfo)
+print(f_saem_dfop_sfo)
+#> Kinetic nonlinear mixed-effects model fit by SAEM
+#> Structural model:
+#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+#>            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+#>            * parent
+#> d_m1/dt = + f_parent_to_m1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
+#>            * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+#>            exp(-k2 * time))) * parent - k_m1 * m1
+#> 
+#> Data:
+#> 171 observations of 2 variable(s) grouped in 5 datasets
+#> 
+#> Likelihood computed by importance sampling
+#>     AIC   BIC logLik
+#>   810.8 805.4 -391.4
+#> 
+#> Fitted parameters:
+#>                      estimate     lower     upper
+#> parent_0           100.966822  97.90584 104.02780
+#> log_k_m1            -4.076164  -4.17485  -3.97748
+#> f_parent_qlogis     -0.940902  -1.35358  -0.52823
+#> log_k1              -2.363988  -2.71690  -2.01107
+#> log_k2              -4.060016  -4.21743  -3.90260
+#> g_qlogis            -0.029999  -0.44766   0.38766
+#> a.1                  0.876272   0.67790   1.07464
+#> b.1                  0.079594   0.06521   0.09398
+#> SD.parent_0          0.076322 -76.45825  76.61089
+#> SD.log_k_m1          0.005052  -1.08943   1.09953
+#> SD.f_parent_qlogis   0.446968   0.16577   0.72816
+#> SD.log_k1            0.348786   0.09502   0.60255
+#> SD.log_k2            0.147456   0.03111   0.26380
+#> SD.g_qlogis          0.348244   0.02794   0.66854
+illparms(f_saem_dfop_sfo)
+#> [1] "sd(parent_0)" "sd(log_k_m1)"
+f_saem_dfop_sfo_2 <- update(f_saem_dfop_sfo,
+  no_random_effect = c("parent_0", "log_k_m1"))
+illparms(f_saem_dfop_sfo_2)
+intervals(f_saem_dfop_sfo_2)
+#> Approximate 95% confidence intervals
+#> 
+#>  Fixed effects:
+#>                      lower         est.        upper
+#> parent_0       98.04247057 101.09950884 104.15654711
+#> k_m1            0.01528983   0.01687734   0.01862969
+#> f_parent_to_m1  0.20447650   0.27932896   0.36887691
+#> k1              0.06779844   0.09638524   0.13702550
+#> k2              0.01495629   0.01741775   0.02028431
+#> g               0.37669311   0.48368409   0.59219202
+#> 
+#>  Random effects:
+#>                          lower      est.     upper
+#> sd(f_parent_qlogis) 0.16515113 0.4448330 0.7245148
+#> sd(log_k1)          0.08982399 0.3447403 0.5996565
+#> sd(log_k2)          0.02806780 0.1419560 0.2558443
+#> sd(g_qlogis)        0.04908644 0.3801993 0.7113121
+#> 
+#>  
+#>          lower       est.      upper
+#> a.1 0.67993373 0.87630147 1.07266921
+#> b.1 0.06522297 0.07920531 0.09318766
+summary(f_saem_dfop_sfo_2, data = TRUE)
+#> saemix version used for fitting:      3.3 
+#> mkin version used for pre-fitting:  1.2.10 
+#> R version used for fitting:         4.4.2 
+#> Date of fit:     Fri Feb 14 07:34:33 2025 
+#> Date of summary: Fri Feb 14 07:34:33 2025 
+#> 
+#> Equations:
+#> d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+#>            time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+#>            * parent
+#> d_m1/dt = + f_parent_to_m1 * ((k1 * g * exp(-k1 * time) + k2 * (1 - g)
+#>            * exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
+#>            exp(-k2 * time))) * parent - k_m1 * m1
+#> 
+#> Data:
+#> 171 observations of 2 variable(s) grouped in 5 datasets
+#> 
+#> Model predictions using solution type analytical 
+#> 
+#> Fitted in 8.903 s
+#> Using 300, 100 iterations and 10 chains
+#> 
+#> Variance model: Two-component variance function 
+#> 
+#> Starting values for degradation parameters:
+#>        parent_0        log_k_m1 f_parent_qlogis          log_k1          log_k2 
+#>       101.65645        -4.05368        -0.94311        -2.35943        -4.07006 
+#>        g_qlogis 
+#>        -0.01133 
+#> 
+#> Fixed degradation parameter values:
+#> None
+#> 
+#> Starting values for random effects (square root of initial entries in omega):
+#>                 parent_0 log_k_m1 f_parent_qlogis log_k1 log_k2 g_qlogis
+#> parent_0           6.742   0.0000          0.0000 0.0000 0.0000    0.000
+#> log_k_m1           0.000   0.2236          0.0000 0.0000 0.0000    0.000
+#> f_parent_qlogis    0.000   0.0000          0.5572 0.0000 0.0000    0.000
+#> log_k1             0.000   0.0000          0.0000 0.8031 0.0000    0.000
+#> log_k2             0.000   0.0000          0.0000 0.0000 0.2931    0.000
+#> g_qlogis           0.000   0.0000          0.0000 0.0000 0.0000    0.807
+#> 
+#> Starting values for error model parameters:
+#> a.1 b.1 
+#>   1   1 
+#> 
+#> Results:
+#> 
+#> Likelihood computed by importance sampling
+#>     AIC   BIC logLik
+#>   806.9 802.2 -391.5
+#> 
+#> Optimised parameters:
+#>                         est.    lower     upper
+#> parent_0           101.09951 98.04247 104.15655
+#> log_k_m1            -4.08178 -4.18057  -3.98300
+#> f_parent_qlogis     -0.94779 -1.35855  -0.53704
+#> log_k1              -2.33940 -2.69122  -1.98759
+#> log_k2              -4.05027 -4.20262  -3.89791
+#> g_qlogis            -0.06529 -0.50361   0.37303
+#> a.1                  0.87630  0.67993   1.07267
+#> b.1                  0.07921  0.06522   0.09319
+#> SD.f_parent_qlogis   0.44483  0.16515   0.72451
+#> SD.log_k1            0.34474  0.08982   0.59966
+#> SD.log_k2            0.14196  0.02807   0.25584
+#> SD.g_qlogis          0.38020  0.04909   0.71131
+#> 
+#> Correlation: 
+#>                 parnt_0 lg_k_m1 f_prnt_ log_k1  log_k2 
+#> log_k_m1        -0.4716                                
+#> f_parent_qlogis -0.2394  0.2617                        
+#> log_k1           0.1677 -0.1566 -0.0659                
+#> log_k2           0.0165  0.0638  0.0045  0.2013        
+#> g_qlogis         0.1118 -0.1118 -0.0340 -0.2324 -0.3419
+#> 
+#> Random effects:
+#>                      est.   lower  upper
+#> SD.f_parent_qlogis 0.4448 0.16515 0.7245
+#> SD.log_k1          0.3447 0.08982 0.5997
+#> SD.log_k2          0.1420 0.02807 0.2558
+#> SD.g_qlogis        0.3802 0.04909 0.7113
+#> 
+#> Variance model:
+#>        est.   lower   upper
+#> a.1 0.87630 0.67993 1.07267
+#> b.1 0.07921 0.06522 0.09319
+#> 
+#> Backtransformed parameters:
+#>                     est.    lower     upper
+#> parent_0       101.09951 98.04247 104.15655
+#> k_m1             0.01688  0.01529   0.01863
+#> f_parent_to_m1   0.27933  0.20448   0.36888
+#> k1               0.09639  0.06780   0.13703
+#> k2               0.01742  0.01496   0.02028
+#> g                0.48368  0.37669   0.59219
+#> 
+#> Resulting formation fractions:
+#>                 ff
+#> parent_m1   0.2793
+#> parent_sink 0.7207
+#> 
+#> Estimated disappearance times:
+#>         DT50   DT90 DT50back DT50_k1 DT50_k2
+#> parent 15.66  94.28    28.38   7.191    39.8
+#> m1     41.07 136.43       NA      NA      NA
+#> 
+#> Data:
+#>    ds   name time observed  predicted  residual    std standardized
+#>  ds 1 parent    0     89.8  1.011e+02 -11.29951 8.0554    -1.402721
+#>  ds 1 parent    0    104.1  1.011e+02   3.00049 8.0554     0.372481
+#>  ds 1 parent    1     88.7  9.624e+01  -7.53600 7.6726    -0.982195
+#>  ds 1 parent    1     95.5  9.624e+01  -0.73600 7.6726    -0.095925
+#>  ds 1 parent    3     81.8  8.736e+01  -5.55672 6.9744    -0.796732
+#>  ds 1 parent    3     94.5  8.736e+01   7.14328 6.9744     1.024217
+#>  ds 1 parent    7     71.5  7.251e+01  -1.00511 5.8093    -0.173019
+#>  ds 1 parent    7     70.3  7.251e+01  -2.20511 5.8093    -0.379585
+#>  ds 1 parent   14     54.2  5.356e+01   0.63921 4.3319     0.147560
+#>  ds 1 parent   14     49.6  5.356e+01  -3.96079 4.3319    -0.914340
+#>  ds 1 parent   28     31.5  3.175e+01  -0.25429 2.6634    -0.095475
+#>  ds 1 parent   28     28.8  3.175e+01  -2.95429 2.6634    -1.109218
+#>  ds 1 parent   60     12.1  1.281e+01  -0.71388 1.3409    -0.532390
+#>  ds 1 parent   60     13.6  1.281e+01   0.78612 1.3409     0.586271
+#>  ds 1 parent   90      6.2  6.405e+00  -0.20462 1.0125    -0.202083
+#>  ds 1 parent   90      8.3  6.405e+00   1.89538 1.0125     1.871910
+#>  ds 1 parent  120      2.2  3.329e+00  -1.12941 0.9151    -1.234165
+#>  ds 1 parent  120      2.4  3.329e+00  -0.92941 0.9151    -1.015615
+#>  ds 1     m1    1      0.3  1.177e+00  -0.87699 0.8812    -0.995168
+#>  ds 1     m1    1      0.2  1.177e+00  -0.97699 0.8812    -1.108644
+#>  ds 1     m1    3      2.2  3.268e+00  -1.06821 0.9137    -1.169063
+#>  ds 1     m1    3      3.0  3.268e+00  -0.26821 0.9137    -0.293536
+#>  ds 1     m1    7      6.5  6.555e+00  -0.05539 1.0186    -0.054377
+#>  ds 1     m1    7      5.0  6.555e+00  -1.55539 1.0186    -1.527022
+#>  ds 1     m1   14     10.2  1.017e+01   0.03108 1.1902     0.026117
+#>  ds 1     m1   14      9.5  1.017e+01  -0.66892 1.1902    -0.562010
+#>  ds 1     m1   28     12.2  1.270e+01  -0.50262 1.3342    -0.376708
+#>  ds 1     m1   28     13.4  1.270e+01   0.69738 1.3342     0.522686
+#>  ds 1     m1   60     11.8  1.078e+01   1.01734 1.2236     0.831403
+#>  ds 1     m1   60     13.2  1.078e+01   2.41734 1.2236     1.975530
+#>  ds 1     m1   90      6.6  7.686e+00  -1.08586 1.0670    -1.017675
+#>  ds 1     m1   90      9.3  7.686e+00   1.61414 1.0670     1.512779
+#>  ds 1     m1  120      3.5  5.205e+00  -1.70467 0.9684    -1.760250
+#>  ds 1     m1  120      5.4  5.205e+00   0.19533 0.9684     0.201701
+#>  ds 2 parent    0    118.0  1.011e+02  16.90049 8.0554     2.098026
+#>  ds 2 parent    0     99.8  1.011e+02  -1.29951 8.0554    -0.161321
+#>  ds 2 parent    1     90.2  9.574e+01  -5.53784 7.6334    -0.725473
+#>  ds 2 parent    1     94.6  9.574e+01  -1.13784 7.6334    -0.149060
+#>  ds 2 parent    3     96.1  8.638e+01   9.72233 6.8975     1.409551
+#>  ds 2 parent    3     78.4  8.638e+01  -7.97767 6.8975    -1.156610
+#>  ds 2 parent    7     77.9  7.194e+01   5.95854 5.7651     1.033547
+#>  ds 2 parent    7     77.7  7.194e+01   5.75854 5.7651     0.998856
+#>  ds 2 parent   14     56.0  5.558e+01   0.42141 4.4885     0.093888
+#>  ds 2 parent   14     54.7  5.558e+01  -0.87859 4.4885    -0.195742
+#>  ds 2 parent   28     36.6  3.852e+01  -1.92382 3.1746    -0.605999
+#>  ds 2 parent   28     36.8  3.852e+01  -1.72382 3.1746    -0.543000
+#>  ds 2 parent   60     22.1  2.108e+01   1.02043 1.8856     0.541168
+#>  ds 2 parent   60     24.7  2.108e+01   3.62043 1.8856     1.920034
+#>  ds 2 parent   90     12.4  1.250e+01  -0.09675 1.3220    -0.073184
+#>  ds 2 parent   90     10.8  1.250e+01  -1.69675 1.3220    -1.283492
+#>  ds 2 parent  120      6.8  7.426e+00  -0.62587 1.0554    -0.593027
+#>  ds 2 parent  120      7.9  7.426e+00   0.47413 1.0554     0.449242
+#>  ds 2     m1    1      1.3  1.417e+00  -0.11735 0.8835    -0.132825
+#>  ds 2     m1    3      3.7  3.823e+00  -0.12301 0.9271    -0.132673
+#>  ds 2     m1    3      4.7  3.823e+00   0.87699 0.9271     0.945909
+#>  ds 2     m1    7      8.1  7.288e+00   0.81180 1.0494     0.773619
+#>  ds 2     m1    7      7.9  7.288e+00   0.61180 1.0494     0.583025
+#>  ds 2     m1   14     10.1  1.057e+01  -0.46957 1.2119    -0.387459
+#>  ds 2     m1   14     10.3  1.057e+01  -0.26957 1.2119    -0.222432
+#>  ds 2     m1   28     10.7  1.234e+01  -1.63555 1.3124    -1.246185
+#>  ds 2     m1   28     12.2  1.234e+01  -0.13555 1.3124    -0.103281
+#>  ds 2     m1   60     10.7  1.065e+01   0.04641 1.2165     0.038151
+#>  ds 2     m1   60     12.5  1.065e+01   1.84641 1.2165     1.517773
+#>  ds 2     m1   90      9.1  8.177e+00   0.92337 1.0896     0.847403
+#>  ds 2     m1   90      7.4  8.177e+00  -0.77663 1.0896    -0.712734
+#>  ds 2     m1  120      6.1  5.966e+00   0.13404 0.9956     0.134631
+#>  ds 2     m1  120      4.5  5.966e+00  -1.46596 0.9956    -1.472460
+#>  ds 3 parent    0    106.2  1.011e+02   5.10049 8.0554     0.633175
+#>  ds 3 parent    0    106.9  1.011e+02   5.80049 8.0554     0.720073
+#>  ds 3 parent    1    107.4  9.365e+01  13.74627 7.4695     1.840332
+#>  ds 3 parent    1     96.1  9.365e+01   2.44627 7.4695     0.327504
+#>  ds 3 parent    3     79.4  8.139e+01  -1.99118 6.5059    -0.306058
+#>  ds 3 parent    3     82.6  8.139e+01   1.20882 6.5059     0.185803
+#>  ds 3 parent    7     63.9  6.445e+01  -0.54666 5.1792    -0.105549
+#>  ds 3 parent    7     62.4  6.445e+01  -2.04666 5.1792    -0.395170
+#>  ds 3 parent   14     51.0  4.830e+01   2.69944 3.9247     0.687800
+#>  ds 3 parent   14     47.1  4.830e+01  -1.20056 3.9247    -0.305896
+#>  ds 3 parent   28     36.1  3.426e+01   1.83885 2.8516     0.644839
+#>  ds 3 parent   28     36.6  3.426e+01   2.33885 2.8516     0.820177
+#>  ds 3 parent   60     20.1  1.968e+01   0.42208 1.7881     0.236053
+#>  ds 3 parent   60     19.8  1.968e+01   0.12208 1.7881     0.068273
+#>  ds 3 parent   90     11.3  1.194e+01  -0.64013 1.2893    -0.496496
+#>  ds 3 parent   90     10.7  1.194e+01  -1.24013 1.2893    -0.961865
+#>  ds 3 parent  120      8.2  7.247e+00   0.95264 1.0476     0.909381
+#>  ds 3 parent  120      7.3  7.247e+00   0.05264 1.0476     0.050254
+#>  ds 3     m1    0      0.8 -2.956e-12   0.80000 0.8763     0.912928
+#>  ds 3     m1    1      1.8  1.757e+00   0.04318 0.8873     0.048666
+#>  ds 3     m1    1      2.3  1.757e+00   0.54318 0.8873     0.612186
+#>  ds 3     m1    3      4.2  4.566e+00  -0.36607 0.9480    -0.386149
+#>  ds 3     m1    3      4.1  4.566e+00  -0.46607 0.9480    -0.491634
+#>  ds 3     m1    7      6.8  8.157e+00  -1.35680 1.0887    -1.246241
+#>  ds 3     m1    7     10.1  8.157e+00   1.94320 1.0887     1.784855
+#>  ds 3     m1   14     11.4  1.085e+01   0.55367 1.2272     0.451182
+#>  ds 3     m1   14     12.8  1.085e+01   1.95367 1.2272     1.592023
+#>  ds 3     m1   28     11.5  1.149e+01   0.01098 1.2633     0.008689
+#>  ds 3     m1   28     10.6  1.149e+01  -0.88902 1.2633    -0.703717
+#>  ds 3     m1   60      7.5  9.295e+00  -1.79500 1.1445    -1.568351
+#>  ds 3     m1   60      8.6  9.295e+00  -0.69500 1.1445    -0.607245
+#>  ds 3     m1   90      7.3  7.017e+00   0.28305 1.0377     0.272775
+#>  ds 3     m1   90      8.1  7.017e+00   1.08305 1.0377     1.043720
+#>  ds 3     m1  120      5.3  5.087e+00   0.21272 0.9645     0.220547
+#>  ds 3     m1  120      3.8  5.087e+00  -1.28728 0.9645    -1.334660
+#>  ds 4 parent    0    104.7  1.011e+02   3.60049 8.0554     0.446965
+#>  ds 4 parent    0     88.3  1.011e+02 -12.79951 8.0554    -1.588930
+#>  ds 4 parent    1     94.2  9.755e+01  -3.35176 7.7762    -0.431030
+#>  ds 4 parent    1     94.6  9.755e+01  -2.95176 7.7762    -0.379591
+#>  ds 4 parent    3     78.1  9.095e+01 -12.85198 7.2570    -1.770981
+#>  ds 4 parent    3     96.5  9.095e+01   5.54802 7.2570     0.764508
+#>  ds 4 parent    7     76.2  7.949e+01  -3.29267 6.3569    -0.517966
+#>  ds 4 parent    7     77.8  7.949e+01  -1.69267 6.3569    -0.266272
+#>  ds 4 parent   14     70.8  6.384e+01   6.95621 5.1321     1.355423
+#>  ds 4 parent   14     67.3  6.384e+01   3.45621 5.1321     0.673445
+#>  ds 4 parent   28     43.1  4.345e+01  -0.35291 3.5515    -0.099370
+#>  ds 4 parent   28     45.1  4.345e+01   1.64709 3.5515     0.463771
+#>  ds 4 parent   60     21.3  2.137e+01  -0.07478 1.9063    -0.039229
+#>  ds 4 parent   60     23.5  2.137e+01   2.12522 1.9063     1.114813
+#>  ds 4 parent   90     11.8  1.205e+01  -0.24925 1.2957    -0.192375
+#>  ds 4 parent   90     12.1  1.205e+01   0.05075 1.2957     0.039168
+#>  ds 4 parent  120      7.0  6.967e+00   0.03315 1.0356     0.032013
+#>  ds 4 parent  120      6.2  6.967e+00  -0.76685 1.0356    -0.740510
+#>  ds 4     m1    0      1.6  1.421e-13   1.60000 0.8763     1.825856
+#>  ds 4     m1    1      0.9  7.250e-01   0.17503 0.8782     0.199310
+#>  ds 4     m1    3      3.7  2.038e+00   1.66201 0.8910     1.865236
+#>  ds 4     m1    3      2.0  2.038e+00  -0.03799 0.8910    -0.042637
+#>  ds 4     m1    7      3.6  4.186e+00  -0.58623 0.9369    -0.625692
+#>  ds 4     m1    7      3.8  4.186e+00  -0.38623 0.9369    -0.412230
+#>  ds 4     m1   14      7.1  6.752e+00   0.34768 1.0266     0.338666
+#>  ds 4     m1   14      6.6  6.752e+00  -0.15232 1.0266    -0.148372
+#>  ds 4     m1   28      9.5  9.034e+00   0.46628 1.1313     0.412159
+#>  ds 4     m1   28      9.3  9.034e+00   0.26628 1.1313     0.235373
+#>  ds 4     m1   60      8.3  8.634e+00  -0.33359 1.1115    -0.300112
+#>  ds 4     m1   60      9.0  8.634e+00   0.36641 1.1115     0.329645
+#>  ds 4     m1   90      6.6  6.671e+00  -0.07091 1.0233    -0.069295
+#>  ds 4     m1   90      7.7  6.671e+00   1.02909 1.0233     1.005691
+#>  ds 4     m1  120      3.7  4.823e+00  -1.12301 0.9559    -1.174763
+#>  ds 4     m1  120      3.5  4.823e+00  -1.32301 0.9559    -1.383979
+#>  ds 5 parent    0    110.4  1.011e+02   9.30049 8.0554     1.154563
+#>  ds 5 parent    0    112.1  1.011e+02  11.00049 8.0554     1.365601
+#>  ds 5 parent    1     93.5  9.440e+01  -0.90098 7.5282    -0.119681
+#>  ds 5 parent    1     91.0  9.440e+01  -3.40098 7.5282    -0.451764
+#>  ds 5 parent    3     71.0  8.287e+01 -11.86698 6.6217    -1.792122
+#>  ds 5 parent    3     89.7  8.287e+01   6.83302 6.6217     1.031907
+#>  ds 5 parent    7     60.4  6.562e+01  -5.22329 5.2711    -0.990936
+#>  ds 5 parent    7     59.1  6.562e+01  -6.52329 5.2711    -1.237566
+#>  ds 5 parent   14     56.5  4.739e+01   9.10588 3.8548     2.362225
+#>  ds 5 parent   14     47.0  4.739e+01  -0.39412 3.8548    -0.102240
+#>  ds 5 parent   28     30.2  3.118e+01  -0.98128 2.6206    -0.374451
+#>  ds 5 parent   28     23.9  3.118e+01  -7.28128 2.6206    -2.778500
+#>  ds 5 parent   60     17.0  1.804e+01  -1.03959 1.6761    -0.620224
+#>  ds 5 parent   60     18.7  1.804e+01   0.66041 1.6761     0.394008
+#>  ds 5 parent   90     11.3  1.165e+01  -0.35248 1.2727    -0.276958
+#>  ds 5 parent   90     11.9  1.165e+01   0.24752 1.2727     0.194488
+#>  ds 5 parent  120      9.0  7.556e+00   1.44368 1.0612     1.360449
+#>  ds 5 parent  120      8.1  7.556e+00   0.54368 1.0612     0.512338
+#>  ds 5     m1    0      0.7 -1.421e-14   0.70000 0.8763     0.798812
+#>  ds 5     m1    1      3.0  3.160e+00  -0.15979 0.9113    -0.175340
+#>  ds 5     m1    1      2.6  3.160e+00  -0.55979 0.9113    -0.614254
+#>  ds 5     m1    3      5.1  8.448e+00  -3.34789 1.1026    -3.036487
+#>  ds 5     m1    3      7.5  8.448e+00  -0.94789 1.1026    -0.859720
+#>  ds 5     m1    7     16.5  1.581e+01   0.68760 1.5286     0.449839
+#>  ds 5     m1    7     19.0  1.581e+01   3.18760 1.5286     2.085373
+#>  ds 5     m1   14     22.9  2.218e+01   0.71983 1.9632     0.366658
+#>  ds 5     m1   14     23.2  2.218e+01   1.01983 1.9632     0.519469
+#>  ds 5     m1   28     22.2  2.425e+01  -2.05105 2.1113    -0.971479
+#>  ds 5     m1   28     24.4  2.425e+01   0.14895 2.1113     0.070552
+#>  ds 5     m1   60     15.5  1.876e+01  -3.25968 1.7250    -1.889646
+#>  ds 5     m1   60     19.8  1.876e+01   1.04032 1.7250     0.603074
+#>  ds 5     m1   90     14.9  1.365e+01   1.25477 1.3914     0.901806
+#>  ds 5     m1   90     14.2  1.365e+01   0.55477 1.3914     0.398714
+#>  ds 5     m1  120     10.9  9.726e+00   1.17443 1.1667     1.006587
+#>  ds 5     m1  120     10.4  9.726e+00   0.67443 1.1667     0.578044
+# Add a correlation between random effects of g and k2
+cov_model_3 <- f_saem_dfop_sfo_2$so@model@covariance.model
+cov_model_3["log_k2", "g_qlogis"] <- 1
+cov_model_3["g_qlogis", "log_k2"] <- 1
+f_saem_dfop_sfo_3 <- update(f_saem_dfop_sfo,
+  covariance.model = cov_model_3)
+intervals(f_saem_dfop_sfo_3)
+#> Approximate 95% confidence intervals
+#> 
+#>  Fixed effects:
+#>                      lower         est.        upper
+#> parent_0       98.42519529 101.51623115 104.60726702
+#> k_m1            0.01505059   0.01662123   0.01835577
+#> f_parent_to_m1  0.20100222   0.27477835   0.36332008
+#> k1              0.07347479   0.10139028   0.13991179
+#> k2              0.01469861   0.01771120   0.02134125
+#> g               0.35506898   0.46263682   0.57379888
+#> 
+#>  Random effects:
+#>                             lower       est.     upper
+#> sd(f_parent_qlogis)    0.16472883  0.4435866 0.7224443
+#> sd(log_k1)             0.05323856  0.2981783 0.5431180
+#> sd(log_k2)             0.05013379  0.1912531 0.3323723
+#> sd(g_qlogis)           0.04710647  0.3997298 0.7523531
+#> corr(log_k2,g_qlogis) -1.31087397 -0.5845703 0.1417334
+#> 
+#>  
+#>          lower       est.      upper
+#> a.1 0.67769608 0.87421677 1.07073746
+#> b.1 0.06525119 0.07925135 0.09325151
+# The correlation does not improve the fit judged by AIC and BIC, although
+# the likelihood is higher with the additional parameter
+anova(f_saem_dfop_sfo, f_saem_dfop_sfo_2, f_saem_dfop_sfo_3)
+#> Data: 171 observations of 2 variable(s) grouped in 5 datasets
+#> 
+#>                   npar    AIC    BIC     Lik
+#> f_saem_dfop_sfo_2   12 806.91 802.23 -391.46
+#> f_saem_dfop_sfo_3   13 807.96 802.88 -390.98
+#> f_saem_dfop_sfo     14 810.83 805.36 -391.41
+# }
+
+

Summary method for class "saem.mmkin"

Usage

Arguments

Value

Author

Examples