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.
an object of class saem.mmkin
logical, indicating whether the full data should be included in the summary.
Should the summary be verbose?
Numeric vector with covariate values for all variables in any covariate models in the object. If given, it overrides '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).
logical, indicating whether DT50 and DT90 values should be included.
optional arguments passed to methods like print.
an object of class summary.saem.mmkin
Number of digits to use for printing
The summary function returns a list based on the saemix::SaemixObject
obtained in the fit, with at least the following additional components
The saemix, mkin and R versions used
The dates where the fit and the summary were produced
The differential equations used in the degradation model
Was maximum or minimum use made of formation fractions
The data
Transformed parameters as used in the optimisation, with confidence intervals
Backtransformed parameters, with confidence intervals if available
Error model parameters with confidence intervals
The estimated formation fractions derived from the fitted model.
The DT50 and DT90 values for each observed variable.
If applicable, eigenvalues of SFORB components of the model.
The print method is called for its side effect, i.e. printing the summary.
# 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_0 100.86947 97.81542 103.92353
#> log_k_m1 -4.06947 -4.16944 -3.96950
#> f_parent_qlogis -0.93256 -1.34200 -0.52312
#> log_k1 -2.37017 -2.72660 -2.01375
#> log_k2 -4.06264 -4.21344 -3.91184
#> g_qlogis -0.02174 -0.45898 0.41549
#> a.1 0.87598 0.67275 1.07922
#> b.1 0.07949 0.06389 0.09509
#> SD.parent_0 0.19170 -30.36286 30.74626
#> SD.log_k_m1 0.01883 -0.28736 0.32502
#> SD.f_parent_qlogis 0.44300 0.16391 0.72209
#> SD.log_k1 0.35320 0.09661 0.60978
#> SD.log_k2 0.13707 0.02359 0.25056
#> SD.g_qlogis 0.37478 0.04490 0.70467
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 98.36731429 101.42508066 104.48284703
#> k_m1 0.01513234 0.01670094 0.01843214
#> f_parent_to_m1 0.20221431 0.27608850 0.36461630
#> k1 0.06915073 0.09759718 0.13774560
#> k2 0.01487068 0.01740389 0.02036863
#> g 0.37365671 0.48384821 0.59563299
#>
#> Random effects:
#> lower est. upper
#> sd(f_parent_qlogis) 0.16439770 0.4427585 0.7211193
#> sd(log_k1) 0.08304243 0.3345213 0.5860002
#> sd(log_k2) 0.03146410 0.1490210 0.2665779
#> sd(g_qlogis) 0.06216385 0.4023430 0.7425221
#>
#>
#> lower est. upper
#> a.1 0.67696663 0.87777355 1.07858048
#> b.1 0.06363957 0.07878001 0.09392044
summary(f_saem_dfop_sfo_2, data = TRUE)
#> saemix version used for fitting: 3.2
#> mkin version used for pre-fitting: 1.2.5
#> R version used for fitting: 4.3.0
#> Date of fit: Fri May 19 17:33:55 2023
#> Date of summary: Fri May 19 17:33:55 2023
#>
#> 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 9.133 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
#> -0.01132
#>
#> 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
#> 807 802.3 -391.5
#>
#> Optimised parameters:
#> est. lower upper
#> parent_0 101.42508 98.36731 104.48285
#> log_k_m1 -4.09229 -4.19092 -3.99366
#> f_parent_qlogis -0.96395 -1.37251 -0.55538
#> log_k1 -2.32691 -2.67147 -1.98235
#> log_k2 -4.05106 -4.20836 -3.89376
#> g_qlogis -0.06463 -0.51656 0.38730
#> a.1 0.87777 0.67697 1.07858
#> b.1 0.07878 0.06364 0.09392
#> SD.f_parent_qlogis 0.44276 0.16440 0.72112
#> SD.log_k1 0.33452 0.08304 0.58600
#> SD.log_k2 0.14902 0.03146 0.26658
#> SD.g_qlogis 0.40234 0.06216 0.74252
#>
#> Correlation:
#> parnt_0 lg_k_m1 f_prnt_ log_k1 log_k2
#> log_k_m1 -0.4693
#> f_parent_qlogis -0.2378 0.2595
#> log_k1 0.1720 -0.1593 -0.0669
#> log_k2 0.0179 0.0594 0.0035 0.1995
#> g_qlogis 0.1073 -0.1060 -0.0322 -0.2299 -0.3168
#>
#> Random effects:
#> est. lower upper
#> SD.f_parent_qlogis 0.4428 0.16440 0.7211
#> SD.log_k1 0.3345 0.08304 0.5860
#> SD.log_k2 0.1490 0.03146 0.2666
#> SD.g_qlogis 0.4023 0.06216 0.7425
#>
#> Variance model:
#> est. lower upper
#> a.1 0.87777 0.67697 1.07858
#> b.1 0.07878 0.06364 0.09392
#>
#> Backtransformed parameters:
#> est. lower upper
#> parent_0 101.4251 98.36731 104.48285
#> k_m1 0.0167 0.01513 0.01843
#> f_parent_to_m1 0.2761 0.20221 0.36462
#> k1 0.0976 0.06915 0.13775
#> k2 0.0174 0.01487 0.02037
#> g 0.4838 0.37366 0.59563
#>
#> Resulting formation fractions:
#> ff
#> parent_m1 0.2761
#> parent_sink 0.7239
#>
#> Estimated disappearance times:
#> DT50 DT90 DT50back DT50_k1 DT50_k2
#> parent 15.54 94.33 28.4 7.102 39.83
#> m1 41.50 137.87 NA NA NA
#>
#> Data:
#> ds name time observed predicted residual std standardized
#> ds 1 parent 0 89.8 1.014e+02 -11.62508 8.0383 -1.44620
#> ds 1 parent 0 104.1 1.014e+02 2.67492 8.0383 0.33277
#> ds 1 parent 1 88.7 9.650e+01 -7.80311 7.6530 -1.01961
#> ds 1 parent 1 95.5 9.650e+01 -1.00311 7.6530 -0.13107
#> ds 1 parent 3 81.8 8.753e+01 -5.72638 6.9510 -0.82382
#> ds 1 parent 3 94.5 8.753e+01 6.97362 6.9510 1.00326
#> ds 1 parent 7 71.5 7.254e+01 -1.04133 5.7818 -0.18010
#> ds 1 parent 7 70.3 7.254e+01 -2.24133 5.7818 -0.38765
#> ds 1 parent 14 54.2 5.349e+01 0.71029 4.3044 0.16502
#> ds 1 parent 14 49.6 5.349e+01 -3.88971 4.3044 -0.90366
#> ds 1 parent 28 31.5 3.167e+01 -0.16616 2.6446 -0.06283
#> ds 1 parent 28 28.8 3.167e+01 -2.86616 2.6446 -1.08379
#> ds 1 parent 60 12.1 1.279e+01 -0.69287 1.3365 -0.51843
#> ds 1 parent 60 13.6 1.279e+01 0.80713 1.3365 0.60392
#> ds 1 parent 90 6.2 6.397e+00 -0.19718 1.0122 -0.19481
#> ds 1 parent 90 8.3 6.397e+00 1.90282 1.0122 1.87996
#> ds 1 parent 120 2.2 3.323e+00 -1.12320 0.9160 -1.22623
#> ds 1 parent 120 2.4 3.323e+00 -0.92320 0.9160 -1.00788
#> ds 1 m1 1 0.3 1.179e+00 -0.87919 0.8827 -0.99605
#> ds 1 m1 1 0.2 1.179e+00 -0.97919 0.8827 -1.10935
#> ds 1 m1 3 2.2 3.273e+00 -1.07272 0.9149 -1.17256
#> ds 1 m1 3 3.0 3.273e+00 -0.27272 0.9149 -0.29811
#> ds 1 m1 7 6.5 6.559e+00 -0.05872 1.0186 -0.05765
#> ds 1 m1 7 5.0 6.559e+00 -1.55872 1.0186 -1.53032
#> ds 1 m1 14 10.2 1.016e+01 0.03787 1.1880 0.03188
#> ds 1 m1 14 9.5 1.016e+01 -0.66213 1.1880 -0.55734
#> ds 1 m1 28 12.2 1.268e+01 -0.47913 1.3297 -0.36032
#> ds 1 m1 28 13.4 1.268e+01 0.72087 1.3297 0.54211
#> ds 1 m1 60 11.8 1.078e+01 1.02493 1.2211 0.83936
#> ds 1 m1 60 13.2 1.078e+01 2.42493 1.2211 1.98588
#> ds 1 m1 90 6.6 7.705e+00 -1.10464 1.0672 -1.03509
#> ds 1 m1 90 9.3 7.705e+00 1.59536 1.0672 1.49491
#> ds 1 m1 120 3.5 5.236e+00 -1.73617 0.9699 -1.79010
#> ds 1 m1 120 5.4 5.236e+00 0.16383 0.9699 0.16892
#> ds 2 parent 0 118.0 1.014e+02 16.57492 8.0383 2.06198
#> ds 2 parent 0 99.8 1.014e+02 -1.62508 8.0383 -0.20217
#> ds 2 parent 1 90.2 9.599e+01 -5.79045 7.6129 -0.76061
#> ds 2 parent 1 94.6 9.599e+01 -1.39045 7.6129 -0.18264
#> ds 2 parent 3 96.1 8.652e+01 9.57931 6.8724 1.39388
#> ds 2 parent 3 78.4 8.652e+01 -8.12069 6.8724 -1.18164
#> ds 2 parent 7 77.9 7.197e+01 5.93429 5.7370 1.03439
#> ds 2 parent 7 77.7 7.197e+01 5.73429 5.7370 0.99953
#> ds 2 parent 14 56.0 5.555e+01 0.44657 4.4637 0.10005
#> ds 2 parent 14 54.7 5.555e+01 -0.85343 4.4637 -0.19120
#> ds 2 parent 28 36.6 3.853e+01 -1.93170 3.1599 -0.61132
#> ds 2 parent 28 36.8 3.853e+01 -1.73170 3.1599 -0.54803
#> ds 2 parent 60 22.1 2.110e+01 1.00360 1.8795 0.53396
#> ds 2 parent 60 24.7 2.110e+01 3.60360 1.8795 1.91728
#> ds 2 parent 90 12.4 1.250e+01 -0.09712 1.3190 -0.07363
#> ds 2 parent 90 10.8 1.250e+01 -1.69712 1.3190 -1.28667
#> ds 2 parent 120 6.8 7.419e+00 -0.61913 1.0546 -0.58709
#> ds 2 parent 120 7.9 7.419e+00 0.48087 1.0546 0.45599
#> ds 2 m1 1 1.3 1.422e+00 -0.12194 0.8849 -0.13781
#> ds 2 m1 3 3.7 3.831e+00 -0.13149 0.9282 -0.14166
#> ds 2 m1 3 4.7 3.831e+00 0.86851 0.9282 0.93567
#> ds 2 m1 7 8.1 7.292e+00 0.80812 1.0490 0.77034
#> ds 2 m1 7 7.9 7.292e+00 0.60812 1.0490 0.57969
#> ds 2 m1 14 10.1 1.055e+01 -0.45332 1.2090 -0.37495
#> ds 2 m1 14 10.3 1.055e+01 -0.25332 1.2090 -0.20953
#> ds 2 m1 28 10.7 1.230e+01 -1.59960 1.3074 -1.22347
#> ds 2 m1 28 12.2 1.230e+01 -0.09960 1.3074 -0.07618
#> ds 2 m1 60 10.7 1.065e+01 0.05342 1.2141 0.04400
#> ds 2 m1 60 12.5 1.065e+01 1.85342 1.2141 1.52661
#> ds 2 m1 90 9.1 8.196e+00 0.90368 1.0897 0.82930
#> ds 2 m1 90 7.4 8.196e+00 -0.79632 1.0897 -0.73078
#> ds 2 m1 120 6.1 5.997e+00 0.10252 0.9969 0.10284
#> ds 2 m1 120 4.5 5.997e+00 -1.49748 0.9969 -1.50220
#> ds 3 parent 0 106.2 1.014e+02 4.77492 8.0383 0.59402
#> ds 3 parent 0 106.9 1.014e+02 5.47492 8.0383 0.68110
#> ds 3 parent 1 107.4 9.390e+01 13.49935 7.4494 1.81214
#> ds 3 parent 1 96.1 9.390e+01 2.19935 7.4494 0.29524
#> ds 3 parent 3 79.4 8.152e+01 -2.12307 6.4821 -0.32753
#> ds 3 parent 3 82.6 8.152e+01 1.07693 6.4821 0.16614
#> ds 3 parent 7 63.9 6.446e+01 -0.55834 5.1533 -0.10834
#> ds 3 parent 7 62.4 6.446e+01 -2.05834 5.1533 -0.39942
#> ds 3 parent 14 51.0 4.826e+01 2.74073 3.9019 0.70241
#> ds 3 parent 14 47.1 4.826e+01 -1.15927 3.9019 -0.29711
#> ds 3 parent 28 36.1 3.424e+01 1.86399 2.8364 0.65718
#> ds 3 parent 28 36.6 3.424e+01 2.36399 2.8364 0.83346
#> ds 3 parent 60 20.1 1.968e+01 0.42172 1.7815 0.23672
#> ds 3 parent 60 19.8 1.968e+01 0.12172 1.7815 0.06833
#> ds 3 parent 90 11.3 1.195e+01 -0.64633 1.2869 -0.50222
#> ds 3 parent 90 10.7 1.195e+01 -1.24633 1.2869 -0.96844
#> ds 3 parent 120 8.2 7.255e+00 0.94532 1.0474 0.90251
#> ds 3 parent 120 7.3 7.255e+00 0.04532 1.0474 0.04327
#> ds 3 m1 0 0.8 2.956e-11 0.80000 0.8778 0.91140
#> ds 3 m1 1 1.8 1.758e+00 0.04187 0.8886 0.04712
#> ds 3 m1 1 2.3 1.758e+00 0.54187 0.8886 0.60978
#> ds 3 m1 3 4.2 4.567e+00 -0.36697 0.9486 -0.38683
#> ds 3 m1 3 4.1 4.567e+00 -0.46697 0.9486 -0.49224
#> ds 3 m1 7 6.8 8.151e+00 -1.35124 1.0876 -1.24242
#> ds 3 m1 7 10.1 8.151e+00 1.94876 1.0876 1.79182
#> ds 3 m1 14 11.4 1.083e+01 0.57098 1.2240 0.46647
#> ds 3 m1 14 12.8 1.083e+01 1.97098 1.2240 1.61022
#> ds 3 m1 28 11.5 1.147e+01 0.03175 1.2597 0.02520
#> ds 3 m1 28 10.6 1.147e+01 -0.86825 1.2597 -0.68928
#> ds 3 m1 60 7.5 9.298e+00 -1.79834 1.1433 -1.57298
#> ds 3 m1 60 8.6 9.298e+00 -0.69834 1.1433 -0.61083
#> ds 3 m1 90 7.3 7.038e+00 0.26249 1.0382 0.25283
#> ds 3 m1 90 8.1 7.038e+00 1.06249 1.0382 1.02340
#> ds 3 m1 120 5.3 5.116e+00 0.18417 0.9659 0.19068
#> ds 3 m1 120 3.8 5.116e+00 -1.31583 0.9659 -1.36232
#> ds 4 parent 0 104.7 1.014e+02 3.27492 8.0383 0.40741
#> ds 4 parent 0 88.3 1.014e+02 -13.12508 8.0383 -1.63281
#> ds 4 parent 1 94.2 9.781e+01 -3.61183 7.7555 -0.46572
#> ds 4 parent 1 94.6 9.781e+01 -3.21183 7.7555 -0.41414
#> ds 4 parent 3 78.1 9.110e+01 -13.00467 7.2307 -1.79853
#> ds 4 parent 3 96.5 9.110e+01 5.39533 7.2307 0.74617
#> ds 4 parent 7 76.2 7.951e+01 -3.30511 6.3246 -0.52258
#> ds 4 parent 7 77.8 7.951e+01 -1.70511 6.3246 -0.26960
#> ds 4 parent 14 70.8 6.376e+01 7.03783 5.0993 1.38016
#> ds 4 parent 14 67.3 6.376e+01 3.53783 5.0993 0.69379
#> ds 4 parent 28 43.1 4.340e+01 -0.30456 3.5303 -0.08627
#> ds 4 parent 28 45.1 4.340e+01 1.69544 3.5303 0.48026
#> ds 4 parent 60 21.3 2.142e+01 -0.12077 1.9022 -0.06349
#> ds 4 parent 60 23.5 2.142e+01 2.07923 1.9022 1.09308
#> ds 4 parent 90 11.8 1.207e+01 -0.26813 1.2940 -0.20721
#> ds 4 parent 90 12.1 1.207e+01 0.03187 1.2940 0.02463
#> ds 4 parent 120 7.0 6.954e+00 0.04554 1.0347 0.04402
#> ds 4 parent 120 6.2 6.954e+00 -0.75446 1.0347 -0.72914
#> ds 4 m1 0 1.6 1.990e-13 1.60000 0.8778 1.82279
#> ds 4 m1 1 0.9 7.305e-01 0.16949 0.8797 0.19267
#> ds 4 m1 3 3.7 2.051e+00 1.64896 0.8925 1.84753
#> ds 4 m1 3 2.0 2.051e+00 -0.05104 0.8925 -0.05719
#> ds 4 m1 7 3.6 4.204e+00 -0.60375 0.9382 -0.64354
#> ds 4 m1 7 3.8 4.204e+00 -0.40375 0.9382 -0.43036
#> ds 4 m1 14 7.1 6.760e+00 0.34021 1.0267 0.33137
#> ds 4 m1 14 6.6 6.760e+00 -0.15979 1.0267 -0.15563
#> ds 4 m1 28 9.5 9.011e+00 0.48856 1.1289 0.43277
#> ds 4 m1 28 9.3 9.011e+00 0.28856 1.1289 0.25561
#> ds 4 m1 60 8.3 8.611e+00 -0.31077 1.1093 -0.28014
#> ds 4 m1 60 9.0 8.611e+00 0.38923 1.1093 0.35086
#> ds 4 m1 90 6.6 6.678e+00 -0.07753 1.0233 -0.07576
#> ds 4 m1 90 7.7 6.678e+00 1.02247 1.0233 0.99915
#> ds 4 m1 120 3.7 4.847e+00 -1.14679 0.9572 -1.19804
#> ds 4 m1 120 3.5 4.847e+00 -1.34679 0.9572 -1.40698
#> ds 5 parent 0 110.4 1.014e+02 8.97492 8.0383 1.11651
#> ds 5 parent 0 112.1 1.014e+02 10.67492 8.0383 1.32800
#> ds 5 parent 1 93.5 9.466e+01 -1.16118 7.5089 -0.15464
#> ds 5 parent 1 91.0 9.466e+01 -3.66118 7.5089 -0.48758
#> ds 5 parent 3 71.0 8.302e+01 -12.01844 6.5988 -1.82130
#> ds 5 parent 3 89.7 8.302e+01 6.68156 6.5988 1.01254
#> ds 5 parent 7 60.4 6.563e+01 -5.22574 5.2440 -0.99652
#> ds 5 parent 7 59.1 6.563e+01 -6.52574 5.2440 -1.24442
#> ds 5 parent 14 56.5 4.727e+01 9.22621 3.8263 2.41128
#> ds 5 parent 14 47.0 4.727e+01 -0.27379 3.8263 -0.07156
#> ds 5 parent 28 30.2 3.103e+01 -0.83405 2.5977 -0.32108
#> ds 5 parent 28 23.9 3.103e+01 -7.13405 2.5977 -2.74634
#> ds 5 parent 60 17.0 1.800e+01 -0.99696 1.6675 -0.59787
#> ds 5 parent 60 18.7 1.800e+01 0.70304 1.6675 0.42161
#> ds 5 parent 90 11.3 1.167e+01 -0.36809 1.2710 -0.28961
#> ds 5 parent 90 11.9 1.167e+01 0.23191 1.2710 0.18246
#> ds 5 parent 120 9.0 7.595e+00 1.40496 1.0623 1.32256
#> ds 5 parent 120 8.1 7.595e+00 0.50496 1.0623 0.47535
#> ds 5 m1 0 0.7 0.000e+00 0.70000 0.8778 0.79747
#> ds 5 m1 1 3.0 3.158e+00 -0.15799 0.9123 -0.17317
#> ds 5 m1 1 2.6 3.158e+00 -0.55799 0.9123 -0.61160
#> ds 5 m1 3 5.1 8.443e+00 -3.34286 1.1013 -3.03535
#> ds 5 m1 3 7.5 8.443e+00 -0.94286 1.1013 -0.85613
#> ds 5 m1 7 16.5 1.580e+01 0.69781 1.5232 0.45811
#> ds 5 m1 7 19.0 1.580e+01 3.19781 1.5232 2.09935
#> ds 5 m1 14 22.9 2.216e+01 0.73604 1.9543 0.37663
#> ds 5 m1 14 23.2 2.216e+01 1.03604 1.9543 0.53014
#> ds 5 m1 28 22.2 2.423e+01 -2.03128 2.1011 -0.96678
#> ds 5 m1 28 24.4 2.423e+01 0.16872 2.1011 0.08030
#> ds 5 m1 60 15.5 1.876e+01 -3.25610 1.7187 -1.89455
#> ds 5 m1 60 19.8 1.876e+01 1.04390 1.7187 0.60739
#> ds 5 m1 90 14.9 1.366e+01 1.23585 1.3890 0.88976
#> ds 5 m1 90 14.2 1.366e+01 0.53585 1.3890 0.38579
#> ds 5 m1 120 10.9 9.761e+00 1.13911 1.1670 0.97613
#> ds 5 m1 120 10.4 9.761e+00 0.63911 1.1670 0.54767
# 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 98.39888363 101.48951337 104.58014311
#> k_m1 0.01508704 0.01665986 0.01839665
#> f_parent_to_m1 0.20141557 0.27540583 0.36418131
#> k1 0.07708759 0.10430866 0.14114200
#> k2 0.01476621 0.01786384 0.02161129
#> g 0.33679867 0.45083525 0.57028162
#>
#> Random effects:
#> lower est. upper
#> sd(f_parent_qlogis) 0.38085375 0.4441841 0.5075145
#> sd(log_k1) 0.04774819 0.2660384 0.4843286
#> sd(log_k2) -0.63842736 0.1977024 1.0338321
#> sd(g_qlogis) 0.22711289 0.4502227 0.6733326
#> corr(log_k2,g_qlogis) -0.83271473 -0.6176939 -0.4026730
#>
#>
#> lower est. upper
#> a.1 0.67347568 0.87437392 1.07527216
#> b.1 0.06393032 0.07912417 0.09431802
# 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 12 806.96 802.27 -391.48
#> f_saem_dfop_sfo_3 13 807.99 802.91 -391.00
#> f_saem_dfop_sfo 14 810.83 805.36 -391.42
# }