From e48c1f2ef990a622722e416c8d301430db4f5081 Mon Sep 17 00:00:00 2001
From: Johannes Ranke 
+# If we disregards ill-defined rate constants, the results
+# look more plausible, but the truth is likely to be in
+# between these variants
+plot(mixed(dmta_sfo_sfo3p_tc), test_log_parms = TRUE)
+
+# Therefore we use nonlinear mixed-effects models
+# f_dmta_nlme_tc <- nlme(dmta_sfo_sfo3p_tc)
+# nlme reaches maxIter = 50 without convergence
+f_dmta_saem_tc <- saem(dmta_sfo_sfo3p_tc)
+# I am commenting out the convergence plot as rendering them
+# with pkgdown fails (at least without further tweaks to the 
+# graphics device used)
+#saemix::plot(f_dmta_saem_tc$so, plot.type = "convergence")
+summary(f_dmta_saem_tc)
+#> saemix version used for fitting:      3.0 
+#> mkin version used for pre-fitting:  1.1.0 
+#> R version used for fitting:         4.1.3 
+#> Date of fit:     Wed Mar 16 14:32:04 2022 
+#> Date of summary: Wed Mar 16 14:32:04 2022 
+#> 
+#> Equations:
+#> d_DMTA/dt = - k_DMTA * DMTA
+#> d_M23/dt = + f_DMTA_to_M23 * k_DMTA * DMTA - k_M23 * M23
+#> d_M27/dt = + f_DMTA_to_M27 * k_DMTA * DMTA - k_M27 * M27 + k_M31 * M31
+#> d_M31/dt = + f_DMTA_to_M31 * k_DMTA * DMTA - k_M31 * M31
+#> 
+#> Data:
+#> 563 observations of 4 variable(s) grouped in 6 datasets
+#> 
+#> Model predictions using solution type deSolve 
+#> 
+#> Fitted in 927.963 s
+#> Using 300, 100 iterations and 9 chains
+#> 
+#> Variance model: Two-component variance function 
+#> 
+#> Mean of starting values for individual parameters:
+#>       DMTA_0   log_k_DMTA    log_k_M23    log_k_M27    log_k_M31 f_DMTA_ilr_1 
+#>      95.5662      -2.9048      -3.8130      -4.1600      -4.1486       0.1341 
+#> f_DMTA_ilr_2 f_DMTA_ilr_3 
+#>       0.1385      -1.6700 
+#> 
+#> Fixed degradation parameter values:
+#> None
+#> 
+#> Results:
+#> 
+#> Likelihood computed by importance sampling
+#>    AIC  BIC logLik
+#>   2276 2272  -1120
+#> 
+#> Optimised parameters:
+#>                 est.   lower   upper
+#> DMTA_0       88.5943 84.3961 92.7925
+#> log_k_DMTA   -3.0466 -3.5609 -2.5322
+#> log_k_M23    -4.0684 -4.9340 -3.2029
+#> log_k_M27    -3.8628 -4.2627 -3.4628
+#> log_k_M31    -3.9803 -4.4804 -3.4801
+#> f_DMTA_ilr_1  0.1304 -0.2186  0.4795
+#> f_DMTA_ilr_2  0.1490 -0.2559  0.5540
+#> f_DMTA_ilr_3 -1.3970 -1.6976 -1.0964
+#> 
+#> Correlation: 
+#>              DMTA_0  l__DMTA lg__M23 lg__M27 lg__M31 f_DMTA__1 f_DMTA__2
+#> log_k_DMTA    0.0309                                                    
+#> log_k_M23    -0.0231 -0.0031                                            
+#> log_k_M27    -0.0381 -0.0048  0.0039                                    
+#> log_k_M31    -0.0251 -0.0031  0.0021  0.0830                            
+#> f_DMTA_ilr_1 -0.0046 -0.0006  0.0417 -0.0437  0.0328                    
+#> f_DMTA_ilr_2 -0.0008 -0.0002  0.0214 -0.0270 -0.0909 -0.0361            
+#> f_DMTA_ilr_3 -0.1832 -0.0135  0.0434  0.0804  0.0395 -0.0070    0.0059  
+#> 
+#> Random effects:
+#>                   est.   lower  upper
+#> SD.DMTA_0       3.3651 -0.9655 7.6956
+#> SD.log_k_DMTA   0.6415  0.2774 1.0055
+#> SD.log_k_M23    1.0176  0.3809 1.6543
+#> SD.log_k_M27    0.4538  0.1522 0.7554
+#> SD.log_k_M31    0.5684  0.1905 0.9464
+#> SD.f_DMTA_ilr_1 0.4111  0.1524 0.6699
+#> SD.f_DMTA_ilr_2 0.4788  0.1808 0.7768
+#> SD.f_DMTA_ilr_3 0.3501  0.1316 0.5685
+#> 
+#> Variance model:
+#>       est.  lower  upper
+#> a.1 0.9349 0.8395 1.0302
+#> b.1 0.1344 0.1176 0.1512
+#> 
+#> Backtransformed parameters:
+#>                   est.     lower    upper
+#> DMTA_0        88.59431 84.396147 92.79246
+#> k_DMTA         0.04752  0.028413  0.07948
+#> k_M23          0.01710  0.007198  0.04064
+#> k_M27          0.02101  0.014084  0.03134
+#> k_M31          0.01868  0.011329  0.03080
+#> f_DMTA_to_M23  0.14498        NA       NA
+#> f_DMTA_to_M27  0.12056        NA       NA
+#> f_DMTA_to_M31  0.11015        NA       NA
+#> 
+#> Resulting formation fractions:
+#>               ff
+#> DMTA_M23  0.1450
+#> DMTA_M27  0.1206
+#> DMTA_M31  0.1101
+#> DMTA_sink 0.6243
+#> 
+#> Estimated disappearance times:
+#>       DT50   DT90
+#> DMTA 14.59  48.45
+#> M23  40.52 134.62
+#> M27  32.99 109.60
+#> M31  37.11 123.26
+# As the confidence interval for the random effects of DMTA_0
+# includes zero, we could try an alternative model without
+# such random effects
+# f_dmta_saem_tc_2 <- saem(dmta_sfo_sfo3p_tc,
+#   covariance.model = diag(c(0, rep(1, 7))))
+# saemix::plot(f_dmta_saem_tc_2$so, plot.type = "convergence")
+# This does not perform better judged by AIC and BIC
+saemix::compare.saemix(f_dmta_saem_tc$so, f_dmta_saem_tc_2$so)
+#> Error in saemix::compare.saemix(f_dmta_saem_tc$so, f_dmta_saem_tc_2$so): object 'f_dmta_saem_tc_2' not found
 # }
 
     
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