The purpose of this document is to demonstrate how nonlinear
+hierarchical models (NLHM) based on the parent degradation models SFO,
+FOMC, DFOP and HS can be fitted with the mkin package.
+
The mkin package is used in version 1.2.2. It contains the test data
+and the functions used in the evaluations. The saemix
+package is used as a backend for fitting the NLHM, but is also loaded to
+make the convergence plot function available.
+
This document is processed with the knitr package, which
+also provides the kable function that is used to improve
+the display of tabular data in R markdown documents. For parallel
+processing, the parallel package is used.
The test data are available in the mkin package as an object of class
+mkindsg (mkin dataset group) under the identifier
+dimethenamid_2018. The following preprocessing steps are
+still necessary:
+
+
The data available for the enantiomer dimethenamid-P (DMTAP) are
+renamed to have the same substance name as the data for the racemic
+mixture dimethenamid (DMTA). The reason for this is that no difference
+between their degradation behaviour was identified in the EU risk
+assessment.
+
The data for transformation products and unnecessary columns are
+discarded
+
The observation times of each dataset are multiplied with the
+corresponding normalisation factor also available in the dataset, in
+order to make it possible to describe all datasets with a single set of
+parameters that are independent of temperature
+
Finally, datasets observed in the same soil (Elliot 1
+and Elliot 2) are combined, resulting in dimethenamid
+(DMTA) data from six soils.
+
+
The following commented R code performs this preprocessing.
+
+# Apply a function to each of the seven datasets in the mkindsg object to create a list
+dmta_ds<-lapply(1:7, function(i){
+ds_i<-dimethenamid_2018$ds[[i]]$data# Get a dataset
+ds_i[ds_i$name=="DMTAP", "name"]<-"DMTA"# Rename DMTAP to DMTA
+ds_i<-subset(ds_i, name=="DMTA", c("name", "time", "value"))# Select data
+ds_i$time<-ds_i$time*dimethenamid_2018$f_time_norm[i]# Normalise time
+ds_i# Return the dataset
+})
+
+# Use dataset titles as names for the list elements
+names(dmta_ds)<-sapply(dimethenamid_2018$ds, function(ds)ds$title)
+
+# Combine data for Elliot soil to obtain a named list with six elements
+dmta_ds[["Elliot"]]<-rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]])#
+dmta_ds[["Elliot 1"]]<-NULL
+dmta_ds[["Elliot 2"]]<-NULL
In order to obtain suitable starting parameters for the NLHM fits,
+separate fits of the four models to the data for each soil are generated
+using the mmkin function from the mkin
+package. In a first step, constant variance is assumed. Convergence is
+checked with the status function.
In the table above, OK indicates convergence, and C indicates failure
+to converge. All separate fits with constant variance converged, with
+the sole exception of the HS fit to the BBA 2.2 data. To prepare for
+fitting NLHM using the two-component error model, the separate fits are
+updated assuming two-component error.
Using the two-component error model, the one fit that did not
+converge with constant variance did converge, but other non-SFO fits
+failed to converge.
+
+
+
Hierarchichal model fits
+
+
The following code fits eight versions of hierarchical models to the
+data, using SFO, FOMC, DFOP and HS for the parent compound, and using
+either constant variance or two-component error for the error model. The
+default parameter distribution model in mkin allows for variation of all
+degradation parameters across the assumed population of soils. In other
+words, each degradation parameter is associated with a random effect as
+a first step. The mhmkin function makes it possible to fit
+all eight versions in parallel (given a sufficient number of computing
+cores being available) to save execution time.
+
Convergence plots and summaries for these fits are shown in the
+appendix.
The DFOP model is preferred here, as it has a better mechanistic
+basis for batch experiments with constant incubation conditions. Also,
+it shows the lowest AIC and BIC values in the first set of fits when
+combined with the two-component error model. Therefore, the DFOP model
+was selected for further refinements of the fits with the aim to make
+the model fully identifiable.
+
+
Parameter identifiability based on the Fisher Information
+Matrix
+
+
Using the illparms function, ill-defined statistical
+model parameters such as standard deviations of the degradation
+parameters in the population and error model parameters can be
+found.
According to the illparms function, the fitted standard
+deviation of the second kinetic rate constant k2 is
+ill-defined in both DFOP fits. This suggests that different values would
+be obtained for this standard deviation when using different starting
+values.
+
The thus identified overparameterisation is addressed by removing the
+random effect for k2 from the parameter model.
which is not the case. Below, the refined model is compared with the
+previous best model. The model without random effect for k2
+is a reduced version of the previous model. Therefore, the models are
+nested and can be compared using the likelihood ratio test. This is
+achieved with the argument test = TRUE to the
+anova function.
+
+anova(f_saem[["DFOP", "tc"]], f_saem_dfop_tc_no_ranef_k2, test =TRUE)|>
+kable(format.args =list(digits =4))
+
+
+
+
+
+
+
+
+
+
+
+
+
+
npar
+
AIC
+
BIC
+
Lik
+
Chisq
+
Df
+
Pr(>Chisq)
+
+
+
+
f_saem_dfop_tc_no_ranef_k2
+
9
+
663.8
+
661.9
+
-322.9
+
NA
+
NA
+
NA
+
+
+
f_saem[[“DFOP”, “tc”]]
+
10
+
665.5
+
663.4
+
-322.8
+
0.2809
+
1
+
0.5961
+
+
+
+
The AIC and BIC criteria are lower after removal of the ill-defined
+random effect for k2. The p value of the likelihood ratio
+test is much greater than 0.05, indicating that the model with the
+higher likelihood (here the model with random effects for all
+degradation parameters f_saem[["DFOP", "tc"]]) does not fit
+significantly better than the model with the lower likelihood (the
+reduced model f_saem_dfop_tc_no_ranef_k2).
+
Therefore, AIC, BIC and likelihood ratio test suggest the use of the
+reduced model.
+
The convergence of the fit is checked visually.
+
+
+Convergence plot for the NLHM DFOP fit with two-component error and
+without a random effect on ‘k2’
+
+
+
All parameters appear to have converged to a satisfactory degree. The
+final fit is plotted using the plot method from the mkin package.
saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:13 2023
+Date of summary: Thu Jan 5 08:19:13 2023
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+ time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+ * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 4.075 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function
+
+Starting values for degradation parameters:
+ DMTA_0 k1 k2 g
+98.759266 0.087034 0.009933 0.930827
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k1 k2 g
+DMTA_0 98.76 0 0 0
+k1 0.00 1 0 0
+k2 0.00 0 1 0
+g 0.00 0 0 1
+
+Starting values for error model parameters:
+a.1 b.1
+ 1 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 663.8 661.9 -322.9
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.228939 96.285869 100.17201
+k1 0.064063 0.033477 0.09465
+k2 0.008297 0.005824 0.01077
+g 0.953821 0.914328 0.99331
+a.1 1.068479 0.869538 1.26742
+b.1 0.029424 0.022406 0.03644
+SD.DMTA_0 2.030437 0.404824 3.65605
+SD.k1 0.594692 0.256660 0.93272
+SD.g 1.006754 0.361327 1.65218
+
+Correlation:
+ DMTA_0 k1 k2
+k1 0.0218
+k2 0.0556 0.0355
+g -0.0516 -0.0284 -0.2800
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 2.0304 0.4048 3.6560
+SD.k1 0.5947 0.2567 0.9327
+SD.g 1.0068 0.3613 1.6522
+
+Variance model:
+ est. lower upper
+a.1 1.06848 0.86954 1.26742
+b.1 0.02942 0.02241 0.03644
+
+Estimated disappearance times:
+ DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.45 41.4 12.46 10.82 83.54
+
+
+
Alternative check of parameter identifiability
+
+
The parameter check used in the illparms function is
+based on a quadratic approximation of the likelihood surface near its
+optimum, which is calculated using the Fisher Information Matrix (FIM).
+An alternative way to check parameter identifiability based on a
+multistart approach has recently been implemented in mkin.
+
The graph below shows boxplots of the parameters obtained in 50 runs
+of the saem algorithm with different parameter combinations, sampled
+from the range of the parameters obtained for the individual datasets
+fitted separately using nonlinear regression.
+
+f_saem_dfop_tc_multi<-multistart(f_saem[["DFOP", "tc"]], n =50, cores =15)
+Scaled parameters from the multistart runs, full model
+
+
+
The graph clearly confirms the lack of identifiability of the
+variance of k2 in the full model. The overparameterisation
+of the model also indicates a lack of identifiability of the variance of
+parameter g.
+
The parameter boxplots of the multistart runs with the reduced model
+shown below indicate that all runs give similar results, regardless of
+the starting parameters.
+
+f_saem_dfop_tc_no_ranef_k2_multi<-multistart(f_saem_dfop_tc_no_ranef_k2,
+ n =50, cores =15)
+Scaled parameters from the multistart runs, reduced model
+
+
+
When only the parameters of the top 25% of the fits are shown (based
+on a feature introduced in mkin 1.2.2 currently under development), the
+scatter is even less as shown below.
+Scaled parameters from the multistart runs, reduced model, fits with the
+top 25% likelihood values
+
+
+
+
+
+
Conclusions
+
+
Fitting the four parent degradation models SFO, FOMC, DFOP and HS as
+part of hierarchical model fits with two different error models and
+normal distributions of the transformed degradation parameters works
+without technical problems. The biphasic models DFOP and HS gave the
+best fit to the data, but the default parameter distribution model was
+not fully identifiable. Removing the random effect for the second
+kinetic rate constant of the DFOP model resulted in a reduced model that
+was fully identifiable and showed the lowest values for the model
+selection criteria AIC and BIC. The reliability of the identification of
+all model parameters was confirmed using multiple starting values.
+
+
+
Appendix
+
+
+
Hierarchical model fit listings
+
+
+Hierarchical mkin fit of the SFO model with error model const
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:06 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 1.09 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance
+
+Starting values for degradation parameters:
+ DMTA_0 k_DMTA
+97.2953 0.0566
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k_DMTA
+DMTA_0 97.3 0
+k_DMTA 0.0 1
+
+Starting values for error model parameters:
+a.1
+ 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 796.3 795.3 -393.2
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 97.28130 95.71113 98.8515
+k_DMTA 0.05665 0.02909 0.0842
+a.1 2.66442 2.35579 2.9731
+SD.DMTA_0 1.54776 0.15447 2.9411
+SD.k_DMTA 0.60690 0.26248 0.9513
+
+Correlation:
+ DMTA_0
+k_DMTA 0.0168
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.5478 0.1545 2.9411
+SD.k_DMTA 0.6069 0.2625 0.9513
+
+Variance model:
+ est. lower upper
+a.1 2.664 2.356 2.973
+
+Estimated disappearance times:
+ DT50 DT90
+DMTA 12.24 40.65
+
+
+
+
+Hierarchical mkin fit of the SFO model with error model tc
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:07 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - k_DMTA * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 2.441 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function
+
+Starting values for degradation parameters:
+ DMTA_0 k_DMTA
+96.99175 0.05603
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k_DMTA
+DMTA_0 96.99 0
+k_DMTA 0.00 1
+
+Starting values for error model parameters:
+a.1 b.1
+ 1 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 798.3 797.1 -393.2
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 97.271822 95.703157 98.84049
+k_DMTA 0.056638 0.029110 0.08417
+a.1 2.660081 2.230398 3.08976
+b.1 0.001665 -0.006911 0.01024
+SD.DMTA_0 1.545520 0.145035 2.94601
+SD.k_DMTA 0.606422 0.262274 0.95057
+
+Correlation:
+ DMTA_0
+k_DMTA 0.0169
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.5455 0.1450 2.9460
+SD.k_DMTA 0.6064 0.2623 0.9506
+
+Variance model:
+ est. lower upper
+a.1 2.660081 2.230398 3.08976
+b.1 0.001665 -0.006911 0.01024
+
+Estimated disappearance times:
+ DT50 DT90
+DMTA 12.24 40.65
+
+
+
+
+Hierarchical mkin fit of the FOMC model with error model const
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:06 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 1.156 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance
+
+Starting values for degradation parameters:
+ DMTA_0 alpha beta
+ 98.292 9.909 156.341
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 alpha beta
+DMTA_0 98.29 0 0
+alpha 0.00 1 0
+beta 0.00 0 1
+
+Starting values for error model parameters:
+a.1
+ 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 734.2 732.7 -360.1
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.3435 96.9033 99.784
+alpha 7.2007 2.5889 11.812
+beta 112.8746 34.8816 190.868
+a.1 2.0459 1.8054 2.286
+SD.DMTA_0 1.4795 0.2717 2.687
+SD.alpha 0.6396 0.1509 1.128
+SD.beta 0.6874 0.1587 1.216
+
+Correlation:
+ DMTA_0 alpha
+alpha -0.1125
+beta -0.1227 0.3632
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.4795 0.2717 2.687
+SD.alpha 0.6396 0.1509 1.128
+SD.beta 0.6874 0.1587 1.216
+
+Variance model:
+ est. lower upper
+a.1 2.046 1.805 2.286
+
+Estimated disappearance times:
+ DT50 DT90 DT50back
+DMTA 11.41 42.53 12.8
+
+
+
+
+Hierarchical mkin fit of the FOMC model with error model tc
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:07 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - (alpha/beta) * 1/((time/beta) + 1) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 2.729 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function
+
+Starting values for degradation parameters:
+DMTA_0 alpha beta
+98.772 4.663 92.597
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 alpha beta
+DMTA_0 98.77 0 0
+alpha 0.00 1 0
+beta 0.00 0 1
+
+Starting values for error model parameters:
+a.1 b.1
+ 1 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 720.4 718.8 -352.2
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.99136 97.26011 100.72261
+alpha 5.86312 2.57485 9.15138
+beta 88.55571 29.20889 147.90254
+a.1 1.51063 1.24384 1.77741
+b.1 0.02824 0.02040 0.03609
+SD.DMTA_0 1.57436 -0.04867 3.19739
+SD.alpha 0.59871 0.17132 1.02611
+SD.beta 0.72994 0.22849 1.23139
+
+Correlation:
+ DMTA_0 alpha
+alpha -0.1363
+beta -0.1414 0.2542
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.5744 -0.04867 3.197
+SD.alpha 0.5987 0.17132 1.026
+SD.beta 0.7299 0.22849 1.231
+
+Variance model:
+ est. lower upper
+a.1 1.51063 1.2438 1.77741
+b.1 0.02824 0.0204 0.03609
+
+Estimated disappearance times:
+ DT50 DT90 DT50back
+DMTA 11.11 42.6 12.82
+
+
+
+
+Hierarchical mkin fit of the DFOP model with error model const
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:07 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+ time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+ * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 2.007 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance
+
+Starting values for degradation parameters:
+ DMTA_0 k1 k2 g
+98.64383 0.09211 0.02999 0.76814
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k1 k2 g
+DMTA_0 98.64 0 0 0
+k1 0.00 1 0 0
+k2 0.00 0 1 0
+g 0.00 0 0 1
+
+Starting values for error model parameters:
+a.1
+ 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 711.8 710 -346.9
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.092481 96.573898 99.61106
+k1 0.062499 0.030336 0.09466
+k2 0.009065 -0.005133 0.02326
+g 0.948967 0.862079 1.03586
+a.1 1.821671 1.604774 2.03857
+SD.DMTA_0 1.677785 0.472066 2.88350
+SD.k1 0.634962 0.270788 0.99914
+SD.k2 1.033498 -0.205994 2.27299
+SD.g 1.710046 0.428642 2.99145
+
+Correlation:
+ DMTA_0 k1 k2
+k1 0.0246
+k2 0.0491 0.0953
+g -0.0552 -0.0889 -0.4795
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.678 0.4721 2.8835
+SD.k1 0.635 0.2708 0.9991
+SD.k2 1.033 -0.2060 2.2730
+SD.g 1.710 0.4286 2.9914
+
+Variance model:
+ est. lower upper
+a.1 1.822 1.605 2.039
+
+Estimated disappearance times:
+ DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.79 42.8 12.88 11.09 76.46
+
+
+
+
+Hierarchical mkin fit of the DFOP model with error model tc
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:08 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
+ time)) / (g * exp(-k1 * time) + (1 - g) * exp(-k2 * time)))
+ * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 3.033 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function
+
+Starting values for degradation parameters:
+ DMTA_0 k1 k2 g
+98.759266 0.087034 0.009933 0.930827
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k1 k2 g
+DMTA_0 98.76 0 0 0
+k1 0.00 1 0 0
+k2 0.00 0 1 0
+g 0.00 0 0 1
+
+Starting values for error model parameters:
+a.1 b.1
+ 1 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 665.5 663.4 -322.8
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.377019 96.447952 100.30609
+k1 0.064843 0.034607 0.09508
+k2 0.008895 0.006368 0.01142
+g 0.949696 0.903815 0.99558
+a.1 1.065241 0.865754 1.26473
+b.1 0.029340 0.022336 0.03634
+SD.DMTA_0 2.007754 0.387982 3.62753
+SD.k1 0.580473 0.250286 0.91066
+SD.k2 0.006105 -4.920337 4.93255
+SD.g 1.097149 0.412779 1.78152
+
+Correlation:
+ DMTA_0 k1 k2
+k1 0.0235
+k2 0.0595 0.0424
+g -0.0470 -0.0278 -0.2731
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 2.007754 0.3880 3.6275
+SD.k1 0.580473 0.2503 0.9107
+SD.k2 0.006105 -4.9203 4.9325
+SD.g 1.097149 0.4128 1.7815
+
+Variance model:
+ est. lower upper
+a.1 1.06524 0.86575 1.26473
+b.1 0.02934 0.02234 0.03634
+
+Estimated disappearance times:
+ DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.36 41.32 12.44 10.69 77.92
+
+
+
+
+Hierarchical mkin fit of the HS model with error model const
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:07 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 2.004 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Constant variance
+
+Starting values for degradation parameters:
+ DMTA_0 k1 k2 tb
+97.82176 0.06931 0.02997 11.13945
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k1 k2 tb
+DMTA_0 97.82 0 0 0
+k1 0.00 1 0 0
+k2 0.00 0 1 0
+tb 0.00 0 0 1
+
+Starting values for error model parameters:
+a.1
+ 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 714 712.1 -348
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 98.16102 96.47747 99.84456
+k1 0.07876 0.05261 0.10491
+k2 0.02227 0.01706 0.02747
+tb 13.99089 -7.40049 35.38228
+a.1 1.82305 1.60700 2.03910
+SD.DMTA_0 1.88413 0.56204 3.20622
+SD.k1 0.34292 0.10482 0.58102
+SD.k2 0.19851 0.01718 0.37985
+SD.tb 1.68168 0.58064 2.78272
+
+Correlation:
+ DMTA_0 k1 k2
+k1 0.0142
+k2 0.0001 -0.0025
+tb 0.0165 -0.1256 -0.0301
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 1.8841 0.56204 3.2062
+SD.k1 0.3429 0.10482 0.5810
+SD.k2 0.1985 0.01718 0.3798
+SD.tb 1.6817 0.58064 2.7827
+
+Variance model:
+ est. lower upper
+a.1 1.823 1.607 2.039
+
+Estimated disappearance times:
+ DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 8.801 67.91 20.44 8.801 31.13
+
+
+
+
+Hierarchical mkin fit of the HS model with error model tc
+
+
+saemix version used for fitting: 3.2
+mkin version used for pre-fitting: 1.2.2
+R version used for fitting: 4.2.2
+Date of fit: Thu Jan 5 08:19:08 2023
+Date of summary: Thu Jan 5 08:20:11 2023
+
+Equations:
+d_DMTA/dt = - ifelse(time <= tb, k1, k2) * DMTA
+
+Data:
+155 observations of 1 variable(s) grouped in 6 datasets
+
+Model predictions using solution type analytical
+
+Fitted in 3.287 s
+Using 300, 100 iterations and 9 chains
+
+Variance model: Two-component variance function
+
+Starting values for degradation parameters:
+ DMTA_0 k1 k2 tb
+98.45190 0.07525 0.02576 19.19375
+
+Fixed degradation parameter values:
+None
+
+Starting values for random effects (square root of initial entries in omega):
+ DMTA_0 k1 k2 tb
+DMTA_0 98.45 0 0 0
+k1 0.00 1 0 0
+k2 0.00 0 1 0
+tb 0.00 0 0 1
+
+Starting values for error model parameters:
+a.1 b.1
+ 1 1
+
+Results:
+
+Likelihood computed by importance sampling
+ AIC BIC logLik
+ 667.1 665 -323.6
+
+Optimised parameters:
+ est. lower upper
+DMTA_0 97.76570 95.81350 99.71791
+k1 0.05855 0.03080 0.08630
+k2 0.02337 0.01664 0.03010
+tb 31.09638 29.38289 32.80987
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+SD.DMTA_0 2.04877 0.42607 3.67147
+SD.k1 0.59166 0.25621 0.92711
+SD.k2 0.30698 0.09561 0.51835
+SD.tb 0.01274 -0.10914 0.13462
+
+Correlation:
+ DMTA_0 k1 k2
+k1 0.0160
+k2 -0.0070 -0.0024
+tb -0.0668 -0.0103 -0.2013
+
+Random effects:
+ est. lower upper
+SD.DMTA_0 2.04877 0.42607 3.6715
+SD.k1 0.59166 0.25621 0.9271
+SD.k2 0.30698 0.09561 0.5183
+SD.tb 0.01274 -0.10914 0.1346
+
+Variance model:
+ est. lower upper
+a.1 1.08835 0.88590 1.29080
+b.1 0.02964 0.02257 0.03671
+
+Estimated disappearance times:
+ DT50 DT90 DT50back DT50_k1 DT50_k2
+DMTA 11.84 51.71 15.57 11.84 29.66
+
+
+
+
+
+
Hierarchical model convergence plots
+
+
+
+Convergence plot for the NLHM SFO fit with constant variance
+
+
+
+
+Convergence plot for the NLHM SFO fit with two-component error
+
+
+
+
+Convergence plot for the NLHM FOMC fit with constant variance
+
+
+
+
+Convergence plot for the NLHM FOMC fit with two-component error
+
+
+
+
+Convergence plot for the NLHM DFOP fit with constant variance
+
+
+
+
+Convergence plot for the NLHM DFOP fit with two-component error
+
+
+
+
+Convergence plot for the NLHM HS fit with constant variance
+
+
+
+
+Convergence plot for the NLHM HS fit with two-component error
+
diff --git a/docs/dev/index.html b/docs/dev/index.html
index 4723879e..993b8eea 100644
--- a/docs/dev/index.html
+++ b/docs/dev/index.html
@@ -19,11 +19,11 @@
equation models are solved using automatically generated C functions.
Heteroscedasticity can be taken into account using variance by variable or
two-component error models as described by Ranke and Meinecke (2018)
- <doi:10.3390/environments6120124>. Interfaces to several nonlinear
- mixed-effects model packages are available, some of which are described by
- Ranke et al. (2021) <doi:10.3390/environments8080071>. Please note that no
- warranty is implied for correctness of results or fitness for a particular
- purpose.">
+ <doi:10.3390/environments6120124>. Hierarchical degradation models can
+ be fitted using nonlinear mixed-effects model packages as a backend as
+ described by Ranke et al. (2021) <doi:10.3390/environments8080071>. Please
+ note that no warranty is implied for correctness of results or fitness for a
+ particular purpose.">
Hierarchical kinetics template — hierarchical_kinetics • mkin
+
+
+
diff --git a/docs/dev/reference/mkinmod.html b/docs/dev/reference/mkinmod.html
index 251215a7..145dee83 100644
--- a/docs/dev/reference/mkinmod.html
+++ b/docs/dev/reference/mkinmod.html
@@ -132,7 +132,7 @@ the source compartment.
Additionally, mkinsub() has an argument to, specifying names of
variables to which a transfer is to be assumed in the model.
If the argument use_of_ff is set to "min"
-(default) and the model for the compartment is "SFO" or "SFORB", an
+and the model for the compartment is "SFO" or "SFORB", an
additional mkinsub() argument can be sink = FALSE, effectively
fixing the flux to sink to zero.
In print.mkinmod, this argument is currently not used.
@@ -247,7 +247,7 @@ in the FOCUS and NAFTA guidance documents are used.
For kinetic models with more than one observed variable, a symbolic solution
of the system of differential equations is included in the resulting
mkinmod object in some cases, speeding up the solution.
If a C compiler is found by pkgbuild::has_compiler() and there
is more than one observed variable in the specification, C code is generated
for evaluating the differential equations, compiled using
inline::cfunction() and added to the resulting mkinmod object.
@@ -310,7 +310,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media
parent =mkinsub("SFO", "m1", full_name ="Test compound"), m1 =mkinsub("SFO", full_name ="Metabolite M1"), name ="SFO_SFO", dll_dir =DLL_dir, unload =TRUE, overwrite =TRUE)
-#> Copied DLL from /tmp/RtmpbZbZ8Y/file8c6a9f402f42.so to /home/jranke/.local/share/mkin/SFO_SFO.so
+#> Copied DLL from /tmp/RtmpelWAOB/fileb43c31a25a86.so to /home/jranke/.local/share/mkin/SFO_SFO.so# Now we can save the model and restore it in a new sessionsaveRDS(SFO_SFO.2, file ="~/SFO_SFO.rds")# Terminate the R session here if you would like to check, and then do
@@ -363,7 +363,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media
#> })#> return(predicted)#> }
-#> <environment: 0x55556029f678>
+#> <environment: 0x55555f013820># If we have several parallel metabolites# (compare tests/testthat/test_synthetic_data_for_UBA_2014.R)
@@ -392,7 +392,7 @@ Evaluating and Calculating Degradation Kinetics in Environmental Media
diff --git a/docs/dev/reference/summary_listing.html b/docs/dev/reference/summary_listing.html
new file mode 100644
index 00000000..876412cc
--- /dev/null
+++ b/docs/dev/reference/summary_listing.html
@@ -0,0 +1,147 @@
+
+Display the output of a summary function according to the output format — summary_listing • mkin
+
+
+
Should a new page be started after the listing? Ignored in html output
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/docs/dev/sitemap.xml b/docs/dev/sitemap.xml
index 06f56c5d..6e51371c 100644
--- a/docs/dev/sitemap.xml
+++ b/docs/dev/sitemap.xml
@@ -3,6 +3,9 @@
https://pkgdown.jrwb.de/mkin/404.html
+
+ https://pkgdown.jrwb.de/mkin/articles/2022_wp_1.1_dmta_parent.html
+ https://pkgdown.jrwb.de/mkin/articles/FOCUS_D.html
@@ -138,6 +141,9 @@
https://pkgdown.jrwb.de/mkin/reference/get_deg_func.html
+
+ https://pkgdown.jrwb.de/mkin/reference/hierarchical_kinetics.html
+ https://pkgdown.jrwb.de/mkin/reference/illparms.html
@@ -306,6 +312,9 @@
https://pkgdown.jrwb.de/mkin/reference/summary.saem.mmkin.html
+
+ https://pkgdown.jrwb.de/mkin/reference/summary_listing.html
+ https://pkgdown.jrwb.de/mkin/reference/synthetic_data_for_UBA_2014.html
diff --git a/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx b/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx
new file mode 100644
index 00000000..3252fdf1
Binary files /dev/null and b/inst/testdata/cyantraniliprole_soil_efsa_2014.xlsx differ
diff --git a/log/check.log b/log/check.log
index aec61e33..a81475d9 100644
--- a/log/check.log
+++ b/log/check.log
@@ -7,11 +7,28 @@
* checking extension type ... Package
* this is package ‘mkin’ version ‘1.2.2’
* package encoding: UTF-8
-* checking CRAN incoming feasibility ... Note_to_CRAN_maintainers
+* checking CRAN incoming feasibility ... NOTE
Maintainer: ‘Johannes Ranke ’
+
+Size of tarball: 6636884 bytes
* checking package namespace information ... OK
* checking package dependencies ... OK
-* checking if this is a source package ... OK
+* checking if this is a source package ... NOTE
+Found the following apparent object files/libraries:
+ vignettes/2022_wp_1/cyan_dlls/dfop_path_1.so
+ vignettes/2022_wp_1/cyan_dlls/dfop_path_2.so
+ vignettes/2022_wp_1/cyan_dlls/fomc_path_1.so
+ vignettes/2022_wp_1/cyan_dlls/fomc_path_2.so
+ vignettes/2022_wp_1/cyan_dlls/hs_path_1.so
+ vignettes/2022_wp_1/cyan_dlls/sfo_path_1.so
+ vignettes/2022_wp_1/cyan_dlls/sforb_path_1.so
+ vignettes/2022_wp_1/cyan_dlls/sforb_path_2.so
+ vignettes/2022_wp_1/dmta_dlls/m_dfop_path.so
+ vignettes/2022_wp_1/dmta_dlls/m_fomc_path.so
+ vignettes/2022_wp_1/dmta_dlls/m_hs_path.so
+ vignettes/2022_wp_1/dmta_dlls/m_sfo_path.so
+ vignettes/2022_wp_1/dmta_dlls/m_sforb_path.so
+Object files/libraries should not be included in a source package.
* checking if there is a namespace ... OK
* checking for executable files ... OK
* checking for hidden files and directories ... OK
@@ -41,14 +58,7 @@ Maintainer: ‘Johannes Ranke ’
* checking S3 generic/method consistency ... OK
* checking replacement functions ... OK
* checking foreign function calls ... OK
-* checking R code for possible problems ... NOTE
-parplot.multistart.saem.mmkin: no visible global function definition
- for ‘quantile’
-Undefined global functions or variables:
- quantile
-Consider adding
- importFrom("stats", "quantile")
-to your NAMESPACE file.
+* checking R code for possible problems ... OK
* checking Rd files ... OK
* checking Rd metadata ... OK
* checking Rd line widths ... OK
@@ -64,7 +74,7 @@ to your NAMESPACE file.
* checking data for ASCII and uncompressed saves ... OK
* checking installed files from ‘inst/doc’ ... OK
* checking files in ‘vignettes’ ... OK
-* checking examples ... [11s/11s] OK
+* checking examples ... [10s/10s] OK
* checking for unstated dependencies in ‘tests’ ... OK
* checking tests ... SKIPPED
* checking for unstated dependencies in vignettes ... OK
@@ -76,7 +86,7 @@ to your NAMESPACE file.
* checking for detritus in the temp directory ... OK
* DONE
-Status: 1 NOTE
+Status: 2 NOTEs
See
‘/home/jranke/git/mkin/mkin.Rcheck/00check.log’
for details.
diff --git a/man/hierarchical_kinetics.Rd b/man/hierarchical_kinetics.Rd
index 4bb82a4c..2a8e211c 100644
--- a/man/hierarchical_kinetics.Rd
+++ b/man/hierarchical_kinetics.Rd
@@ -23,7 +23,7 @@ provided with the mkin package.
\dontrun{
library(rmarkdown)
-draft("New analysis.rmd", template = "hierarchical_kinetics", package = "mkin")
+draft("example_analysis.rmd", template = "hierarchical_kinetics", package = "mkin")
}
}
diff --git a/man/mkinmod.Rd b/man/mkinmod.Rd
index 87ce9016..65b5de1a 100644
--- a/man/mkinmod.Rd
+++ b/man/mkinmod.Rd
@@ -33,7 +33,7 @@ the source compartment.
Additionally, \code{\link[=mkinsub]{mkinsub()}} has an argument \code{to}, specifying names of
variables to which a transfer is to be assumed in the model.
If the argument \code{use_of_ff} is set to "min"
-(default) and the model for the compartment is "SFO" or "SFORB", an
+and the model for the compartment is "SFO" or "SFORB", an
additional \code{\link[=mkinsub]{mkinsub()}} argument can be \code{sink = FALSE}, effectively
fixing the flux to sink to zero.
In print.mkinmod, this argument is currently not used.}
diff --git a/man/summary_listing.Rd b/man/summary_listing.Rd
new file mode 100644
index 00000000..995ebd8d
--- /dev/null
+++ b/man/summary_listing.Rd
@@ -0,0 +1,27 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/summary_listing.R
+\name{summary_listing}
+\alias{summary_listing}
+\alias{tex_listing}
+\alias{html_listing}
+\title{Display the output of a summary function according to the output format}
+\usage{
+summary_listing(object, caption = NULL, label = NULL, clearpage = TRUE)
+
+tex_listing(object, caption = NULL, label = NULL, clearpage = TRUE)
+
+html_listing(object, caption = NULL)
+}
+\arguments{
+\item{object}{The object for which the summary is to be listed}
+
+\item{caption}{An optional caption}
+
+\item{label}{An optional label, ignored in html output}
+
+\item{clearpage}{Should a new page be started after the listing? Ignored in html output}
+}
+\description{
+This function is intended for use in a R markdown code chunk with the chunk
+option \code{results = "asis"}.
+}
diff --git a/man/tex_listing.Rd b/man/tex_listing.Rd
deleted file mode 100644
index 2f11d211..00000000
--- a/man/tex_listing.Rd
+++ /dev/null
@@ -1,21 +0,0 @@
-% Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/tex_listing.R
-\name{tex_listing}
-\alias{tex_listing}
-\title{Wrap the output of a summary function in tex listing environment}
-\usage{
-tex_listing(object, caption = NULL, label = NULL, clearpage = TRUE)
-}
-\arguments{
-\item{object}{The object for which the summary is to be listed}
-
-\item{caption}{An optional caption}
-
-\item{label}{An optional label}
-
-\item{clearpage}{Should a new page be started after the listing?}
-}
-\description{
-This function can be used in a R markdown code chunk with the chunk
-option \code{results = "asis"}.
-}
diff --git a/vignettes/FOCUS_D.html b/vignettes/FOCUS_D.html
index b8a63a7b..c729e3c2 100644
--- a/vignettes/FOCUS_D.html
+++ b/vignettes/FOCUS_D.html
@@ -31,7 +31,7 @@ document.addEventListener('DOMContentLoaded', function(e) {
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