The dimethenamid data from 2018 from seven soils is used as example data in this vignette.
library(mkin) dmta_ds <- lapply(1:7, function(i) { ds_i <- dimethenamid_2018$ds[[i]]$data ds_i[ds_i$name == "DMTAP", "name"] <- "DMTA" ds_i$time <- ds_i$time * dimethenamid_2018$f_time_norm[i] ds_i }) names(dmta_ds) <- sapply(dimethenamid_2018$ds, function(ds) ds$title) dmta_ds[["Elliot"]] <- rbind(dmta_ds[["Elliot 1"]], dmta_ds[["Elliot 2"]]) dmta_ds[["Elliot 1"]] <- dmta_ds[["Elliot 2"]] <- NULL
First, we check the DFOP model with the two-component error model and random effects for all degradation parameters.
f_mmkin <- mmkin("DFOP", dmta_ds, error_model = "tc", cores = 7, quiet = TRUE) f_saem_full <- saem(f_mmkin) illparms(f_saem_full)
We see that not all variability parameters are identifiable. The illparms
function tells us that the confidence interval for the standard deviation
of 'log_k2' includes zero. We check this assessment using multiple runs
with different starting values.
f_saem_full_multi <- multistart(f_saem_full, n = 16, cores = 16) parplot(f_saem_full_multi, lpos = "topleft")
This confirms that the variance of k2 is the most problematic parameter, so we reduce the parameter distribution model by removing the intersoil variability for k2.
f_saem_reduced <- stats::update(f_saem_full, no_random_effect = "log_k2") illparms(f_saem_reduced) f_saem_reduced_multi <- multistart(f_saem_reduced, n = 16, cores = 16) parplot(f_saem_reduced_multi, lpos = "topright", ylim = c(0.5, 2))
The results confirm that all remaining parameters can be determined with sufficient certainty.
We can also analyse the log-likelihoods obtained in the multiple runs:
llhist(f_saem_reduced_multi)
We can use the anova
method to compare the models.
anova(f_saem_full, best(f_saem_full_multi), f_saem_reduced, best(f_saem_reduced_multi), test = TRUE)
The reduced model results in lower AIC and BIC values, so it is clearly preferable. Using multiple starting values gives a large improvement in case of the full model, because it is less well-defined, which impedes convergence. For the reduced model, using multiple starting values only results in a small improvement of the model fit.
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