Short demo of the multistart method

+ + + +

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)

## [1] "sd(log_k2)"

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)

## Data: 155 observations of 1 variable(s) grouped in 6 datasets
+## 
+##                            npar    AIC    BIC     Lik  Chisq Df Pr(>Chisq)
+## f_saem_reduced                9 663.67 661.80 -322.84                     
+## best(f_saem_reduced_multi)    9 663.65 661.78 -322.82 0.0219  0           
+## f_saem_full                  10 670.09 668.01 -325.05 0.0000  1          1
+## best(f_saem_full_multi)      10 665.61 663.52 -322.80 4.4870  0

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.

Johannes +Ranke

Last change 20 April 2023 +(rebuilt 2025-02-14)