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                9 663.73 661.86 -322.86                     
-## best(f_saem_reduced_multi)    9 663.69 661.82 -322.85 0.0361  0           
-## f_saem_full                  10 669.77 667.69 -324.89 0.0000  1          1
-## best(f_saem_full_multi)      10 665.56 663.48 -322.78 4.2060  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 2023-04-20)