Short demo of the multistart method

This is a vignette, because the multistart method does not seem to work in pkgdown example code and I wanted to show the plots in the online docs. The dimethenamid data from 2018 from seven soils is used as example data.

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)
f_saem_full_multi <- multistart(f_saem_full, n = 16, cores = 16)
parhist(f_saem_full_multi)

We see that not all variability parameters are identifiable, most problematic is the variance of k2. So we reduce the parameter distribution model by removing the intersoil variability for this parameter.

f_saem_reduced <- update(f_saem_full, covariance.model = diag(c(1, 1, 0, 1)))
f_saem_reduced_multi <- multistart(f_saem_reduced, n = 16, cores = 16)
parhist(f_saem_reduced_multi, lpos = "topright")

We can also analyse the log-likelihoods obtained in the multiple runs:

llhist(f_saem_reduced_multi)

The one run with the lower likelihood is probably responsible for the outliers in the boxplots above, and caused by some weird starting value combination. In any case, the converged values from the original fit (red circles) appear perfectly acceptable, supporting the choice of starting values made by mkin.

Johannes Ranke

Last change 19 September 2022 (rebuilt 2022-09-28)