# Short demo of the multistart method

#### Johannes Ranke

#### Last change 20 April 2023 (rebuilt 2023-11-16)

Source:`vignettes/web_only/multistart.rmd`

`multistart.rmd`

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.