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)

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 <- 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")

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)

The parameter histograms can be further improved by excluding the result with the low likelihood.

+parplot(f_saem_reduced_multi, lpos = "topright", llmin = -326, ylim = c(0.5, 2))

We can use the anova method to compare the models, including a likelihood ratio test if the models are nested.

+anova(f_saem_full, 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)
+## best(f_saem_reduced_multi)    9 663.69 661.82 -322.85                    
+## f_saem_full                  10 669.77 667.69 -324.89     0  1          1

While AIC and BIC are lower for the reduced model, the likelihood ratio test does not indicate a significant difference between the fits.

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Johannes Ranke

Last change 26 September 2022 (rebuilt 2022-11-17)