From 91c5db736a4d3f2290a0cc5698fb4e35ae7bda59 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Wed, 18 May 2022 21:26:17 +0200 Subject: Remove outdated comment in FOCUS L vignette, update docs This also adds the first benchmark results obtained on my laptop system --- docs/articles/web_only/dimethenamid_2018.html | 93 +++++++++++++++------------ 1 file changed, 52 insertions(+), 41 deletions(-) (limited to 'docs/articles/web_only/dimethenamid_2018.html') diff --git a/docs/articles/web_only/dimethenamid_2018.html b/docs/articles/web_only/dimethenamid_2018.html index 09aa5150..7650f06f 100644 --- a/docs/articles/web_only/dimethenamid_2018.html +++ b/docs/articles/web_only/dimethenamid_2018.html @@ -105,7 +105,7 @@

Example evaluations of the dimethenamid data from 2018

Johannes Ranke

-

Last change 7 March 2022, built on 16 Mar 2022

+

Last change 7 March 2022, built on 18 May 2022

Source: vignettes/web_only/dimethenamid_2018.rmd @@ -178,7 +178,7 @@ Status of individual fits: dataset model Calke Borstel Flaach BBA 2.2 BBA 2.3 Elliot - DFOP OK OK C OK C OK + DFOP OK OK OK OK C OK OK: No warnings C: Optimisation did not converge: @@ -231,32 +231,41 @@ f_parent_nlme_dfop_tc 3 10 671.91 702.34 -325.96 2 vs 3 134.69 <.0001

The saemix package provided the first Open Source implementation of the Stochastic Approximation to the Expectation Maximisation (SAEM) algorithm. SAEM fits of degradation models can be conveniently performed using an interface to the saemix package available in current development versions of the mkin package.

The corresponding SAEM fits of the four combinations of degradation and error models are fitted below. As there is no convergence criterion implemented in the saemix package, the convergence plots need to be manually checked for every fit. We define control settings that work well for all the parent data fits shown in this vignette.

-library(saemix)
-saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
+library(saemix)
+
Loading required package: npde
+
Package saemix, version 3.0
+  please direct bugs, questions and feedback to emmanuelle.comets@inserm.fr
+

+Attaching package: 'saemix'
+
The following objects are masked from 'package:npde':
+
+    kurtosis, skewness
+
+saemix_control <- saemixControl(nbiter.saemix = c(800, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 saemix_control_moreiter <- saemixControl(nbiter.saemix = c(1600, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)
 saemix_control_10k <- saemixControl(nbiter.saemix = c(10000, 300), nb.chains = 15,
     print = FALSE, save = FALSE, save.graphs = FALSE, displayProgress = FALSE)

The convergence plot for the SFO model using constant variance is shown below.

-
+
 f_parent_saemix_sfo_const <- mkin::saem(f_parent_mkin_const["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_const$so, plot.type = "convergence")

 

 
Obviously the selected number of iterations is sufficient to reach convergence. This can also be said for the SFO fit using the two-component error model.

-
+
 f_parent_saemix_sfo_tc <- mkin::saem(f_parent_mkin_tc["SFO", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_sfo_tc$so, plot.type = "convergence")

 

 
When fitting the DFOP model with constant variance (see below), parameter convergence is not as unambiguous.

-
+
 f_parent_saemix_dfop_const <- mkin::saem(f_parent_mkin_const["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 plot(f_parent_saemix_dfop_const$so, plot.type = "convergence")

 

-
+
 print(f_parent_saemix_dfop_const)

 
Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -277,21 +286,23 @@ DMTA_0    97.99583 96.50079 99.4909
 k1         0.06377  0.03432  0.0932
 k2         0.00848  0.00444  0.0125
 g          0.95701  0.91313  1.0009
-a.1        1.82141  1.65974  1.9831
-SD.DMTA_0  1.64787  0.45779  2.8379
+a.1        1.82141  1.60516  2.0377
+SD.DMTA_0  1.64787  0.45729  2.8384
 SD.k1      0.57439  0.24731  0.9015
-SD.k2      0.03296 -2.50143  2.5673
-SD.g       1.10266  0.32371  1.8816

+SD.k2      0.03296 -2.50524  2.5712
+SD.g       1.10266  0.32354  1.8818

 
While the other parameters converge to credible values, the variance of k2 (omega2.k2) converges to a very small value. The printout of the saem.mmkin model shows that the estimated standard deviation of k2 across the population of soils (SD.k2) is ill-defined, indicating overparameterisation of this model.

 
When the DFOP model is fitted with the two-component error model, we also observe that the estimated variance of k2 becomes very small, while being ill-defined, as illustrated by the excessive confidence interval of SD.k2.

-
+
 f_parent_saemix_dfop_tc <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
   control = saemix_control, transformations = "saemix")
 f_parent_saemix_dfop_tc_moreiter <- mkin::saem(f_parent_mkin_tc["DFOP", ], quiet = TRUE,
-  control = saemix_control_moreiter, transformations = "saemix")
-plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")

+  control = saemix_control_moreiter, transformations = "saemix")

+
Likelihood cannot be computed by Importance Sampling.

+
+plot(f_parent_saemix_dfop_tc$so, plot.type = "convergence")

 

-
+
 print(f_parent_saemix_dfop_tc)

 
Kinetic nonlinear mixed-effects model fit by SAEM
 Structural model:
@@ -307,21 +318,21 @@ Likelihood computed by importance sampling
   666 664   -323
 
 Fitted parameters:
-          estimate    lower    upper
-DMTA_0    98.27617  96.3088 100.2436
-k1         0.06437   0.0337   0.0950
-k2         0.00880   0.0063   0.0113
-g          0.95249   0.9100   0.9949
-a.1        1.06161   0.8625   1.2607
-b.1        0.02967   0.0226   0.0367
-SD.DMTA_0  2.06075   0.4187   3.7028
-SD.k1      0.59357   0.2561   0.9310
-SD.k2      0.00292 -10.2960  10.3019
-SD.g       1.05725   0.3808   1.7337

+          estimate     lower    upper
+DMTA_0    9.82e+01  96.27937 100.1783
+k1        6.41e-02   0.03333   0.0948
+k2        8.56e-03   0.00608   0.0110
+g         9.55e-01   0.91440   0.9947
+a.1       1.07e+00   0.86542   1.2647
+b.1       2.96e-02   0.02258   0.0367
+SD.DMTA_0 2.04e+00   0.40629   3.6678
+SD.k1     5.98e-01   0.25796   0.9373
+SD.k2     5.28e-04 -58.93251  58.9336
+SD.g      1.04e+00   0.36509   1.7083

 
Doubling the number of iterations in the first phase of the algorithm leads to a slightly lower likelihood, and therefore to slightly higher AIC and BIC values. With even more iterations, the algorithm stops with an error message. This is related to the variance of k2 approximating zero and has been submitted as a bug to the saemix package, as the algorithm does not converge in this case.

 
An alternative way to fit DFOP in combination with the two-component error model is to use the model formulation with transformed parameters as used per default in mkin. When using this option, convergence is slower, but eventually the algorithm stops as well with the same error message.

 
The four combinations (SFO/const, SFO/tc, DFOP/const and DFOP/tc) and the version with increased iterations can be compared using the model comparison function of the saemix package:

-
+
 AIC_parent_saemix <- saemix::compare.saemix(
   f_parent_saemix_sfo_const$so,
   f_parent_saemix_sfo_tc$so,
@@ -329,7 +340,7 @@ SD.g       1.05725   0.3808   1.7337

   f_parent_saemix_dfop_tc$so,
   f_parent_saemix_dfop_tc_moreiter$so)

 
Likelihoods calculated by importance sampling

-
+
 rownames(AIC_parent_saemix) <- c(
   "SFO const", "SFO tc", "DFOP const", "DFOP tc", "DFOP tc more iterations")
 print(AIC_parent_saemix)

@@ -337,10 +348,10 @@ SD.g       1.05725   0.3808   1.7337

 SFO const               796.38 795.34
 SFO tc                  798.38 797.13
 DFOP const              705.75 703.88
-DFOP tc                 665.65 663.57
-DFOP tc more iterations 665.88 663.80

+DFOP tc                 665.72 663.63
+DFOP tc more iterations    NaN    NaN

 
In order to check the influence of the likelihood calculation algorithms implemented in saemix, the likelihood from Gaussian quadrature is added to the best fit, and the AIC values obtained from the three methods are compared.

-
+
 f_parent_saemix_dfop_tc$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc$so)
 AIC_parent_saemix_methods <- c(
@@ -350,9 +361,9 @@ DFOP tc more iterations 665.88 663.80

 )
 print(AIC_parent_saemix_methods)

 
    is     gq    lin 
-665.65 665.68 665.11 

+665.72 665.88 665.15

The AIC values based on importance sampling and Gaussian quadrature are very similar. Using linearisation is known to be less accurate, but still gives a similar value. In order to illustrate that the comparison of the three method depends on the degree of convergence obtained in the fit, the same comparison is shown below for the fit using the defaults for the number of iterations and the number of MCMC chains.

-
+
 f_parent_saemix_dfop_tc_defaults <- mkin::saem(f_parent_mkin_tc["DFOP", ])
 f_parent_saemix_dfop_tc_defaults$so <-
   saemix::llgq.saemix(f_parent_saemix_dfop_tc_defaults$so)
@@ -363,14 +374,14 @@ DFOP tc more iterations 665.88 663.80

 )
 print(AIC_parent_saemix_methods_defaults)
    is     gq    lin 
-668.27 718.36 666.49
+668.91 663.61 667.40

Comparison

The following table gives the AIC values obtained with both backend packages using the same control parameters (800 iterations burn-in, 300 iterations second phase, 15 chains). Note that

-
+
 AIC_all <- data.frame(
   check.names = FALSE,
   "Degradation model" = c("SFO", "SFO", "DFOP", "DFOP"),
@@ -395,7 +406,7 @@ DFOP tc more iterations 665.88 663.80

 SFO
 const
 796.60
-796.60
+794.17
 796.38
 
 
@@ -409,15 +420,15 @@ DFOP tc more iterations 665.88 663.80
DFOP const NA -671.98 +704.95 705.75 DFOP tc 671.91 -665.11 -665.65 +665.15 +665.72 @@ -464,7 +475,7 @@ DFOP tc more iterations 665.88 663.80

-

Site built with pkgdown 2.0.2.

+

Site built with pkgdown 2.0.3.

-- cgit v1.2.3