From 03e1598a3c79911a497758fe382461f288bf05e6 Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Fri, 16 Sep 2022 10:12:54 +0200 Subject: Diagnostic plots for multistart method --- vignettes/FOCUS_L.html | 151 ++++++++++++++++++++++++++----------------------- 1 file changed, 79 insertions(+), 72 deletions(-) (limited to 'vignettes') diff --git a/vignettes/FOCUS_L.html b/vignettes/FOCUS_L.html index 13d0d9eb..da6c11fe 100644 --- a/vignettes/FOCUS_L.html +++ b/vignettes/FOCUS_L.html @@ -1517,7 +1517,7 @@ div.tocify {

Example evaluation of FOCUS Laboratory Data L1 to L3

Johannes Ranke

-

Last change 18 May 2022 (rebuilt 2022-07-08)

+

Last change 18 May 2022 (rebuilt 2022-09-14)

@@ -1536,17 +1536,17 @@ FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)

Since mkin version 0.9-32 (July 2014), we can use shorthand notation like "SFO" for parent only degradation models. The following two lines fit the model and produce the summary report of the model fit. This covers the numerical analysis given in the FOCUS report.

m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
 summary(m.L1.SFO)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:39 2022 
-## Date of summary: Fri Jul  8 15:44:39 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 133 model solutions performed in 0.029 s
+## Fitted using 133 model solutions performed in 0.032 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1578,9 +1578,9 @@ summary(m.L1.SFO)

 ## 
 ## Parameter correlation:
 ##                parent_0 log_k_parent      sigma
-## parent_0      1.000e+00    6.186e-01 -1.712e-09
-## log_k_parent  6.186e-01    1.000e+00 -3.237e-09
-## sigma        -1.712e-09   -3.237e-09  1.000e+00
+## parent_0      1.000e+00    6.186e-01 -1.516e-09
+## log_k_parent  6.186e-01    1.000e+00 -3.124e-09
+## sigma        -1.516e-09   -3.124e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1627,25 +1627,27 @@ summary(m.L1.SFO)
mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the χ2 error level is checked.

-
m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
-plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
-

+
m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
+
## Warning in mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet = TRUE): Optimisation did not converge:
+## false convergence (8)
+
plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
+

summary(m.L1.FOMC, data = FALSE)
## Warning in sqrt(diag(covar)): NaNs produced
## Warning in sqrt(1/diag(V)): NaNs produced
## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
 ## doubtful
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:39 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 357 model solutions performed in 0.071 s
+## Fitted using 369 model solutions performed in 0.081 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1666,34 +1668,39 @@ plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")

+##        DT50  DT90 DT50back
+## parent 7.25 24.08     7.25

We get a warning that the default optimisation algorithm Port did not converge, which is an indication that the model is overparameterised, i.e. contains too many parameters that are ill-defined as a consequence.

And in fact, due to the higher number of parameters, and the lower number of degrees of freedom of the fit, the χ2 error level is actually higher for the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the parameters log_alpha and log_beta internally fitted in the model have excessive confidence intervals, that span more than 25 orders of magnitude (!) when backtransformed to the scale of alpha and beta. Also, the t-test for significant difference from zero does not indicate such a significant difference, with p-values greater than 0.1, and finally, the parameter correlation of log_alpha and log_beta is 1.000, clearly indicating that the model is overparameterised.

The χ2 error levels reported in Appendix 3 and Appendix 7 to the FOCUS kinetics report are rounded to integer percentages and partly deviate by one percentage point from the results calculated by mkin. The reason for this is not known. However, mkin gives the same χ2 error levels as the kinfit package and the calculation routines of the kinfit package have been extensively compared to the results obtained by the KinGUI software, as documented in the kinfit package vignette. KinGUI was the first widely used standard package in this field. Also, the calculation of χ2 error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -1735,17 +1742,17 @@ plot(m.L2.FOMC, show_residuals = TRUE, main = "FOCUS L2 - FOMC") 

summary(m.L2.FOMC, data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:35 2022 
+## Date of summary: Wed Sep 14 22:28:35 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 239 model solutions performed in 0.045 s
+## Fitted using 239 model solutions performed in 0.049 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1780,10 +1787,10 @@ plot(m.L2.FOMC, show_residuals = TRUE,
 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.637e-09
-## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.617e-07
-## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.387e-07
-## sigma     -7.637e-09 -1.617e-07 -1.387e-07  1.000e+00
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01 -7.828e-09
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.602e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.372e-07
+## sigma     -7.828e-09 -1.602e-07 -1.372e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1813,10 +1820,10 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
      main = "FOCUS L2 - DFOP")

 

 
summary(m.L2.DFOP, data = FALSE)

-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:40 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:36 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1825,7 +1832,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 581 model solutions performed in 0.119 s
+## Fitted using 581 model solutions performed in 0.135 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1856,18 +1863,18 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## Optimised, transformed parameters with symmetric confidence intervals:
 ##          Estimate Std. Error      Lower     Upper
 ## parent_0   93.950  9.998e-01    91.5900   96.3100
-## log_k1      3.113  1.845e+03 -4360.0000 4367.0000
+## log_k1      3.112  1.842e+03 -4353.0000 4359.0000
 ## log_k2     -1.088  6.285e-02    -1.2370   -0.9394
 ## g_qlogis   -0.399  9.946e-02    -0.6342   -0.1638
 ## sigma       1.414  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
 ##            parent_0     log_k1     log_k2   g_qlogis      sigma
-## parent_0  1.000e+00  6.784e-07 -5.188e-10  2.665e-01 -5.800e-10
-## log_k1    6.784e-07  1.000e+00  1.114e-04 -2.191e-04 -1.029e-05
-## log_k2   -5.188e-10  1.114e-04  1.000e+00 -7.903e-01  5.080e-09
-## g_qlogis  2.665e-01 -2.191e-04 -7.903e-01  1.000e+00 -7.991e-09
-## sigma    -5.800e-10 -1.029e-05  5.080e-09 -7.991e-09  1.000e+00
+## parent_0  1.000e+00  6.783e-07 -3.390e-10  2.665e-01 -2.967e-10
+## log_k1    6.783e-07  1.000e+00  1.116e-04 -2.196e-04 -1.031e-05
+## log_k2   -3.390e-10  1.116e-04  1.000e+00 -7.903e-01  2.917e-09
+## g_qlogis  2.665e-01 -2.196e-04 -7.903e-01  1.000e+00 -4.408e-09
+## sigma    -2.967e-10 -1.031e-05  2.917e-09 -4.408e-09  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -1875,7 +1882,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## for estimators of untransformed parameters.
 ##          Estimate   t value    Pr(>t)   Lower   Upper
 ## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
-## k1        22.4800 5.544e-04 4.998e-01  0.0000     Inf
+## k1        22.4800 5.553e-04 4.998e-01  0.0000     Inf
 ## k2         0.3369 1.591e+01 4.697e-07  0.2904  0.3909
 ## g          0.4016 1.680e+01 3.238e-07  0.3466  0.4591
 ## sigma      1.4140 4.899e+00 8.776e-04  0.7314  2.0960
@@ -1887,7 +1894,7 @@ plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50back DT50_k1 DT50_k2
-## parent 0.5335 5.311    1.599 0.03083   2.058

+## parent 0.5335 5.311    1.599 0.03084   2.058

 
Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion.

 
 
@@ -1913,10 +1920,10 @@ plot(mm.L3)

The objects returned by mmkin are arranged like a matrix, with models as a row index and datasets as a column index.

We can extract the summary and plot for e.g. the DFOP fit, using square brackets for indexing which will result in the use of the summary and plot functions working on mkinfit objects.

summary(mm.L3[["DFOP", 1]])
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:40 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:36 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * exp(-k2 *
@@ -1925,7 +1932,7 @@ plot(mm.L3)

 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 376 model solutions performed in 0.072 s
+## Fitted using 376 model solutions performed in 0.081 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -1963,11 +1970,11 @@ plot(mm.L3)
## ## Parameter correlation: ## parent_0 log_k1 log_k2 g_qlogis sigma -## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.632e-08 -## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.145e-07 -## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.021e-06 -## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.925e-07 -## sigma -9.632e-08 7.145e-07 1.021e-06 -7.925e-07 1.000e+00 +## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 -9.664e-08 +## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 7.147e-07 +## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 1.022e-06 +## g_qlogis 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -7.926e-07 +## sigma -9.664e-08 7.147e-07 1.022e-06 -7.926e-07 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. @@ -2021,17 +2028,17 @@ plot(mm.L4)

The χ2 error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the χ2 test passes is slightly lower for the FOMC model. However, the difference appears negligible.

summary(mm.L4[["SFO", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:41 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:36 2022 
+## Date of summary: Wed Sep 14 22:28:37 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - k_parent * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 142 model solutions performed in 0.027 s
+## Fitted using 142 model solutions performed in 0.034 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2063,9 +2070,9 @@ plot(mm.L4)

 ## 
 ## Parameter correlation:
 ##               parent_0 log_k_parent     sigma
-## parent_0     1.000e+00    5.938e-01 3.440e-07
-## log_k_parent 5.938e-01    1.000e+00 5.885e-07
-## sigma        3.440e-07    5.885e-07 1.000e+00
+## parent_0     1.000e+00    5.938e-01 3.387e-07
+## log_k_parent 5.938e-01    1.000e+00 5.830e-07
+## sigma        3.387e-07    5.830e-07 1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
@@ -2085,17 +2092,17 @@ plot(mm.L4)
## DT50 DT90 ## parent 106 352 
summary(mm.L4[["FOMC", 1]], data = FALSE)
-
## mkin version used for fitting:    1.1.0 
+
## mkin version used for fitting:    1.1.2 
 ## R version used for fitting:       4.2.1 
-## Date of fit:     Fri Jul  8 15:44:41 2022 
-## Date of summary: Fri Jul  8 15:44:41 2022 
+## Date of fit:     Wed Sep 14 22:28:37 2022 
+## Date of summary: Wed Sep 14 22:28:37 2022 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted using 224 model solutions performed in 0.041 s
+## Fitted using 224 model solutions performed in 0.045 s
 ## 
 ## Error model: Constant variance 
 ## 
@@ -2130,10 +2137,10 @@ plot(mm.L4)

 ## 
 ## Parameter correlation:
 ##             parent_0  log_alpha   log_beta      sigma
-## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.563e-07
-## log_alpha -4.696e-01  1.000e+00  9.889e-01  4.066e-08
-## log_beta  -5.543e-01  9.889e-01  1.000e+00  6.818e-08
-## sigma     -2.563e-07  4.066e-08  6.818e-08  1.000e+00
+## parent_0   1.000e+00 -4.696e-01 -5.543e-01 -2.468e-07
+## log_alpha -4.696e-01  1.000e+00  9.889e-01  2.478e-08
+## log_beta  -5.543e-01  9.889e-01  1.000e+00  5.211e-08
+## sigma     -2.468e-07  2.478e-08  5.211e-08  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
-- 
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