## mkin version used for fitting: 0.9.49.4 +## R version used for fitting: 3.5.3 +## Date of fit: Wed Apr 10 10:11:33 2019 +## Date of summary: Wed Apr 10 10:11:33 2019 ## ## Equations: ## d_parent/dt = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Port using 37 model solutions performed in 0.095 s +## Fitted with method using 133 model solutions performed in 0.344 s ## -## Weighting: none +## Error model: +## NULL ## ## Starting values for parameters to be optimised: -## value type -## parent_0 89.85 state -## k_parent_sink 0.10 deparm +## value type +## parent_0 89.850000 state +## k_parent_sink 0.100000 deparm +## sigma 2.779827 error ## ## Starting values for the transformed parameters actually optimised: ## value lower upper ## parent_0 89.850000 -Inf Inf ## log_k_parent_sink -2.302585 -Inf Inf +## sigma 2.779827 0 Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: ## Estimate Std. Error Lower Upper -## parent_0 92.470 1.36800 89.570 95.370 -## log_k_parent_sink -2.347 0.04057 -2.433 -2.261 +## parent_0 92.470 1.28200 89.740 95.200 +## log_k_parent_sink -2.347 0.03763 -2.428 -2.267 +## sigma 2.780 0.46330 1.792 3.767 ## ## Parameter correlation: -## parent_0 log_k_parent_sink -## parent_0 1.0000 0.6248 -## log_k_parent_sink 0.6248 1.0000 -## -## Residual standard error: 2.948 on 16 degrees of freedom +## parent_0 log_k_parent_sink sigma +## parent_0 1.000e+00 6.186e-01 -1.712e-09 +## log_k_parent_sink 6.186e-01 1.000e+00 -3.237e-09 +## sigma -1.712e-09 -3.237e-09 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. ## Estimate t value Pr(>t) Lower Upper -## parent_0 92.47000 67.58 2.170e-21 89.57000 95.3700 -## k_parent_sink 0.09561 24.65 1.867e-14 0.08773 0.1042 +## parent_0 92.47000 72.13 8.824e-21 89.74000 95.2000 +## k_parent_sink 0.09561 26.57 2.487e-14 0.08824 0.1036 +## sigma 2.78000 6.00 1.216e-05 1.79200 3.7670 ## ## Chi2 error levels in percent: ## err.min n.optim df @@ -199,61 +203,76 @@

mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")

For comparison, the FOMC model is fitted as well, and the $\chi^2$ 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)

## mkin version used for fitting:    0.9.48.1 
-## R version used for fitting:       3.5.2 
-## Date of fit:     Mon Mar  4 14:06:43 2019 
-## Date of summary: Mon Mar  4 14:06:43 2019 
+summary(m.L1.FOMC, data = FALSE)
+## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
+## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
+## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non-
+## finite result is doubtful
+## mkin version used for fitting:    0.9.49.4 
+## R version used for fitting:       3.5.3 
+## Date of fit:     Wed Apr 10 10:11:34 2019 
+## Date of summary: Wed Apr 10 10:11:34 2019 
+## 
+## 
+## Warning: Optimisation did not converge:
+## false convergence (8) 
+## 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 611 model solutions performed in 1.502 s
+## Fitted with method using 344 model solutions performed in 0.778 s
 ## 
-## Weighting: none
+## Error model:
+## NULL
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 89.85  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
+##             value   type
+## parent_0 89.85000  state
+## alpha     1.00000 deparm
+## beta     10.00000 deparm
+## sigma     2.77987  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  89.850000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
+## sigma      2.779870     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error    Lower   Upper
-## parent_0     92.47      1.482    89.31   95.63
-## log_alpha    11.25    598.200 -1264.00 1286.00
-## log_beta     13.60    598.200 -1261.00 1289.00
+##           Estimate Std. Error  Lower  Upper
+## parent_0     92.47     1.2810 89.720 95.220
+## log_alpha    10.60        NaN    NaN    NaN
+## log_beta     12.95        NaN    NaN    NaN
+## sigma         2.78     0.4554  1.803  3.757
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta
-## parent_0    1.0000   -0.3016  -0.3016
-## log_alpha  -0.3016    1.0000   1.0000
-## log_beta   -0.3016    1.0000   1.0000
-## 
-## Residual standard error: 3.045 on 15 degrees of freedom
+##           parent_0 log_alpha log_beta    sigma
+## parent_0  1.000000       NaN      NaN 0.008714
+## log_alpha      NaN         1      NaN      NaN
+## log_beta       NaN       NaN        1      NaN
+## sigma     0.008714       NaN      NaN 1.000000
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##           Estimate  t value    Pr(>t) Lower Upper
-## parent_0     92.47 64.45000 4.757e-20 89.31 95.63
-## alpha     76830.00  0.02852 4.888e-01  0.00   Inf
-## beta     803500.00  0.02852 4.888e-01  0.00   Inf
+##           Estimate  t value    Pr(>t)  Lower  Upper
+## parent_0     92.47 72.13000 1.052e-19 89.720 95.220
+## alpha     40090.00  0.02388 4.906e-01     NA     NA
+## beta     419300.00  0.02388 4.906e-01     NA     NA
+## sigma         2.78  6.00000 1.628e-05  1.803  3.757
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -262,7 +281,7 @@
 ## 
 ## Estimated disappearance times:
 ##         DT50  DT90 DT50back
-## parent 7.249 24.08    7.249
+## parent 7.249 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 $\chi^2$ 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 $\chi^2$ 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 $\chi^2$ 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 $\chi^2$ error levels was compared with KinGUII, CAKE and DegKin manager in a project sponsored by the German Umweltbundesamt (Ranke 2014).

@@ -271,19 +290,19 @@

Laboratory Data L2

The following code defines example dataset L2 from the FOCUS kinetics report, p. 287:

FOCUS_2006_L2 = data.frame(
-  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
-  parent = c(96.1, 91.8, 41.4, 38.7,
-             19.3, 22.3, 4.6, 4.6,
-             2.6, 1.2, 0.3, 0.6))
-FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)

FOCUS_2006_L2 = data.frame(
+  t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
+  parent = c(96.1, 91.8, 41.4, 38.7,
+             19.3, 22.3, 4.6, 4.6,
+             2.6, 1.2, 0.3, 0.6))
+FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)

SFO fit for L2

Again, the SFO model is fitted and the result is plotted. The residual plot can be obtained simply by adding the argument show_residuals to the plot command.

m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
-plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - SFO")

m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
+plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - SFO")

The $\chi^2$ error level of 14% suggests that the model does not fit very well. This is also obvious from the plots of the fit, in which we have included the residual plot.

In the FOCUS kinetics report, it is stated that there is no apparent systematic error observed from the residual plot up to the measured DT90 (approximately at day 5), and there is an underestimation beyond that point.

@@ -293,62 +312,66 @@

FOMC fit for L2

For comparison, the FOMC model is fitted as well, and the $\chi^2$ error level is checked.

m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.FOMC, show_residuals = TRUE,
-     main = "FOCUS L2 - FOMC")

m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.FOMC, show_residuals = TRUE,
+     main = "FOCUS L2 - FOMC")

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

## mkin version used for fitting:    0.9.48.1 
-## R version used for fitting:       3.5.2 
-## Date of fit:     Mon Mar  4 14:06:43 2019 
-## Date of summary: Mon Mar  4 14:06:43 2019 
+summary(m.L2.FOMC, data = FALSE)
+## mkin version used for fitting:    0.9.49.4 
+## R version used for fitting:       3.5.3 
+## Date of fit:     Wed Apr 10 10:11:35 2019 
+## Date of summary: Wed Apr 10 10:11:35 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 81 model solutions performed in 0.196 s
+## Fitted with method using 240 model solutions performed in 0.564 s
 ## 
-## Weighting: none
+## Error model:
+## NULL
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## alpha     1.00 deparm
-## beta     10.00 deparm
+##              value   type
+## parent_0 93.950000  state
+## alpha     1.000000 deparm
+## beta     10.000000 deparm
+## sigma     2.275722  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##               value lower upper
 ## parent_0  93.950000  -Inf   Inf
 ## log_alpha  0.000000  -Inf   Inf
 ## log_beta   2.302585  -Inf   Inf
+## sigma      2.275722     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##           Estimate Std. Error   Lower   Upper
-## parent_0   93.7700     1.8560 89.5700 97.9700
-## log_alpha   0.3180     0.1867 -0.1044  0.7405
-## log_beta    0.2102     0.2943 -0.4555  0.8759
+##           Estimate Std. Error    Lower   Upper
+## parent_0   93.7700     1.6130 90.05000 97.4900
+## log_alpha   0.3180     0.1559 -0.04149  0.6776
+## log_beta    0.2102     0.2493 -0.36460  0.7850
+## sigma       2.2760     0.4645  1.20500  3.3470
 ## 
 ## Parameter correlation:
-##           parent_0 log_alpha log_beta
-## parent_0   1.00000  -0.09553  -0.1863
-## log_alpha -0.09553   1.00000   0.9757
-## log_beta  -0.18628   0.97567   1.0000
-## 
-## Residual standard error: 2.628 on 9 degrees of freedom
+##             parent_0  log_alpha   log_beta      sigma
+## parent_0   1.000e+00 -1.151e-01 -2.085e-01  1.606e-08
+## log_alpha -1.151e-01  1.000e+00  9.741e-01 -1.168e-07
+## log_beta  -2.085e-01  9.741e-01  1.000e+00 -1.029e-07
+## sigma      1.606e-08 -1.168e-07 -1.029e-07  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
 ##          Estimate t value    Pr(>t)   Lower  Upper
-## parent_0   93.770  50.510 1.173e-12 89.5700 97.970
-## alpha       1.374   5.355 2.296e-04  0.9009  2.097
-## beta        1.234   3.398 3.949e-03  0.6341  2.401
+## parent_0   93.770  58.120 4.267e-12 90.0500 97.490
+## alpha       1.374   6.414 1.030e-04  0.9594  1.969
+## beta        1.234   4.012 1.942e-03  0.6945  2.192
+## sigma       2.276   4.899 5.977e-04  1.2050  3.347
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -364,17 +387,15 @@
 
 DFOP fit for L2
 Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.
-m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
-plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
-     main = "FOCUS L2 - DFOP")
+m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
+plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
+     main = "FOCUS L2 - DFOP")
 
-summary(m.L2.DFOP, data = FALSE)
-## Warning in summary.mkinfit(m.L2.DFOP, data = FALSE): Could not estimate
-## covariance matrix; singular system.
-## mkin version used for fitting:    0.9.48.1 
-## R version used for fitting:       3.5.2 
-## Date of fit:     Mon Mar  4 14:06:44 2019 
-## Date of summary: Mon Mar  4 14:06:44 2019 
+summary(m.L2.DFOP, data = FALSE)
+## mkin version used for fitting:    0.9.49.4 
+## R version used for fitting:       3.5.3 
+## Date of fit:     Wed Apr 10 10:11:37 2019 
+## Date of summary: Wed Apr 10 10:11:37 2019 
 ## 
 ## Equations:
 ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
@@ -383,16 +404,18 @@
 ## 
 ## Model predictions using solution type analytical 
 ## 
-## Fitted with method Port using 336 model solutions performed in 0.84 s
+## Fitted with method using 585 model solutions performed in 1.296 s
 ## 
-## Weighting: none
+## Error model:
+## NULL
 ## 
 ## Starting values for parameters to be optimised:
-##          value   type
-## parent_0 93.95  state
-## k1        0.10 deparm
-## k2        0.01 deparm
-## g         0.50 deparm
+##              value   type
+## parent_0 93.950000  state
+## k1        0.100000 deparm
+## k2        0.010000 deparm
+## g         0.500000 deparm
+## sigma     1.413899  error
 ## 
 ## Starting values for the transformed parameters actually optimised:
 ##              value lower upper
@@ -400,30 +423,37 @@
 ## log_k1   -2.302585  -Inf   Inf
 ## log_k2   -4.605170  -Inf   Inf
 ## g_ilr     0.000000  -Inf   Inf
+## sigma     1.413899     0   Inf
 ## 
 ## Fixed parameter values:
 ## None
 ## 
 ## Optimised, transformed parameters with symmetric confidence intervals:
-##          Estimate Std. Error Lower Upper
-## parent_0  93.9500         NA    NA    NA
-## log_k1     3.1370         NA    NA    NA
-## log_k2    -1.0880         NA    NA    NA
-## g_ilr     -0.2821         NA    NA    NA
+##          Estimate Std. Error      Lower     Upper
+## parent_0  93.9500  9.998e-01    91.5900   96.3100
+## log_k1     3.1350  2.336e+03 -5522.0000 5528.0000
+## log_k2    -1.0880  6.285e-02    -1.2370   -0.9394
+## g_ilr     -0.2821  7.033e-02    -0.4484   -0.1158
+## sigma      1.4140  2.886e-01     0.7314    2.0960
 ## 
 ## Parameter correlation:
-## Could not estimate covariance matrix; singular system.
-## Residual standard error: 1.732 on 8 degrees of freedom
+##            parent_0     log_k1     log_k2      g_ilr      sigma
+## parent_0  1.000e+00  5.247e-07 -1.026e-10  2.665e-01 -8.076e-11
+## log_k1    5.247e-07  1.000e+00  8.592e-05 -1.690e-04 -7.938e-06
+## log_k2   -1.026e-10  8.592e-05  1.000e+00 -7.903e-01  5.048e-10
+## g_ilr     2.665e-01 -1.690e-04 -7.903e-01  1.000e+00 -6.476e-10
+## sigma    -8.076e-11 -7.938e-06  5.048e-10 -6.476e-10  1.000e+00
 ## 
 ## Backtransformed parameters:
 ## Confidence intervals for internally transformed parameters are asymmetric.
 ## t-test (unrealistically) based on the assumption of normal distribution
 ## for estimators of untransformed parameters.
-##          Estimate t value Pr(>t) Lower Upper
-## parent_0  93.9500      NA     NA    NA    NA
-## k1        23.0400      NA     NA    NA    NA
-## k2         0.3369      NA     NA    NA    NA
-## g          0.4016      NA     NA    NA    NA
+##          Estimate   t value    Pr(>t)   Lower   Upper
+## parent_0  93.9500 9.397e+01 2.036e-12 91.5900 96.3100
+## k1        23.0000 4.377e-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
 ## 
 ## Chi2 error levels in percent:
 ##          err.min n.optim df
@@ -432,7 +462,7 @@
 ## 
 ## Estimated disappearance times:
 ##          DT50  DT90 DT50_k1 DT50_k2
-## parent 0.5335 5.311 0.03009   2.058
+## parent 0.5335 5.311 0.03014   2.058
 Here, the DFOP model is clearly the best-fit model for dataset L2 based on the chi^2 error level criterion. However, the failure to calculate the covariance matrix indicates that the parameter estimates correlate excessively. Therefore, the FOMC model may be preferred for this dataset.

@@ -440,18 +470,18 @@ Laboratory Data L3 The following code defines example dataset L3 from the FOCUS kinetics report, p. 290. -FOCUS_2006_L3 = data.frame( - t = c(0, 3, 7, 14, 30, 60, 91, 120), - parent = c(97.8, 60, 51, 43, 35, 22, 15, 12)) -FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) +FOCUS_2006_L3 = data.frame( + t = c(0, 3, 7, 14, 30, 60, 91, 120), + parent = c(97.8, 60, 51, 43, 35, 22, 15, 12)) +FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3) Fit multiple models As of mkin version 0.9-39 (June 2015), we can fit several models to one or more datasets in one call to the function mmkin. The datasets have to be passed in a list, in this case a named list holding only the L3 dataset prepared above. -# Only use one core here, not to offend the CRAN checks -mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1, - list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE) -plot(mm.L3) +# Only use one core here, not to offend the CRAN checks +mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1, + list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE) +plot(mm.L3) The $\chi^2$ error level of 21% as well as the plot suggest that the SFO model does not fit very well. The FOMC model performs better, with an error level at which the $\chi^2$ test passes of 7%. Fitting the four parameter DFOP model further reduces the $\chi^2$ error level considerably. @@ -460,11 +490,11 @@ Accessing mmkin objects 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: 0.9.48.1 -## R version used for fitting: 3.5.2 -## Date of fit: Mon Mar 4 14:06:45 2019 -## Date of summary: Mon Mar 4 14:06:46 2019 +summary(mm.L3[["DFOP", 1]]) +## mkin version used for fitting: 0.9.49.4 +## R version used for fitting: 3.5.3 +## Date of fit: Wed Apr 10 10:11:39 2019 +## Date of summary: Wed Apr 10 10:11:39 2019 ## ## Equations: ## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) * @@ -473,16 +503,18 @@ ## ## Model predictions using solution type analytical ## -## Fitted with method Port using 137 model solutions performed in 0.343 s +## Fitted with method using 372 model solutions performed in 0.809 s ## -## Weighting: none +## Error model: +## NULL ## ## Starting values for parameters to be optimised: -## value type -## parent_0 97.80 state -## k1 0.10 deparm -## k2 0.01 deparm -## g 0.50 deparm +## value type +## parent_0 97.800000 state +## k1 0.100000 deparm +## k2 0.010000 deparm +## g 0.500000 deparm +## sigma 1.017292 error ## ## Starting values for the transformed parameters actually optimised: ## value lower upper @@ -490,35 +522,37 @@ ## log_k1 -2.302585 -Inf Inf ## log_k2 -4.605170 -Inf Inf ## g_ilr 0.000000 -Inf Inf +## sigma 1.017292 0 Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 97.7500 1.43800 93.7500 101.70000 -## log_k1 -0.6612 0.13340 -1.0310 -0.29100 -## log_k2 -4.2860 0.05902 -4.4500 -4.12200 -## g_ilr -0.1229 0.05121 -0.2651 0.01925 +## Estimate Std. Error Lower Upper +## parent_0 97.7500 1.01900 94.5000 101.000000 +## log_k1 -0.6612 0.10050 -0.9812 -0.341300 +## log_k2 -4.2860 0.04322 -4.4230 -4.148000 +## g_ilr -0.1229 0.03727 -0.2415 -0.004343 +## sigma 1.0170 0.25430 0.2079 1.827000 ## ## Parameter correlation: -## parent_0 log_k1 log_k2 g_ilr -## parent_0 1.00000 0.1640 0.01315 0.4253 -## log_k1 0.16400 1.0000 0.46478 -0.5526 -## log_k2 0.01315 0.4648 1.00000 -0.6631 -## g_ilr 0.42526 -0.5526 -0.66310 1.0000 -## -## Residual standard error: 1.439 on 4 degrees of freedom +## parent_0 log_k1 log_k2 g_ilr sigma +## parent_0 1.000e+00 1.732e-01 2.282e-02 4.009e-01 1.656e-07 +## log_k1 1.732e-01 1.000e+00 4.945e-01 -5.809e-01 6.759e-08 +## log_k2 2.282e-02 4.945e-01 1.000e+00 -6.812e-01 3.867e-07 +## g_ilr 4.009e-01 -5.809e-01 -6.812e-01 1.000e+00 -3.839e-07 +## sigma 1.656e-07 6.759e-08 3.867e-07 -3.839e-07 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. ## Estimate t value Pr(>t) Lower Upper -## parent_0 97.75000 67.970 1.404e-07 93.75000 101.70000 -## k1 0.51620 7.499 8.460e-04 0.35650 0.74750 -## k2 0.01376 16.940 3.557e-05 0.01168 0.01621 -## g 0.45660 25.410 7.121e-06 0.40730 0.50680 +## parent_0 97.75000 95.960 1.248e-06 94.50000 101.00000 +## k1 0.51620 9.947 1.081e-03 0.37490 0.71090 +## k2 0.01376 23.140 8.840e-05 0.01199 0.01579 +## g 0.45660 34.920 2.581e-05 0.41540 0.49850 +## sigma 1.01700 4.000 1.400e-02 0.20790 1.82700 ## ## Chi2 error levels in percent: ## err.min n.optim df @@ -539,7 +573,7 @@ ## 60 parent 22.0 23.26 -1.25919 ## 91 parent 15.0 15.18 -0.18181 ## 120 parent 12.0 10.19 1.81395 -plot(mm.L3[["DFOP", 1]], show_errmin = TRUE) +plot(mm.L3[["DFOP", 1]], show_errmin = TRUE) Here, a look to the model plot, the confidence intervals of the parameters and the correlation matrix suggest that the parameter estimates are reliable, and the DFOP model can be used as the best-fit model based on the $\chi^2$ error level criterion for laboratory data L3. This is also an example where the standard t-test for the parameter g_ilr is misleading, as it tests for a significant difference from zero. In this case, zero appears to be the correct value for this parameter, and the confidence interval for the backtransformed parameter g is quite narrow. @@ -549,65 +583,69 @@ Laboratory Data L4 The following code defines example dataset L4 from the FOCUS kinetics report, p. 293: -FOCUS_2006_L4 = data.frame( - t = c(0, 3, 7, 14, 30, 60, 91, 120), - parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0)) -FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) +FOCUS_2006_L4 = data.frame( + t = c(0, 3, 7, 14, 30, 60, 91, 120), + parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0)) +FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4) Fits of the SFO and FOMC models, plots and summaries are produced below: -# Only use one core here, not to offend the CRAN checks -mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1, - list("FOCUS L4" = FOCUS_2006_L4_mkin), - quiet = TRUE) -plot(mm.L4) +# Only use one core here, not to offend the CRAN checks +mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1, + list("FOCUS L4" = FOCUS_2006_L4_mkin), + quiet = TRUE) +plot(mm.L4) The $\chi^2$ error level of 3.3% as well as the plot suggest that the SFO model fits very well. The error level at which the $\chi^2$ 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: 0.9.48.1 -## R version used for fitting: 3.5.2 -## Date of fit: Mon Mar 4 14:06:46 2019 -## Date of summary: Mon Mar 4 14:06:46 2019 +summary(mm.L4[["SFO", 1]], data = FALSE) +## mkin version used for fitting: 0.9.49.4 +## R version used for fitting: 3.5.3 +## Date of fit: Wed Apr 10 10:11:39 2019 +## Date of summary: Wed Apr 10 10:11:40 2019 ## ## Equations: ## d_parent/dt = - k_parent_sink * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Port using 46 model solutions performed in 0.111 s +## Fitted with method using 146 model solutions performed in 0.306 s ## -## Weighting: none +## Error model: +## NULL ## ## Starting values for parameters to be optimised: -## value type -## parent_0 96.6 state -## k_parent_sink 0.1 deparm +## value type +## parent_0 96.60000 state +## k_parent_sink 0.10000 deparm +## sigma 3.16181 error ## ## Starting values for the transformed parameters actually optimised: ## value lower upper ## parent_0 96.600000 -Inf Inf ## log_k_parent_sink -2.302585 -Inf Inf +## sigma 3.161810 0 Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: ## Estimate Std. Error Lower Upper -## parent_0 96.44 1.94900 91.670 101.200 -## log_k_parent_sink -5.03 0.07999 -5.225 -4.834 +## parent_0 96.440 1.69900 92.070 100.800 +## log_k_parent_sink -5.030 0.07059 -5.211 -4.848 +## sigma 3.162 0.79050 1.130 5.194 ## ## Parameter correlation: -## parent_0 log_k_parent_sink -## parent_0 1.0000 0.5865 -## log_k_parent_sink 0.5865 1.0000 -## -## Residual standard error: 3.651 on 6 degrees of freedom +## parent_0 log_k_parent_sink sigma +## parent_0 1.000e+00 5.938e-01 5.612e-10 +## log_k_parent_sink 5.938e-01 1.000e+00 -4.994e-10 +## sigma 5.612e-10 -4.994e-10 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. ## Estimate t value Pr(>t) Lower Upper -## parent_0 96.440000 49.49 2.283e-09 91.670000 1.012e+02 -## k_parent_sink 0.006541 12.50 8.008e-06 0.005378 7.955e-03 +## parent_0 96.440000 56.77 1.604e-08 92.070000 1.008e+02 +## k_parent_sink 0.006541 14.17 1.578e-05 0.005455 7.842e-03 +## sigma 3.162000 4.00 5.162e-03 1.130000 5.194e+00 ## ## Chi2 error levels in percent: ## err.min n.optim df @@ -621,58 +659,62 @@ ## Estimated disappearance times: ## DT50 DT90 ## parent 106 352 -summary(mm.L4[["FOMC", 1]], data = FALSE) -## mkin version used for fitting: 0.9.48.1 -## R version used for fitting: 3.5.2 -## Date of fit: Mon Mar 4 14:06:46 2019 -## Date of summary: Mon Mar 4 14:06:46 2019 +summary(mm.L4[["FOMC", 1]], data = FALSE) +## mkin version used for fitting: 0.9.49.4 +## R version used for fitting: 3.5.3 +## Date of fit: Wed Apr 10 10:11:40 2019 +## Date of summary: Wed Apr 10 10:11:40 2019 ## ## Equations: ## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent ## ## Model predictions using solution type analytical ## -## Fitted with method Port using 66 model solutions performed in 0.173 s +## Fitted with method using 224 model solutions performed in 0.478 s ## -## Weighting: none +## Error model: +## NULL ## ## Starting values for parameters to be optimised: -## value type -## parent_0 96.6 state -## alpha 1.0 deparm -## beta 10.0 deparm +## value type +## parent_0 96.600000 state +## alpha 1.000000 deparm +## beta 10.000000 deparm +## sigma 1.830055 error ## ## Starting values for the transformed parameters actually optimised: ## value lower upper ## parent_0 96.600000 -Inf Inf ## log_alpha 0.000000 -Inf Inf ## log_beta 2.302585 -Inf Inf +## sigma 1.830055 0 Inf ## ## Fixed parameter values: ## None ## ## Optimised, transformed parameters with symmetric confidence intervals: -## Estimate Std. Error Lower Upper -## parent_0 99.1400 1.6800 94.820 103.5000 -## log_alpha -0.3506 0.3725 -1.308 0.6068 -## log_beta 4.1740 0.5635 2.726 5.6230 +## Estimate Std. Error Lower Upper +## parent_0 99.1400 1.2670 95.6300 102.7000 +## log_alpha -0.3506 0.2616 -1.0770 0.3756 +## log_beta 4.1740 0.3938 3.0810 5.2670 +## sigma 1.8300 0.4575 0.5598 3.1000 ## ## Parameter correlation: -## parent_0 log_alpha log_beta -## parent_0 1.0000 -0.5365 -0.6083 -## log_alpha -0.5365 1.0000 0.9913 -## log_beta -0.6083 0.9913 1.0000 -## -## Residual standard error: 2.315 on 5 degrees of freedom +## parent_0 log_alpha log_beta sigma +## parent_0 1.000e+00 -4.696e-01 -5.543e-01 -2.460e-07 +## log_alpha -4.696e-01 1.000e+00 9.889e-01 2.351e-08 +## log_beta -5.543e-01 9.889e-01 1.000e+00 5.079e-08 +## sigma -2.460e-07 2.351e-08 5.079e-08 1.000e+00 ## ## Backtransformed parameters: ## Confidence intervals for internally transformed parameters are asymmetric. ## t-test (unrealistically) based on the assumption of normal distribution ## for estimators of untransformed parameters. ## Estimate t value Pr(>t) Lower Upper -## parent_0 99.1400 59.020 1.322e-08 94.8200 103.500 -## alpha 0.7042 2.685 2.178e-02 0.2703 1.835 -## beta 64.9800 1.775 6.807e-02 15.2600 276.600 +## parent_0 99.1400 78.250 7.993e-08 95.6300 102.700 +## alpha 0.7042 3.823 9.365e-03 0.3407 1.456 +## beta 64.9800 2.540 3.201e-02 21.7800 193.900 +## sigma 1.8300 4.000 8.065e-03 0.5598 3.100 ## ## Chi2 error levels in percent: ## err.min n.optim df diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png index 770db292..6e4ccb9d 100644 Binary files a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png and b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-12-1.png differ diff --git a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png index ee225461..0a403808 100644 Binary files a/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png and b/docs/articles/FOCUS_L_files/figure-html/unnamed-chunk-6-1.png differ diff --git a/docs/articles/index.html b/docs/articles/index.html index 9381dedb..eb2d55ef 100644 --- a/docs/articles/index.html +++ b/docs/articles/index.html @@ -60,7 +60,7 @@ mkin - 0.9.48.1 + 0.9.49.4 @@ -132,6 +132,7 @@ Calculation of time weighted average concentrations with mkin Example evaluation of FOCUS dataset Z Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance + Benchmark timings for mkin on various systems Performance benefit by using compiled model definitions in mkin diff --git a/docs/articles/mkin.html b/docs/articles/mkin.html index 93ad4b56..2e5cd759 100644 --- a/docs/articles/mkin.html +++ b/docs/articles/mkin.html @@ -30,7 +30,7 @@ mkin - 0.9.48.1 + 0.9.49.4 @@ -88,7 +88,7 @@ Introduction to mkin Johannes Ranke - 2019-03-04 + 2019-04-10 mkin.Rmd diff --git a/docs/articles/twa.html b/docs/articles/twa.html index f58814e3..cdcea4d3 100644 --- a/docs/articles/twa.html +++ b/docs/articles/twa.html @@ -30,7 +30,7 @@ mkin - 0.9.48.1 + 0.9.49.4 @@ -88,7 +88,7 @@ Calculation of time weighted average concentrations with mkin Johannes Ranke - 2019-03-04 + 2019-04-10 twa.Rmd diff --git a/docs/articles/web_only/FOCUS_Z.html b/docs/articles/web_only/FOCUS_Z.html index 79e39e55..33d0c90f 100644 --- a/docs/articles/web_only/FOCUS_Z.html +++ b/docs/articles/web_only/FOCUS_Z.html @@ -30,7 +30,7 @@ mkin - 0.9.48.1 + 0.9.49.4 @@ -88,7 +88,7 @@ Example evaluation of FOCUS dataset Z Johannes Ranke - 2019-03-04 + 2019-04-10 FOCUS_Z.Rmd @@ -125,87 +125,97 @@ Z.2a <- mkinmod(Z0 = mkinsub("SFO", "Z1"), Z1 = mkinsub("SFO")) ## Successfully compiled differential equation model from auto-generated C code. -m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.2a) +m.Z.2a <- mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.2a, FOCUS_2006_Z_mkin, quiet = TRUE): Observations +## with value of zero were removed from the data +plot_sep(m.Z.2a) -summary(m.Z.2a, data = FALSE)$bpar -## Warning in summary.mkinfit(m.Z.2a, data = FALSE): Could not estimate -## covariance matrix; singular system. -## Estimate se_notrans t value Pr(>t) Lower Upper -## Z0_0 9.7015e+01 3.553140 2.7304e+01 1.6793e-21 NA NA -## k_Z0_sink 1.2790e-11 0.226895 5.6368e-11 5.0000e-01 NA NA -## k_Z0_Z1 2.2360e+00 0.165073 1.3546e+01 7.3938e-14 NA NA -## k_Z1_sink 4.8212e-01 0.065854 7.3212e+00 3.5520e-08 NA NA +summary(m.Z.2a, data = FALSE)$bpar +## Estimate se_notrans t value Pr(>t) Lower Upper +## Z0_0 9.7015e+01 3.39373 2.8587e+01 6.4606e-21 91.66556 102.3642 +## k_Z0_sink 4.0181e-10 0.22534 1.7831e-09 5.0000e-01 0.00000 Inf +## k_Z0_Z1 2.2360e+00 0.15915 1.4050e+01 1.1387e-13 1.95303 2.5600 +## k_Z1_sink 4.8212e-01 0.06547 7.3641e+00 5.1396e-08 0.40341 0.5762 +## sigma 4.8041e+00 0.63763 7.5343e+00 3.4444e-08 3.52677 6.0815 As obvious from the parameter summary (the component of the summary), the kinetic rate constant from parent compound Z to sink is very small and the t-test for this parameter suggests that it is not significantly different from zero. This suggests, in agreement with the analysis in the FOCUS kinetics report, to simplify the model by removing the pathway to sink. A similar result can be obtained when formation fractions are used in the model formulation: -Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"), - Z1 = mkinsub("SFO"), - use_of_ff = "max") +Z.2a.ff <- mkinmod(Z0 = mkinsub("SFO", "Z1"), + Z1 = mkinsub("SFO"), + use_of_ff = "max") ## Successfully compiled differential equation model from auto-generated C code. -m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.2a.ff) +m.Z.2a.ff <- mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.2a.ff, FOCUS_2006_Z_mkin, quiet = TRUE): Observations +## with value of zero were removed from the data +plot_sep(m.Z.2a.ff) -summary(m.Z.2a.ff, data = FALSE)$bpar -## Warning in summary.mkinfit(m.Z.2a.ff, data = FALSE): Could not estimate -## covariance matrix; singular system. -## Estimate se_notrans t value Pr(>t) Lower Upper -## Z0_0 97.01488 3.553145 27.3039 1.6793e-21 NA NA -## k_Z0 2.23601 0.216849 10.3114 3.6623e-11 NA NA -## k_Z1 0.48212 0.065854 7.3211 3.5520e-08 NA NA -## f_Z0_to_Z1 1.00000 0.101473 9.8548 9.7068e-11 NA NA +summary(m.Z.2a.ff, data = FALSE)$bpar +## Estimate se_notrans t value Pr(>t) Lower Upper +## Z0_0 97.01488 3.301084 29.3888 3.2971e-21 91.66556 102.3642 +## k_Z0 2.23601 0.207078 10.7979 3.3309e-11 1.95303 2.5600 +## k_Z1 0.48212 0.063265 7.6207 2.8155e-08 0.40341 0.5762 +## f_Z0_to_Z1 1.00000 0.094764 10.5525 5.3560e-11 0.00000 1.0000 +## sigma 4.80411 0.635638 7.5579 3.2592e-08 3.52677 6.0815 Here, the ilr transformed formation fraction fitted in the model takes a very large value, and the backtransformed formation fraction from parent Z to Z1 is practically unity. Here, the covariance matrix used for the calculation of confidence intervals is not returned as the model is overparameterised. A simplified model is obtained by removing the pathway to the sink. In the following, we use the parameterisation with formation fractions in order to be able to compare with the results in the FOCUS guidance, and as it makes it easier to use parameters obtained in a previous fit when adding a further metabolite. -Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO"), use_of_ff = "max") +Z.3 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), + Z1 = mkinsub("SFO"), use_of_ff = "max") ## Successfully compiled differential equation model from auto-generated C code. -m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.3) +m.Z.3 <- mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with +## value of zero were removed from the data +plot_sep(m.Z.3) -summary(m.Z.3, data = FALSE)$bpar -## Estimate se_notrans t value Pr(>t) Lower Upper -## Z0_0 97.01488 2.681772 36.176 2.3636e-25 91.52152 102.508 -## k_Z0 2.23601 0.146861 15.225 2.2464e-15 1.95453 2.558 -## k_Z1 0.48212 0.042687 11.294 3.0686e-12 0.40216 0.578 +summary(m.Z.3, data = FALSE)$bpar +## Estimate se_notrans t value Pr(>t) Lower Upper +## Z0_0 97.01488 2.597342 37.352 2.0106e-24 91.67597 102.3538 +## k_Z0 2.23601 0.146904 15.221 9.1477e-15 1.95354 2.5593 +## k_Z1 0.48212 0.041727 11.554 4.8268e-12 0.40355 0.5760 +## sigma 4.80411 0.620208 7.746 1.6110e-08 3.52925 6.0790 As there is only one transformation product for Z0 and no pathway to sink, the formation fraction is internally fixed to unity. Metabolites Z2 and Z3 As suggested in the FOCUS report, the pathway to sink was removed for metabolite Z1 as well in the next step. While this step appears questionable on the basis of the above results, it is followed here for the purpose of comparison. Also, in the FOCUS report, it is assumed that there is additional empirical evidence that Z1 quickly and exclusively hydrolyses to Z2. -Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO"), use_of_ff = "max") +Z.5 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO"), use_of_ff = "max") ## Successfully compiled differential equation model from auto-generated C code. -m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.5) +m.Z.5 <- mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.5, FOCUS_2006_Z_mkin, quiet = TRUE): Observations with +## value of zero were removed from the data +plot_sep(m.Z.5) Finally, metabolite Z3 is added to the model. We use the optimised differential equation parameter values from the previous fit in order to accelerate the optimization. -Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFO"), - use_of_ff = "max") +Z.FOCUS <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO", "Z3"), + Z3 = mkinsub("SFO"), + use_of_ff = "max") ## Successfully compiled differential equation model from auto-generated C code. -m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, - parms.ini = m.Z.5$bparms.ode, - quiet = TRUE) -## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation by method Port did not converge: +m.Z.FOCUS <- mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, + parms.ini = m.Z.5$bparms.ode, + quiet = TRUE) +## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z. +## 5$bparms.ode, : Observations with value of zero were removed from the data +## Warning in mkinfit(Z.FOCUS, FOCUS_2006_Z_mkin, parms.ini = m.Z.5$bparms.ode, : Optimisation did not converge: ## false convergence (8) -plot_sep(m.Z.FOCUS) +plot_sep(m.Z.FOCUS) -summary(m.Z.FOCUS, data = FALSE)$bpar +summary(m.Z.FOCUS, data = FALSE)$bpar ## Estimate se_notrans t value Pr(>t) Lower Upper -## Z0_0 96.837112 2.058861 47.0343 5.5877e-44 92.703779 100.970445 -## k_Z0 2.215368 0.118098 18.7587 7.6563e-25 1.990525 2.465609 -## k_Z1 0.478302 0.029289 16.3302 3.3408e-22 0.422977 0.540864 -## k_Z2 0.451617 0.044214 10.2144 3.1133e-14 0.371034 0.549702 -## k_Z3 0.058693 0.014296 4.1056 7.2924e-05 0.035994 0.095705 -## f_Z2_to_Z3 0.471516 0.057057 8.2639 2.8156e-11 0.360381 0.585548 -endpoints(m.Z.FOCUS) +## Z0_0 96.838619 1.994272 48.5584 4.0282e-42 92.826596 100.850642 +## k_Z0 2.215408 0.118459 18.7018 1.0415e-23 1.989468 2.467007 +## k_Z1 0.478300 0.028257 16.9267 6.2407e-22 0.424701 0.538663 +## k_Z2 0.451618 0.042138 10.7177 1.6308e-14 0.374327 0.544869 +## k_Z3 0.058693 0.015246 3.8498 1.7805e-04 0.034804 0.098981 +## f_Z2_to_Z3 0.471508 0.058352 8.0804 9.6647e-11 0.357725 0.588332 +## sigma 3.984431 0.383402 10.3923 4.5575e-14 3.213126 4.755736 +endpoints(m.Z.FOCUS) ## $ff ## Z2_Z3 Z2_sink -## 0.47152 0.52848 +## 0.47151 0.52849 ## ## $SFORB ## logical(0) @@ -213,9 +223,9 @@ ## $distimes ## DT50 DT90 ## Z0 0.31288 1.0394 -## Z1 1.44918 4.8141 +## Z1 1.44919 4.8141 ## Z2 1.53481 5.0985 -## Z3 11.80973 39.2311 +## Z3 11.80962 39.2307 This fit corresponds to the final result chosen in Appendix 7 of the FOCUS report. Confidence intervals returned by mkin are based on internally transformed parameters, however. @@ -223,77 +233,116 @@ Using the SFORB model As the FOCUS report states, there is a certain tailing of the time course of metabolite Z3. Also, the time course of the parent compound is not fitted very well using the SFO model, as residues at a certain low level remain. Therefore, an additional model is offered here, using the single first-order reversible binding (SFORB) model for metabolite Z3. As expected, the $\chi^2$ error level is lower for metabolite Z3 using this model and the graphical fit for Z3 is improved. However, the covariance matrix is not returned. -Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFORB")) +Z.mkin.1 <- mkinmod(Z0 = mkinsub("SFO", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO", "Z3"), + Z3 = mkinsub("SFORB")) ## Successfully compiled differential equation model from auto-generated C code. -m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.mkin.1) +m.Z.mkin.1 <- mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.mkin.1, FOCUS_2006_Z_mkin, quiet = TRUE): Observations +## with value of zero were removed from the data +plot_sep(m.Z.mkin.1) -summary(m.Z.mkin.1, data = FALSE)$cov.unscaled -## Warning in summary.mkinfit(m.Z.mkin.1, data = FALSE): Could not estimate -## covariance matrix; singular system. -## NULL +summary(m.Z.mkin.1, data = FALSE)$cov.unscaled +## Z0_0 log_k_Z0_Z1 log_k_Z1_Z2 log_k_Z2_sink +## Z0_0 3.8375e+00 5.4918e-03 3.0584e-02 1.2969e-01 +## log_k_Z0_Z1 5.4918e-03 2.7613e-03 -1.8820e-04 2.6634e-04 +## log_k_Z1_Z2 3.0584e-02 -1.8820e-04 3.3807e-03 3.2177e-03 +## log_k_Z2_sink 1.2969e-01 2.6634e-04 3.2177e-03 3.4256e-02 +## log_k_Z2_Z3_free -2.4223e-02 -2.6169e-04 -1.1845e-03 -8.1134e-03 +## log_k_Z3_free_sink -6.5467e-02 -4.0815e-04 -3.2978e-03 -3.6010e-02 +## log_k_Z3_free_bound -6.0658e-02 -4.4768e-04 -3.0588e-03 -3.9074e-02 +## log_k_Z3_bound_free 4.7821e+00 5.5819e-03 1.0267e-01 1.1956e+00 +## sigma -1.4345e-08 8.6519e-11 -6.1861e-10 -4.7499e-10 +## log_k_Z2_Z3_free log_k_Z3_free_sink +## Z0_0 -2.4223e-02 -6.5467e-02 +## log_k_Z0_Z1 -2.6169e-04 -4.0815e-04 +## log_k_Z1_Z2 -1.1845e-03 -3.2978e-03 +## log_k_Z2_sink -8.1134e-03 -3.6010e-02 +## log_k_Z2_Z3_free 1.5500e-02 2.1583e-02 +## log_k_Z3_free_sink 2.1583e-02 7.5705e-02 +## log_k_Z3_free_bound 2.5836e-02 1.1964e-01 +## log_k_Z3_bound_free -2.1303e-01 -9.0584e-01 +## sigma 5.8776e-10 1.0773e-09 +## log_k_Z3_free_bound log_k_Z3_bound_free sigma +## Z0_0 -6.0658e-02 4.7821e+00 -1.4345e-08 +## log_k_Z0_Z1 -4.4768e-04 5.5819e-03 8.6519e-11 +## log_k_Z1_Z2 -3.0588e-03 1.0267e-01 -6.1861e-10 +## log_k_Z2_sink -3.9074e-02 1.1956e+00 -4.7499e-10 +## log_k_Z2_Z3_free 2.5836e-02 -2.1303e-01 5.8776e-10 +## log_k_Z3_free_sink 1.1964e-01 -9.0584e-01 1.0773e-09 +## log_k_Z3_free_bound 6.5902e-01 4.2011e+00 2.1743e-09 +## log_k_Z3_bound_free 4.2011e+00 3.6036e+08 7.2404e-02 +## sigma 2.1743e-09 7.2404e-02 1.4170e-01 Therefore, a further stepwise model building is performed starting from the stage of parent and two metabolites, starting from the assumption that the model fit for the parent compound can be improved by using the SFORB model. -Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO")) +Z.mkin.3 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO")) ## Successfully compiled differential equation model from auto-generated C code. -m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE) -plot_sep(m.Z.mkin.3) +m.Z.mkin.3 <- mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE) +## Warning in mkinfit(Z.mkin.3, FOCUS_2006_Z_mkin, quiet = TRUE): Observations +## with value of zero were removed from the data +plot_sep(m.Z.mkin.3) This results in a much better representation of the behaviour of the parent compound Z0. Finally, Z3 is added as well. These models appear overparameterised (no covariance matrix returned) if the sink for Z1 is left in the models. -Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFO")) +Z.mkin.4 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO", "Z3"), + Z3 = mkinsub("SFO")) ## Successfully compiled differential equation model from auto-generated C code. -m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, - parms.ini = m.Z.mkin.3$bparms.ode, - quiet = TRUE) -plot_sep(m.Z.mkin.4) +m.Z.mkin.4 <- mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, + parms.ini = m.Z.mkin.3$bparms.ode, + quiet = TRUE) +## Warning in mkinfit(Z.mkin.4, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin. +## 3$bparms.ode, : Observations with value of zero were removed from the data +plot_sep(m.Z.mkin.4) The error level of the fit, but especially of metabolite Z3, can be improved if the SFORB model is chosen for this metabolite, as this model is capable of representing the tailing of the metabolite decline phase. -Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), - Z1 = mkinsub("SFO", "Z2", sink = FALSE), - Z2 = mkinsub("SFO", "Z3"), - Z3 = mkinsub("SFORB")) +Z.mkin.5 <- mkinmod(Z0 = mkinsub("SFORB", "Z1", sink = FALSE), + Z1 = mkinsub("SFO", "Z2", sink = FALSE), + Z2 = mkinsub("SFO", "Z3"), + Z3 = mkinsub("SFORB")) ## Successfully compiled differential equation model from auto-generated C code. -m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, - parms.ini = m.Z.mkin.4$bparms.ode[1:4], - quiet = TRUE) -plot_sep(m.Z.mkin.5) +m.Z.mkin.5 <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, + parms.ini = m.Z.mkin.4$bparms.ode[1:4], + quiet = TRUE) +## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = m.Z.mkin. +## 4$bparms.ode[1:4], : Observations with value of zero were removed from the +## data +plot_sep(m.Z.mkin.5) The summary view of the backtransformed parameters shows that we get no confidence intervals due to overparameterisation. As the optimized is excessively small, it seems reasonable to fix it to zero. -m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, - parms.ini = c(m.Z.mkin.5$bparms.ode[1:7], - k_Z3_bound_free = 0), - fixed_parms = "k_Z3_bound_free", - quiet = TRUE) -plot_sep(m.Z.mkin.5a) +m.Z.mkin.5a <- mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, + parms.ini = c(m.Z.mkin.5$bparms.ode[1:7], + k_Z3_bound_free = 0), + fixed_parms = "k_Z3_bound_free", + quiet = TRUE) +## Warning in mkinfit(Z.mkin.5, FOCUS_2006_Z_mkin, parms.ini = c(m.Z.mkin. +## 5$bparms.ode[1:7], : Observations with value of zero were removed from the +## data +plot_sep(m.Z.mkin.5a) As expected, the residual plots for Z0 and Z3 are more random than in the case of the all SFO model for which they were shown above. In conclusion, the model is proposed as the best-fit model for the dataset from Appendix 7 of the FOCUS report. A graphical representation of the confidence intervals can finally be obtained. -mkinparplot(m.Z.mkin.5a) +mkinparplot(m.Z.mkin.5a) The endpoints obtained with this model are -endpoints(m.Z.mkin.5a) +endpoints(m.Z.mkin.5a) ## $ff ## Z0_free_Z1 Z1_Z2 Z2_sink Z2_Z3_free Z3_free_sink ## 1.00000 1.00000 0.46344 0.53656 1.00000 ## ## $SFORB ## Z0_b1 Z0_b2 Z3_b1 Z3_b2 -## 2.4471382 0.0075127 0.0800075 0.0000000 +## 2.4471355 0.0075125 0.0800068 0.0000000 ## ## $distimes ## DT50 DT90 DT50_Z0_b1 DT50_Z0_b2 DT50_Z3_b1 DT50_Z3_b2 -## Z0 0.3043 1.1848 0.28325 92.264 NA NA +## Z0 0.3043 1.1848 0.28325 92.266 NA NA ## Z1 1.5148 5.0320 NA NA NA NA ## Z2 1.6414 5.4526 NA NA NA NA -## Z3 NA NA NA NA 8.6635 Inf +## Z3 NA NA NA NA 8.6636 Inf It is clear the degradation rate of Z3 towards the end of the experiment is very low as DT50_Z3_b2 (the second Eigenvalue of the system of two differential equations representing the SFORB system for Z3, corresponding to the slower rate constant of the DFOP model) is reported to be infinity. 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-## singular system. ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p5a) +plot(p5a) -print(p5a) +print(p5a) ## Sums of squares: ## SFO IORE DFOP ## 465.21753 56.27506 32.06401 @@ -128,28 +126,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 95.8401 1.10e-21 92.121 99.5597 -## k_parent_sink 0.0102 1.71e-12 0.009 0.0117 +## parent_0 95.8401 4.67e-21 92.245 99.4357 +## k_parent_sink 0.0102 3.92e-12 0.009 0.0117 +## sigma 4.8230 3.81e-06 3.214 6.4318 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 1.01e+02 2.37e-26 9.89e+01 1.03e+02 -## k__iore_parent_sink 1.54e-05 8.73e-02 3.48e-06 6.85e-05 -## N_parent 2.57e+00 1.14e-11 2.22e+00 2.92e+00 +## Estimate Pr(>t) Lower Upper +## parent_0 1.01e+02 NA 9.91e+01 1.02e+02 +## k__iore_parent_sink 1.54e-05 NA 4.08e-06 5.84e-05 +## N_parent 2.57e+00 NA 2.25e+00 2.89e+00 +## sigma 1.68e+00 NA 1.12e+00 2.24e+00 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 9.99e+01 4.33e-27 NA NA -## k1 2.67e-02 3.17e-05 NA NA -## k2 2.16e-12 5.00e-01 NA NA -## g 6.47e-01 2.13e-05 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 9.99e+01 1.41e-26 98.8116 101.0810 +## k1 2.67e-02 5.05e-06 0.0243 0.0295 +## k2 3.41e-12 5.00e-01 0.0000 Inf +## g 6.47e-01 3.67e-06 0.6248 0.6677 +## sigma 1.27e+00 8.91e-06 0.8395 1.6929 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 67.7 2.25e+02 6.77e+01 ## IORE 58.2 1.07e+03 3.22e+02 -## DFOP 55.5 5.84e+11 3.21e+11 +## DFOP 55.5 3.70e+11 2.03e+11 ## ## Representative half-life: ## [1] 321.5119 @@ -157,14 +158,12 @@ Example on page 5, lower panel -p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p5b <- nafta(NAFTA_SOP_Attachment[["p5b"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p5b) +plot(p5b) -print(p5b) +print(p5b) ## Sums of squares: ## SFO IORE DFOP ## 94.81123 10.10936 7.55871 @@ -175,28 +174,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 96.497 2.62e-25 94.77653 98.21774 -## k_parent_sink 0.008 1.35e-14 0.00736 0.00871 +## parent_0 96.497 2.32e-24 94.85271 98.14155 +## k_parent_sink 0.008 3.42e-14 0.00737 0.00869 +## sigma 2.295 1.22e-05 1.47976 3.11036 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 9.85e+01 1.02e-29 9.78e+01 9.93e+01 -## k__iore_parent_sink 1.53e-04 1.15e-02 6.60e-05 3.56e-04 -## N_parent 1.94e+00 8.18e-13 1.74e+00 2.14e+00 +## parent_0 9.85e+01 1.17e-28 9.79e+01 9.92e+01 +## k__iore_parent_sink 1.53e-04 6.50e-03 7.21e-05 3.26e-04 +## N_parent 1.94e+00 5.88e-13 1.76e+00 2.12e+00 +## sigma 7.49e-01 1.63e-05 4.82e-01 1.02e+00 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 9.84e+01 1.90e-28 NA NA -## k1 1.55e-02 2.83e-03 NA NA -## k2 8.17e-12 5.00e-01 NA NA -## g 6.89e-01 1.31e-02 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 9.84e+01 1.24e-27 97.8078 98.9187 +## k1 1.55e-02 4.10e-04 0.0143 0.0167 +## k2 1.09e-11 5.00e-01 0.0000 Inf +## g 6.89e-01 2.92e-03 0.6626 0.7142 +## sigma 6.48e-01 2.38e-05 0.4147 0.8813 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 86.6 2.88e+02 8.66e+01 ## IORE 85.5 7.17e+02 2.16e+02 -## DFOP 83.6 1.39e+11 8.48e+10 +## DFOP 83.6 1.04e+11 6.34e+10 ## ## Representative half-life: ## [1] 215.8655 @@ -204,14 +206,12 @@ Example on page 6 -p6 <- nafta(NAFTA_SOP_Attachment[["p6"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p6 <- nafta(NAFTA_SOP_Attachment[["p6"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p6) +plot(p6) -print(p6) +print(p6) ## Sums of squares: ## SFO IORE DFOP ## 188.45361 51.00699 42.46931 @@ -222,28 +222,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 94.7759 1.25e-24 92.2558 97.2960 -## k_parent_sink 0.0179 2.35e-16 0.0166 0.0194 +## parent_0 94.7759 7.29e-24 92.3479 97.2039 +## k_parent_sink 0.0179 8.02e-16 0.0166 0.0194 +## sigma 3.0696 3.81e-06 2.0456 4.0936 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 97.12446 5.62e-27 95.49343 98.75549 -## k__iore_parent_sink 0.00252 3.54e-03 0.00126 0.00502 -## N_parent 1.49587 6.13e-13 1.32380 1.66794 +## parent_0 97.12446 2.63e-26 95.62461 98.62431 +## k__iore_parent_sink 0.00252 1.95e-03 0.00134 0.00472 +## N_parent 1.49587 4.07e-13 1.33896 1.65279 +## sigma 1.59698 5.05e-06 1.06169 2.13227 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 9.66e+01 4.17e-26 NA NA -## k1 2.55e-02 2.12e-05 NA NA -## k2 3.09e-11 5.00e-01 NA NA -## g 8.61e-01 2.10e-05 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 9.66e+01 1.57e-25 95.3476 97.8979 +## k1 2.55e-02 7.33e-06 0.0233 0.0278 +## k2 3.88e-11 5.00e-01 0.0000 Inf +## g 8.61e-01 7.55e-06 0.8314 0.8867 +## sigma 1.46e+00 6.93e-06 0.9661 1.9483 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 38.6 1.28e+02 3.86e+01 ## IORE 34.0 1.77e+02 5.32e+01 -## DFOP 34.1 1.06e+10 2.24e+10 +## DFOP 34.1 8.42e+09 1.79e+10 ## ## Representative half-life: ## [1] 53.16582 @@ -251,14 +254,12 @@ Example on page 7 -p7 <- nafta(NAFTA_SOP_Attachment[["p7"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p7 <- nafta(NAFTA_SOP_Attachment[["p7"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p7) +plot(p7) -print(p7) +print(p7) ## Sums of squares: ## SFO IORE DFOP ## 3661.661 3195.030 3174.145 @@ -269,28 +270,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 96.41796 1.52e-53 93.29554 99.54038 -## k_parent_sink 0.00735 3.59e-21 0.00641 0.00842 +## parent_0 96.41796 4.80e-53 93.32245 99.51347 +## k_parent_sink 0.00735 7.64e-21 0.00641 0.00843 +## sigma 7.94557 1.83e-15 6.46713 9.42401 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 9.92e+01 7.33e-49 9.53e+01 1.03e+02 -## k__iore_parent_sink 1.60e-05 3.47e-01 9.98e-08 2.57e-03 -## N_parent 2.45e+00 6.14e-05 1.26e+00 3.63e+00 +## Estimate Pr(>t) Lower Upper +## parent_0 9.92e+01 NA 9.55e+01 1.03e+02 +## k__iore_parent_sink 1.60e-05 NA 1.45e-07 1.77e-03 +## N_parent 2.45e+00 NA 1.35e+00 3.54e+00 +## sigma 7.42e+00 NA 6.04e+00 8.80e+00 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 9.89e+01 8.13e-48 NA NA -## k1 1.81e-02 2.20e-01 NA NA -## k2 3.28e-10 5.00e-01 NA NA -## g 6.06e-01 2.60e-01 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 9.89e+01 9.44e-49 95.4640 102.2573 +## k1 1.81e-02 1.75e-01 0.0116 0.0281 +## k2 2.57e-10 5.00e-01 0.0000 Inf +## g 6.06e-01 2.19e-01 0.4826 0.7178 +## sigma 7.40e+00 2.97e-15 6.0201 8.7754 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 94.3 3.13e+02 9.43e+01 ## IORE 96.7 1.51e+03 4.55e+02 -## DFOP 96.4 4.18e+09 2.11e+09 +## DFOP 96.4 5.32e+09 2.69e+09 ## ## Representative half-life: ## [1] 454.5528 @@ -303,7 +307,7 @@ Example on page 8 For this dataset, the IORE fit does not converge when the default starting values used by mkin for the IORE model are used. Therefore, a lower value for the rate constant is used here. -p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3)) +p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3)) ## Warning in summary.mkinfit(x): Could not estimate covariance matrix; ## singular system. @@ -311,9 +315,9 @@ ## singular system. ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p8) +plot(p8) -print(p8) +print(p8) ## Sums of squares: ## SFO IORE DFOP ## 1996.9408 444.9237 547.5616 @@ -327,12 +331,14 @@ ## parent_0 88.16549 NA NA NA ## k__iore_parent_sink 0.00100 NA NA NA ## k_parent_sink 0.00803 NA NA NA +## sigma 7.44786 NA NA NA ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 9.77e+01 1.05e-35 9.44e+01 1.01e+02 -## k__iore_parent_sink 6.14e-05 2.76e-02 2.21e-05 1.71e-04 -## N_parent 2.27e+00 6.00e-19 2.02e+00 2.53e+00 +## parent_0 9.77e+01 7.03e-35 9.44e+01 1.01e+02 +## k__iore_parent_sink 6.14e-05 3.20e-02 2.12e-05 1.78e-04 +## N_parent 2.27e+00 4.23e-18 2.00e+00 2.54e+00 +## sigma 3.52e+00 5.36e-10 2.67e+00 4.36e+00 ## ## $DFOP ## Estimate Pr(>t) Lower Upper @@ -341,6 +347,7 @@ ## k1 0.02500 NA NA NA ## k2 0.00273 NA NA NA ## g 0.58835 NA NA NA +## sigma 3.90001 NA NA NA ## ## ## DTx values: @@ -359,14 +366,12 @@ Example on page 9, upper panel -p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p9a <- nafta(NAFTA_SOP_Attachment[["p9a"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p9a) +plot(p9a) -print(p9a) +print(p9a) ## Sums of squares: ## SFO IORE DFOP ## 839.35238 88.57064 9.93363 @@ -377,28 +382,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 88.1933 1.12e-12 79.7671 96.6195 -## k_parent_sink 0.0409 9.50e-08 0.0326 0.0513 +## parent_0 88.1933 3.06e-12 79.9447 96.4419 +## k_parent_sink 0.0409 2.07e-07 0.0324 0.0516 +## sigma 7.2429 3.92e-05 4.4768 10.0090 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 9.89e+01 5.16e-17 9.50e+01 1.03e+02 -## k__iore_parent_sink 1.93e-05 1.48e-01 2.65e-06 1.40e-04 -## N_parent 2.91e+00 3.74e-09 2.43e+00 3.39e+00 +## parent_0 9.89e+01 1.12e-16 9.54e+01 1.02e+02 +## k__iore_parent_sink 1.93e-05 1.13e-01 3.49e-06 1.06e-04 +## N_parent 2.91e+00 1.45e-09 2.50e+00 3.32e+00 +## sigma 2.35e+00 5.31e-05 1.45e+00 3.26e+00 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 9.85e+01 1.31e-21 NA NA -## k1 1.38e-01 3.63e-09 NA NA -## k2 6.02e-13 5.00e-01 NA NA -## g 6.52e-01 1.50e-10 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 9.85e+01 2.54e-20 97.390 99.672 +## k1 1.38e-01 3.52e-05 0.131 0.146 +## k2 5.75e-13 5.00e-01 0.000 Inf +## g 6.52e-01 8.13e-06 0.642 0.661 +## sigma 7.88e-01 6.13e-02 0.481 1.095 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 16.9 5.63e+01 1.69e+01 ## IORE 11.6 3.37e+02 1.01e+02 -## DFOP 10.5 2.07e+12 1.15e+12 +## DFOP 10.5 2.17e+12 1.21e+12 ## ## Representative half-life: ## [1] 101.4264 @@ -407,14 +415,17 @@ Example on page 9, lower panel -p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p9b <- nafta(NAFTA_SOP_Attachment[["p9b"]]) +## Warning in sqrt(diag(covar)): NaNs wurden erzeugt +## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt +## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt +## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non- +## finite result is doubtful ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p9b) +plot(p9b) -print(p9b) +print(p9b) ## Sums of squares: ## SFO IORE DFOP ## 35.64867 23.22334 35.64867 @@ -424,22 +435,25 @@ ## ## Parameters: ## $SFO -## Estimate Pr(>t) Lower Upper -## parent_0 94.7123 2.21e-20 93.0673 96.357 -## k_parent_sink 0.0389 1.48e-14 0.0369 0.041 +## Estimate Pr(>t) Lower Upper +## parent_0 94.7123 2.15e-19 93.178 96.2464 +## k_parent_sink 0.0389 4.47e-14 0.037 0.0408 +## sigma 1.5957 1.28e-04 0.932 2.2595 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 93.863 2.91e-19 92.2996 95.426 -## k__iore_parent_sink 0.127 2.73e-02 0.0457 0.354 -## N_parent 0.711 3.13e-05 0.4605 0.961 +## parent_0 93.863 2.32e-18 92.4565 95.269 +## k__iore_parent_sink 0.127 1.85e-02 0.0504 0.321 +## N_parent 0.711 1.88e-05 0.4843 0.937 +## sigma 1.288 1.76e-04 0.7456 1.830 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 94.7123 NA NA NA -## k1 0.0389 NA NA NA -## k2 0.0389 NA NA NA -## g 0.7742 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 94.7123 1.61e-16 93.1355 96.2891 +## k1 0.0389 NaN 0.0316 0.0478 +## k2 0.0389 1.13e-08 0.0203 0.0743 +## g 0.7599 NaN NA NA +## sigma 1.5957 2.50e-04 0.9135 2.2779 ## ## ## DTx values: @@ -455,14 +469,12 @@ Example on page 10 -p10 <- nafta(NAFTA_SOP_Attachment[["p10"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p10 <- nafta(NAFTA_SOP_Attachment[["p10"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p10) +plot(p10) -print(p10) +print(p10) ## Sums of squares: ## SFO IORE DFOP ## 899.4089 336.4348 899.4089 @@ -473,21 +485,24 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 101.7315 4.95e-11 90.9683 112.4947 -## k_parent_sink 0.0495 3.40e-07 0.0393 0.0624 +## parent_0 101.7315 6.42e-11 91.9259 111.5371 +## k_parent_sink 0.0495 1.70e-07 0.0404 0.0607 +## sigma 8.0152 1.28e-04 4.6813 11.3491 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 96.86 2.71e-12 89.884 103.826 -## k__iore_parent_sink 2.96 1.31e-01 0.461 19.020 -## N_parent 0.00 5.00e-01 -0.473 0.473 +## parent_0 96.86 3.32e-12 90.848 102.863 +## k__iore_parent_sink 2.96 7.91e-02 0.687 12.761 +## N_parent 0.00 5.00e-01 -0.372 0.372 +## sigma 4.90 1.77e-04 2.837 6.968 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 101.7315 NA NA NA -## k1 0.0495 NA NA NA -## k2 0.0495 NA NA NA -## g 0.6634 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 101.7315 1.41e-09 91.6534 111.8097 +## k1 0.0495 6.41e-04 0.0303 0.0809 +## k2 0.0495 1.66e-02 0.0201 0.1219 +## g 0.6634 5.00e-01 0.0000 1.0000 +## sigma 8.0152 2.50e-04 4.5886 11.4418 ## ## ## DTx values: @@ -507,14 +522,12 @@ Example on page 11 -p11 <- nafta(NAFTA_SOP_Attachment[["p11"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p11 <- nafta(NAFTA_SOP_Attachment[["p11"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p11) +plot(p11) -print(p11) +print(p11) ## Sums of squares: ## SFO IORE DFOP ## 579.6805 204.7932 144.7783 @@ -525,28 +538,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 96.15820 1.56e-13 89.91373 1.02e+02 -## k_parent_sink 0.00321 5.27e-05 0.00218 4.71e-03 +## parent_0 96.15820 4.83e-13 90.24934 1.02e+02 +## k_parent_sink 0.00321 4.71e-05 0.00222 4.64e-03 +## sigma 6.43473 1.28e-04 3.75822 9.11e+00 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 1.05e+02 NA 9.80e+01 1.11e+02 -## k__iore_parent_sink 3.11e-17 NA 6.88e-25 1.41e-09 -## N_parent 8.36e+00 NA 4.40e+00 1.23e+01 +## parent_0 1.05e+02 NA 9.90e+01 1.10e+02 +## k__iore_parent_sink 3.11e-17 NA 1.35e-20 7.18e-14 +## N_parent 8.36e+00 NA 6.62e+00 1.01e+01 +## sigma 3.82e+00 NA 2.21e+00 5.44e+00 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 1.05e+02 7.50e-13 NA NA -## k1 4.41e-02 3.34e-02 NA NA -## k2 7.25e-13 5.00e-01 NA NA -## g 3.22e-01 7.87e-03 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 1.05e+02 9.47e-13 99.9990 109.1224 +## k1 4.41e-02 5.95e-03 0.0296 0.0658 +## k2 9.20e-13 5.00e-01 0.0000 Inf +## g 3.22e-01 1.45e-03 0.2814 0.3650 +## sigma 3.22e+00 3.52e-04 1.8410 4.5906 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 2.16e+02 7.18e+02 2.16e+02 ## IORE 9.73e+02 1.37e+08 4.11e+07 -## DFOP 4.21e+11 2.64e+12 9.56e+11 +## DFOP 3.31e+11 2.08e+12 7.53e+11 ## ## Representative half-life: ## [1] 41148169 @@ -560,9 +576,14 @@ Example on page 12, upper panel -p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]]) +p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]]) ## Warning in summary.mkinfit(x): Could not estimate covariance matrix; ## singular system. +## Warning in sqrt(diag(covar)): NaNs wurden erzeugt +## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt +## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt +## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non- +## finite result is doubtful ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used plot(p12a) @@ -578,21 +599,24 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 100.521 5.61e-12 91.687 109.355 -## k_parent_sink 0.124 7.24e-08 0.102 0.152 +## parent_0 100.521 8.75e-12 92.461 108.581 +## k_parent_sink 0.124 3.61e-08 0.104 0.148 +## sigma 7.048 1.28e-04 4.116 9.980 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 96.823 1.24e-13 91.5691 102.078 -## k__iore_parent_sink 2.436 3.89e-02 0.7854 7.556 -## N_parent 0.263 3.64e-02 -0.0288 0.554 +## Estimate Pr(>t) Lower Upper +## parent_0 96.823 NA NA NA +## k__iore_parent_sink 2.436 NA NA NA +## N_parent 0.263 NA NA NA +## sigma 3.965 NA NA NA ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 100.521 NA NA NA -## k1 0.124 NA NA NA -## k2 0.124 NA NA NA -## g 0.877 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 100.521 2.74e-10 92.2366 108.805 +## k1 0.124 5.43e-06 0.0959 0.161 +## k2 0.124 6.45e-02 0.0315 0.490 +## g 0.880 NaN NA NA +## sigma 7.048 2.50e-04 4.0349 10.061 ## ## ## DTx values: @@ -608,13 +632,19 @@ Example on page 12, lower panel p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +## Warning in sqrt(diag(covar)): NaNs wurden erzeugt +## Warning in qt(alpha/2, rdf): NaNs wurden erzeugt +## Warning in qt(1 - alpha/2, rdf): NaNs wurden erzeugt +## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt +## Warning in pt(abs(tval), rdf, lower.tail = FALSE): NaNs wurden erzeugt +## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt +## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non- +## finite result is doubtful ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p12b) +plot(p12b) -print(p12b) +print(p12b) ## Sums of squares: ## SFO IORE DFOP ## 58.90242 19.06353 58.90242 @@ -624,22 +654,25 @@ ## ## Parameters: ## $SFO -## Estimate Pr(>t) Lower Upper -## parent_0 97.6840 5.36e-05 86.3205 109.0475 -## k_parent_sink 0.0589 9.87e-04 0.0432 0.0803 +## Estimate Pr(>t) Lower Upper +## parent_0 97.6840 0.00039 85.9388 109.4292 +## k_parent_sink 0.0589 0.00261 0.0431 0.0805 +## sigma 3.4323 0.04356 -1.2377 8.1023 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 95.523 0.000386 84.0963 106.95 -## k__iore_parent_sink 0.333 0.170886 0.0103 10.80 -## N_parent 0.568 0.054881 -0.3161 1.45 +## Estimate Pr(>t) Lower Upper +## parent_0 95.523 0.0055 74.539157 116.51 +## k__iore_parent_sink 0.333 0.1433 0.000717 154.57 +## N_parent 0.568 0.0677 -0.989464 2.13 +## sigma 1.953 0.0975 -5.893100 9.80 ## ## $DFOP ## Estimate Pr(>t) Lower Upper -## parent_0 97.6840 NA NA NA -## k1 0.0589 NA NA NA -## k2 0.0589 NA NA NA -## g 0.6902 NA NA NA +## parent_0 97.6840 NaN NaN NaN +## k1 0.0589 NaN NA NA +## k2 0.0589 NaN NA NA +## g 0.8275 NaN NA NA +## sigma 3.4323 NaN NaN NaN ## ## ## DTx values: @@ -654,14 +687,12 @@ Example on page 13 -p13 <- nafta(NAFTA_SOP_Attachment[["p13"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p13 <- nafta(NAFTA_SOP_Attachment[["p13"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p13) +plot(p13) -print(p13) +print(p13) ## Sums of squares: ## SFO IORE DFOP ## 174.5971 142.3951 174.5971 @@ -671,22 +702,25 @@ ## ## Parameters: ## $SFO -## Estimate Pr(>t) Lower Upper -## parent_0 92.73500 1.45e-17 89.3891 96.08094 -## k_parent_sink 0.00258 2.63e-09 0.0022 0.00303 +## Estimate Pr(>t) Lower Upper +## parent_0 92.73500 5.99e-17 89.61936 95.85065 +## k_parent_sink 0.00258 2.42e-09 0.00223 0.00299 +## sigma 3.41172 7.07e-05 2.05455 4.76888 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 91.6016 2.93e-16 88.08711 95.12 -## k__iore_parent_sink 0.0396 2.81e-01 0.00102 1.53 -## N_parent 0.3541 1.97e-01 -0.51943 1.23 +## Estimate Pr(>t) Lower Upper +## parent_0 91.6016 6.34e-16 88.53086 94.672 +## k__iore_parent_sink 0.0396 2.36e-01 0.00207 0.759 +## N_parent 0.3541 1.46e-01 -0.35153 1.060 +## sigma 3.0811 9.64e-05 1.84296 4.319 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 92.73500 NA NA NA -## k1 0.00258 NA NA NA -## k2 0.00258 NA NA NA -## g 0.00442 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 92.73500 9.25e-15 8.95e+01 9.59e+01 +## k1 0.00258 4.28e-01 1.38e-08 4.82e+02 +## k2 0.00258 3.69e-08 2.20e-03 3.03e-03 +## g 0.00442 5.00e-01 0.00e+00 1.00e+00 +## sigma 3.41172 1.35e-04 2.02e+00 4.80e+00 ## ## ## DTx values: @@ -702,14 +736,16 @@ DT50 not observed in the study and DFOP problems in PestDF -p14 <- nafta(NAFTA_SOP_Attachment[["p14"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p14 <- nafta(NAFTA_SOP_Attachment[["p14"]]) +## Warning in sqrt(diag(covar)): NaNs wurden erzeugt +## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt +## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non- +## finite result is doubtful ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p14) +plot(p14) -print(p14) +print(p14) ## Sums of squares: ## SFO IORE DFOP ## 48.43249 28.67746 27.26248 @@ -720,28 +756,31 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 99.47124 1.71e-31 98.37313 1.01e+02 -## k_parent_sink 0.00279 2.22e-15 0.00255 3.05e-03 +## parent_0 99.47124 2.06e-30 98.42254 1.01e+02 +## k_parent_sink 0.00279 3.75e-15 0.00256 3.04e-03 +## sigma 1.55616 3.81e-06 1.03704 2.08e+00 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 1.00e+02 NA 9.93e+01 1.01e+02 -## k__iore_parent_sink 9.44e-08 NA 6.81e-11 1.31e-04 -## N_parent 3.31e+00 NA 1.69e+00 4.93e+00 +## Estimate Pr(>t) Lower Upper +## parent_0 1.00e+02 NA NaN NaN +## k__iore_parent_sink 9.44e-08 NA NaN NaN +## N_parent 3.31e+00 NA NaN NaN +## sigma 1.20e+00 NA 0.796 1.6 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 1.00e+02 2.70e-28 NA NA -## k1 9.53e-03 3.39e-01 NA NA -## k2 9.19e-12 5.00e-01 NA NA -## g 3.98e-01 3.92e-01 NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 1.00e+02 2.96e-28 99.40280 101.2768 +## k1 9.53e-03 1.20e-01 0.00638 0.0143 +## k2 6.17e-12 5.00e-01 0.00000 Inf +## g 3.98e-01 2.19e-01 0.30481 0.4998 +## sigma 1.17e+00 7.68e-06 0.77406 1.5610 ## ## ## DTx values: ## DT50 DT90 DT50_rep ## SFO 2.48e+02 8.25e+02 2.48e+02 ## IORE 4.34e+02 2.22e+04 6.70e+03 -## DFOP 2.02e+10 1.95e+11 7.54e+10 +## DFOP 3.00e+10 2.91e+11 1.12e+11 ## ## Representative half-life: ## [1] 6697.437 @@ -750,14 +789,17 @@ N is less than 1 and DFOP fraction parameter is below zero -p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p15a <- nafta(NAFTA_SOP_Attachment[["p15a"]]) +## Warning in sqrt(diag(covar)): NaNs wurden erzeugt +## Warning in sqrt(diag(covar_notrans)): NaNs wurden erzeugt +## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt +## Warning in cov2cor(ans$cov.unscaled): diag(.) had 0 or NA entries; non- +## finite result is doubtful ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p15a) +plot(p15a) -print(p15a) +print(p15a) ## Sums of squares: ## SFO IORE DFOP ## 245.5248 135.0132 245.5248 @@ -767,22 +809,25 @@ ## ## Parameters: ## $SFO -## Estimate Pr(>t) Lower Upper -## parent_0 97.96751 4.98e-16 94.03829 101.8967 -## k_parent_sink 0.00952 5.24e-09 0.00813 0.0112 +## Estimate Pr(>t) Lower Upper +## parent_0 97.96751 2.00e-15 94.32049 101.615 +## k_parent_sink 0.00952 4.93e-09 0.00824 0.011 +## sigma 4.18778 1.28e-04 2.44588 5.930 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 95.874 8.30e-16 92.5802 99.167 -## k__iore_parent_sink 0.629 2.39e-01 0.0316 12.519 -## N_parent 0.000 5.00e-01 -0.7219 0.722 +## Estimate Pr(>t) Lower Upper +## parent_0 95.874 2.94e-15 92.937 98.811 +## k__iore_parent_sink 0.629 2.11e-01 0.044 8.982 +## N_parent 0.000 5.00e-01 -0.642 0.642 +## sigma 3.105 1.78e-04 1.795 4.416 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 97.96752 NA NA NA -## k1 0.00952 NA NA NA -## k2 0.00952 NA NA NA -## g 0.17247 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 97.96751 2.85e-13 94.21913 101.7159 +## k1 0.00952 5.68e-02 0.00262 0.0347 +## k2 0.00952 1.52e-04 0.00639 0.0142 +## g 0.22357 NaN NA NA +## sigma 4.18778 2.50e-04 2.39747 5.9781 ## ## ## DTx values: @@ -793,14 +838,12 @@ ## ## Representative half-life: ## [1] 41.32749 -p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]]) -## Warning in summary.mkinfit(x): Could not estimate covariance matrix; -## singular system. +p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The half-life obtained from the IORE model may be used -plot(p15b) +plot(p15b) -print(p15b) +print(p15b) ## Sums of squares: ## SFO IORE DFOP ## 106.91629 68.55574 106.91629 @@ -811,21 +854,24 @@ ## Parameters: ## $SFO ## Estimate Pr(>t) Lower Upper -## parent_0 1.01e+02 4.99e-18 98.12761 1.04e+02 -## k_parent_sink 4.86e-03 1.76e-10 0.00432 5.46e-03 +## parent_0 1.01e+02 3.06e-17 98.31594 1.03e+02 +## k_parent_sink 4.86e-03 2.48e-10 0.00435 5.42e-03 +## sigma 2.76e+00 1.28e-04 1.61402 3.91e+00 ## ## $IORE -## Estimate Pr(>t) Lower Upper -## parent_0 99.83 4.49e-17 97.19753 102.5 -## k__iore_parent_sink 0.38 3.41e-01 0.00206 70.0 -## N_parent 0.00 5.00e-01 -1.20105 1.2 +## Estimate Pr(>t) Lower Upper +## parent_0 99.83 1.81e-16 97.51349 102.14 +## k__iore_parent_sink 0.38 3.22e-01 0.00352 41.05 +## N_parent 0.00 5.00e-01 -1.07695 1.08 +## sigma 2.21 2.57e-04 1.23245 3.19 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 1.01e+02 NA NA NA -## k1 4.86e-03 NA NA NA -## k2 4.86e-03 NA NA NA -## g 1.50e-01 NA NA NA +## Estimate Pr(>t) Lower Upper +## parent_0 1.01e+02 NA 9.82e+01 1.04e+02 +## k1 4.86e-03 NA 6.49e-04 3.64e-02 +## k2 4.86e-03 NA 3.36e-03 7.03e-03 +## g 1.50e-01 NA 0.00e+00 1.00e+00 +## sigma 2.76e+00 NA 1.58e+00 3.94e+00 ## ## ## DTx values: @@ -841,14 +887,14 @@ The DFOP fraction parameter is greater than 1 -p16 <- nafta(NAFTA_SOP_Attachment[["p16"]]) +p16 <- nafta(NAFTA_SOP_Attachment[["p16"]]) ## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c ## The representative half-life of the IORE model is longer than the one corresponding ## to the terminal degradation rate found with the DFOP model. ## The representative half-life obtained from the DFOP model may be used -plot(p16) +plot(p16) -print(p16) +print(p16) ## Sums of squares: ## SFO IORE DFOP ## 3831.804 2062.008 1550.980 @@ -858,22 +904,25 @@ ## ## Parameters: ## $SFO -## Estimate Pr(>t) Lower Upper -## parent_0 71.953 3.92e-14 61.087 82.819 -## k_parent_sink 0.159 2.27e-06 0.111 0.229 +## Estimate Pr(>t) Lower Upper +## parent_0 71.953 2.33e-13 60.509 83.40 +## k_parent_sink 0.159 4.86e-05 0.102 0.25 +## sigma 11.302 1.25e-08 8.308 14.30 ## ## $IORE ## Estimate Pr(>t) Lower Upper -## parent_0 8.74e+01 1.74e-16 7.71e+01 97.70701 -## k__iore_parent_sink 4.55e-04 2.28e-01 3.01e-05 0.00688 -## N_parent 2.70e+00 1.87e-08 1.97e+00 3.42611 +## parent_0 8.74e+01 2.48e-16 7.72e+01 97.52972 +## k__iore_parent_sink 4.55e-04 2.16e-01 3.48e-05 0.00595 +## N_parent 2.70e+00 1.21e-08 1.99e+00 3.40046 +## sigma 8.29e+00 1.61e-08 6.09e+00 10.49062 ## ## $DFOP -## Estimate Pr(>t) Lower Upper -## parent_0 88.5333 NA 79.3673 97.699 -## k1 18.5562 NA 0.0000 Inf -## k2 0.0776 NA 0.0471 0.128 -## g 0.4733 NA 0.3138 0.639 +## Estimate Pr(>t) Lower Upper +## parent_0 88.5333 7.40e-18 79.9836 97.083 +## k1 18.6317 5.00e-01 0.0000 Inf +## k2 0.0776 1.41e-05 0.0518 0.116 +## g 0.4733 1.41e-09 0.3674 0.582 +## sigma 7.1902 2.11e-08 5.2785 9.102 ## ## ## DTx values: diff --git 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mkin + 0.9.49.4 + + + + + + + Functions and data + + + + Articles + + + + + + Introduction to mkin + + + Example evaluation of FOCUS Example Dataset D + + + Example evaluation of FOCUS Laboratory Data L1 to L3 + + + Example evaluation of FOCUS Example Dataset Z + + + Performance benefit by using compiled model definitions in mkin + + + Calculation of time weighted average concentrations with mkin + + + Example evaluation of NAFTA SOP Attachment examples + + + + + News + + + + + + + + + + + + + + + Benchmark timings for mkin on various systems + Johannes Ranke + + 2019-04-10 + + + benchmarks.Rmd + + + + + + + +Systems +Each system is characterized by its CPU type, the operating system type and the mkin version. +cpu_model <- benchmarkme::get_cpu()$model_name +operating_system <- Sys.info()[["sysname"]] +mkin_version <- as.character(packageVersion("mkin")) +system_string <- paste0(operating_system, ", ", cpu_model, ", mkin version ", mkin_version) +load("~/git/mkin/inst/benchmark_data/mkin_benchmarks.rda") +mkin_benchmarks[system_string, c("CPU", "OS", "mkin")] <- c(cpu_model, operating_system, mkin_version) + +if (mkin_version > "0.9.48.1") { + mmkin_bench <- function(models, datasets, error_model = "const") mmkin(models, datasets, error_model = error_model, cores = 1, quiet = TRUE) +} else { + mmkin_bench <- function(models, datasets, error_model = NULL) mmkin(models, datasets, reweight.method = error_model, cores = 1, quiet = TRUE) +} +# Parent only +t1 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D)))[["elapsed"]] +t2 <- system.time(mmkin_bench(c("SFO", "FOMC", "DFOP", "HS"), list(FOCUS_2006_C, FOCUS_2006_D), error_model = "tc"))[["elapsed"]] + +# One metabolite +SFO_SFO <- mkinmod( + parent = mkinsub("SFO", "m1"), + m1 = mkinsub("SFO")) +## Successfully compiled differential equation model from auto-generated C code. +FOMC_SFO <- mkinmod( + parent = mkinsub("FOMC", "m1"), + m1 = mkinsub("SFO")) +## Successfully compiled differential equation model from auto-generated C code. +DFOP_SFO <- mkinmod( + parent = mkinsub("FOMC", "m1"), + m1 = mkinsub("SFO")) +## Successfully compiled differential equation model from auto-generated C code. +t3 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D)))[["elapsed"]] +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data + +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data + +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data +t4 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(subset(FOCUS_2006_D, value != 0)), error_model = "tc"))[["elapsed"]] +t5 <- system.time(mmkin_bench(list(SFO_SFO, FOMC_SFO, DFOP_SFO), list(FOCUS_2006_D), error_model = "obs"))[["elapsed"]] +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data + +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data + +## Warning in mkinfit(models[[model_index]], datasets[[dataset_index]], ...): +## Observations with value of zero were removed from the data +# Two metabolites, synthetic data +m_synth_SFO_lin <- mkinmod(parent = mkinsub("SFO", "M1"), + M1 = mkinsub("SFO", "M2"), + M2 = mkinsub("SFO"), + use_of_ff = "max", quiet = TRUE) + +m_synth_DFOP_par <- mkinmod(parent = mkinsub("DFOP", c("M1", "M2")), + M1 = mkinsub("SFO"), + M2 = mkinsub("SFO"), + use_of_ff = "max", quiet = TRUE) + +SFO_lin_a <- synthetic_data_for_UBA_2014[[1]]$data + +DFOP_par_c <- synthetic_data_for_UBA_2014[[12]]$data + +t6 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a)))["elapsed"] +t7 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c)))["elapsed"] + +t8 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "tc"))["elapsed"] +t9 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "tc"))["elapsed"] + +t10 <- system.time(mmkin_bench(list(m_synth_SFO_lin), list(SFO_lin_a), error_model = "obs"))["elapsed"] +t11 <- system.time(mmkin_bench(list(m_synth_DFOP_par), list(DFOP_par_c), error_model = "obs"))["elapsed"] + +mkin_benchmarks[system_string, paste0("t", 1:11)] <- c(t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11) +mkin_benchmarks +## CPU +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 AMD Ryzen 7 1700 Eight-Core Processor +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 AMD Ryzen 7 1700 Eight-Core Processor +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 AMD Ryzen 7 1700 Eight-Core Processor +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 AMD Ryzen 7 1700 Eight-Core Processor +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 AMD Ryzen 7 1700 Eight-Core Processor +## OS +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 Linux +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 Linux +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 Linux +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 Linux +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 Linux +## mkin +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 0.9.48.1 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 0.9.49.1 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 0.9.49.2 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 0.9.49.3 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 0.9.49.4 +## t1 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.610 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.184 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.064 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.296 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.303 +## t2 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 11.019 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 22.889 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 12.558 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 21.239 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 21.837 +## t3 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 3.764 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.649 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.786 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.510 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.487 +## t4 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 14.347 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 13.789 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 8.461 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 13.805 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 14.162 +## t5 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 9.495 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 6.395 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.675 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.386 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 6.021 +## t6 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 2.623 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 2.542 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 2.723 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 2.643 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 2.657 +## t7 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 4.587 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.128 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.478 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 4.374 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.523 +## t8 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 7.525 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 4.632 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 4.862 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.02 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 4.72 +## t9 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 16.621 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 8.171 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 7.618 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 11.124 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 8.364 +## t10 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 8.576 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 3.676 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 3.579 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 5.388 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 3.623 +## t11 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.48.1 31.267 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.1 5.636 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.2 5.574 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.3 7.365 +## Linux, AMD Ryzen 7 1700 Eight-Core Processor, mkin version 0.9.49.4 5.95 +save(mkin_benchmarks, file = "~/git/mkin/inst/benchmark_data/mkin_benchmarks.rda") + + + + + + +Contents + +Systems + + + + + + + + + Developed by Johannes Ranke. + + + + Site built with pkgdown 1.3.0.9000. + + + + + + + + diff --git a/docs/articles/web_only/compiled_models.html b/docs/articles/web_only/compiled_models.html index 269b1098..597b7c55 100644 --- a/docs/articles/web_only/compiled_models.html +++ b/docs/articles/web_only/compiled_models.html @@ -30,7 +30,7 @@ mkin - 0.9.48.1 + 0.9.49.4 @@ -88,7 +88,7 @@ Performance benefit by using compiled model definitions in mkin Johannes Ranke - 2019-03-04 + 2019-04-10 compiled_models.Rmd @@ -125,49 +125,103 @@ factor_SFO_SFO <- round(b.1["1", "relative"]) } else { factor_SFO_SFO <- NA - print("R package benchmark is not available") + print("R package rbenchmark is not available") } ## Lade nötiges Paket: rbenchmark +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", +## use_compiled = FALSE, : Observations with value of zero were removed from +## the data +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = +## TRUE): Observations with value of zero were removed from the data +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet +## = TRUE): Observations with value of zero were removed from the data +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", +## use_compiled = FALSE, : Observations with value of zero were removed from +## the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", +## use_compiled = FALSE, : Observations with value of zero were removed from +## the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", +## use_compiled = FALSE, : Observations with value of zero were removed from +## the data +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = +## TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = +## TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "eigen", quiet = +## TRUE): Observations with value of zero were removed from the data +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet +## = TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet +## = TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(SFO_SFO, FOCUS_2006_D, solution_type = "deSolve", quiet +## = TRUE): Observations with value of zero were removed from the data ## test replications elapsed relative user.self sys.self -## 3 deSolve, compiled 3 2.310 1.000 2.308 0 -## 1 deSolve, not compiled 3 17.509 7.580 17.500 0 -## 2 Eigenvalue based 3 2.859 1.238 2.858 0 +## 3 deSolve, compiled 3 3.215 1.000 3.213 0 +## 1 deSolve, not compiled 3 42.468 13.209 42.445 0 +## 2 Eigenvalue based 3 4.666 1.451 4.663 0 ## user.child sys.child ## 3 0 0 ## 1 0 0 ## 2 0 0 -We see that using the compiled model is by a factor of around 8 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs. +We see that using the compiled model is by a factor of around 13 faster than using the R version with the default ode solver, and it is even faster than the Eigenvalue based solution implemented in R which does not need iterative solution of the ODEs. Model that can not be solved with Eigenvalues This evaluation is also taken from the example section of mkinfit. -if (require(rbenchmark)) { - FOMC_SFO <- mkinmod( - parent = mkinsub("FOMC", "m1"), - m1 = mkinsub( "SFO")) - - b.2 <- benchmark( - "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, - use_compiled = FALSE, quiet = TRUE), - "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE), - replications = 3) - print(b.2) - factor_FOMC_SFO <- round(b.2["1", "relative"]) -} else { - factor_FOMC_SFO <- NA - print("R package benchmark is not available") -} +if (require(rbenchmark)) { + FOMC_SFO <- mkinmod( + parent = mkinsub("FOMC", "m1"), + m1 = mkinsub( "SFO")) + + b.2 <- benchmark( + "deSolve, not compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, + use_compiled = FALSE, quiet = TRUE), + "deSolve, compiled" = mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE), + replications = 3) + print(b.2) + factor_FOMC_SFO <- round(b.2["1", "relative"]) +} else { + factor_FOMC_SFO <- NA + print("R package benchmark is not available") +} ## Successfully compiled differential equation model from auto-generated C code. +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet = +## TRUE): Observations with value of zero were removed from the data +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with +## value of zero were removed from the data +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet = +## TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet = +## TRUE): Observations with value of zero were removed from the data + +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, use_compiled = FALSE, quiet = +## TRUE): Observations with value of zero were removed from the data +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with +## value of zero were removed from the data + +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with +## value of zero were removed from the data + +## Warning in mkinfit(FOMC_SFO, FOCUS_2006_D, quiet = TRUE): Observations with +## value of zero were removed from the data ## test replications elapsed relative user.self sys.self -## 2 deSolve, compiled 3 4.074 1.000 4.072 0 -## 1 deSolve, not compiled 3 37.219 9.136 37.203 0 +## 2 deSolve, compiled 3 4.906 1.000 4.902 0 +## 1 deSolve, not compiled 3 70.459 14.362 70.421 0 ## user.child sys.child ## 2 0 0 ## 1 0 0 -Here we get a performance benefit of a factor of 9 using the version of the differential equation model compiled from C code! -This vignette was built with mkin 0.9.48.1 on -## R version 3.5.2 (2018-12-20) +Here we get a performance benefit of a factor of 14 using the version of the differential equation model compiled from C code! +This vignette was built with mkin 0.9.49.4 on +## R version 3.5.3 (2019-03-11) ## Platform: x86_64-pc-linux-gnu (64-bit) ## Running under: Debian GNU/Linux 9 (stretch) ## CPU model: AMD Ryzen 7 1700 Eight-Core Processor -- cgit v1.2.1