NAFTA_examples.Rmd
In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance (US EPA 2015) are repeated using mkin. The original evaluations reported in the attachment were performed using PestDF in version 0.8.4. Note that PestDF 0.8.13 is the version distributed at the US EPA website today (2019-02-26).
The datasets are now distributed with the mkin package.
In attachment 1, it is reported that the DFOP model does not converge for these datasets when PestDF 0.8.4 was used. For all four datasets, the DFOP model can be fitted with mkin (see below). The negative half-life given by PestDF 0.8.4 for these fits appears to be the result of a bug. The results for the other two models (SFO and IORE) are the same.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 465.21753 56.27506 32.06401
##
## Critical sum of squares for checking the SFO model:
## [1] 64.4304
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 95.8401 NA NA NA
## k_parent_sink 0.0102 NA NA NA
## sigma 4.8230 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.01e+02 NA NA NA
## k__iore_parent_sink 1.54e-05 NA NA NA
## N_parent 2.57e+00 NA NA NA
## sigma 1.68e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.99e+01 NA NA NA
## k1 2.67e-02 NA NA NA
## k2 2.86e-12 NA NA NA
## g 6.47e-01 NA NA NA
## sigma 1.27e+00 NA NA NA
##
##
## 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 4.42e+11 2.42e+11
##
## Representative half-life:
## [1] 321.51
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 94.81123 10.10936 7.55871
##
## Critical sum of squares for checking the SFO model:
## [1] 11.77879
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 96.497 NA NA NA
## k_parent_sink 0.008 NA NA NA
## sigma 2.295 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.85e+01 NA NA NA
## k__iore_parent_sink 1.53e-04 NA NA NA
## N_parent 1.94e+00 NA NA NA
## sigma 7.49e-01 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.84e+01 NA NA NA
## k1 1.55e-02 NA NA NA
## k2 1.16e-11 NA NA NA
## g 6.89e-01 NA NA NA
## sigma 6.48e-01 NA NA NA
##
##
## 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 9.80e+10 5.98e+10
##
## Representative half-life:
## [1] 215.87
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 188.45361 51.00699 42.46931
##
## Critical sum of squares for checking the SFO model:
## [1] 58.39888
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 94.7759 NA NA NA
## k_parent_sink 0.0179 NA NA NA
## sigma 3.0696 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 97.12446 NA NA NA
## k__iore_parent_sink 0.00252 NA NA NA
## N_parent 1.49587 NA NA NA
## sigma 1.59698 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.66e+01 NA NA NA
## k1 2.55e-02 NA NA NA
## k2 4.90e-11 NA NA NA
## g 8.61e-01 NA NA NA
## sigma 1.46e+00 NA NA NA
##
##
## 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 6.66e+09 1.41e+10
##
## Representative half-life:
## [1] 53.17
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 3661.661 3195.030 3174.145
##
## Critical sum of squares for checking the SFO model:
## [1] 3334.194
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 96.41796 NA NA NA
## k_parent_sink 0.00735 NA NA NA
## sigma 7.94557 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.92e+01 NA NA NA
## k__iore_parent_sink 1.60e-05 NA NA NA
## N_parent 2.45e+00 NA NA NA
## sigma 7.42e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.89e+01 NA NA NA
## k1 1.81e-02 NA NA NA
## k2 1.97e-10 NA NA NA
## g 6.06e-01 NA NA NA
## sigma 7.40e+00 NA NA NA
##
##
## 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 6.97e+09 3.52e+09
##
## Representative half-life:
## [1] 454.55
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.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 1996.9408 444.9237 547.5616
##
## Critical sum of squares for checking the SFO model:
## [1] 477.4924
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## 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 NA NA NA
## k__iore_parent_sink 6.14e-05 NA NA NA
## N_parent 2.27e+00 NA NA NA
## sigma 3.52e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 95.70619 NA NA NA
## k__iore_parent_sink 0.00100 NA NA NA
## 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:
## DT50 DT90 DT50_rep
## SFO 86.3 287 86.3
## IORE 53.4 668 201.0
## DFOP 55.6 517 253.0
##
## Representative half-life:
## [1] 201.03
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 839.35238 88.57064 9.93363
##
## Critical sum of squares for checking the SFO model:
## [1] 105.5678
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 88.1933 NA NA NA
## k_parent_sink 0.0409 NA NA NA
## sigma 7.2429 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 9.89e+01 NA NA NA
## k__iore_parent_sink 1.93e-05 NA NA NA
## N_parent 2.91e+00 NA NA NA
## sigma 2.35e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.85e+01 NA NA NA
## k1 1.38e-01 NA NA NA
## k2 6.02e-13 NA NA NA
## g 6.52e-01 NA NA NA
## sigma 7.88e-01 NA NA NA
##
##
## 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
##
## Representative half-life:
## [1] 101.43
In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 35.64867 23.22334 35.64867
##
## Critical sum of squares for checking the SFO model:
## [1] 28.54188
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 94.7123 NA NA NA
## k_parent_sink 0.0389 NA NA NA
## sigma 1.5957 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 93.863 NA NA NA
## k__iore_parent_sink 0.127 NA NA NA
## N_parent 0.711 NA NA NA
## sigma 1.288 NA NA NA
##
## $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
## sigma 1.5957 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 17.8 59.2 17.8
## IORE 18.4 49.2 14.8
## DFOP 17.8 59.2 17.8
##
## Representative half-life:
## [1] 14.8
Here, mkin gives a longer slow DT50 for the DFOP model (17.8 days) than PestDF (13.5 days). Presumably, this is related to the fact that PestDF gives a negative value for the proportion of the fast degradation which should be between 0 and 1, inclusive. This parameter is called f in PestDF and g in mkin. In mkin, it is restricted to the interval from 0 to 1.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 899.4089 336.4348 899.4089
##
## Critical sum of squares for checking the SFO model:
## [1] 413.4841
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 101.7315 NA NA NA
## k_parent_sink 0.0495 NA NA NA
## sigma 8.0152 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 96.86 NA NA NA
## k__iore_parent_sink 2.96 NA NA NA
## N_parent 0.00 NA NA NA
## sigma 4.90 NA NA NA
##
## $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
## sigma 8.0152 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 14.0 46.5 14.00
## IORE 16.4 29.4 8.86
## DFOP 14.0 46.5 14.00
##
## Representative half-life:
## [1] 8.86
Here, a value below N is given for the IORE model, because the data suggests a faster decline towards the end of the experiment, which appears physically rather unlikely in the case of a photolysis study. It seems PestDF does not constrain N to values above zero, thus the slight difference in IORE model parameters between PestDF and mkin.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 579.6805 204.7932 144.7783
##
## Critical sum of squares for checking the SFO model:
## [1] 251.6944
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 96.15820 NA NA NA
## k_parent_sink 0.00321 NA NA NA
## sigma 6.43473 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.05e+02 NA NA NA
## k__iore_parent_sink 3.11e-17 NA NA NA
## N_parent 8.36e+00 NA NA NA
## sigma 3.82e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.05e+02 NA NA NA
## k1 4.41e-02 NA NA NA
## k2 7.25e-13 NA NA NA
## g 3.22e-01 NA NA NA
## sigma 3.22e+00 NA NA NA
##
##
## 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
##
## Representative half-life:
## [1] 41148169
In this case, the DFOP fit reported for PestDF resulted in a negative value for the slower rate constant, which is not possible in mkin. The other results are in agreement.
In the following three examples, the same results are obtained with mkin as reported for PestDF. As in the case on page 10, the N values below 1 are deemed unrealistic and appear to be the result of an overparameterisation.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 695.4440 220.0685 695.4440
##
## Critical sum of squares for checking the SFO model:
## [1] 270.4679
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 100.521 NA NA NA
## k_parent_sink 0.124 NA NA NA
## sigma 7.048 NA NA NA
##
## $IORE
## 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
## sigma 7.048 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 5.58 18.5 5.58
## IORE 6.49 13.2 3.99
## DFOP 5.58 18.5 5.58
##
## Representative half-life:
## [1] 3.99
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 58.90242 19.06353 58.90242
##
## Critical sum of squares for checking the SFO model:
## [1] 51.51756
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 97.6840 NA NA NA
## k_parent_sink 0.0589 NA NA NA
## sigma 3.4323 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 95.523 NA NA NA
## k__iore_parent_sink 0.333 NA NA NA
## N_parent 0.568 NA NA NA
## sigma 1.953 NA NA NA
##
## $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
## sigma 3.4323 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 11.8 39.1 11.80
## IORE 12.9 31.4 9.46
## DFOP 11.8 39.1 11.80
##
## Representative half-life:
## [1] 9.46
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 174.5971 142.3951 174.5971
##
## Critical sum of squares for checking the SFO model:
## [1] 172.131
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 92.73500 NA NA NA
## k_parent_sink 0.00258 NA NA NA
## sigma 3.41172 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 91.6016 NA NA NA
## k__iore_parent_sink 0.0396 NA NA NA
## N_parent 0.3541 NA NA NA
## sigma 3.0811 NA NA NA
##
## $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
## sigma 3.41172 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 269 892 269
## IORE 261 560 169
## DFOP 269 892 269
##
## Representative half-life:
## [1] 168.51
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 48.43249 28.67746 27.26248
##
## Critical sum of squares for checking the SFO model:
## [1] 32.83337
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 99.47124 NA NA NA
## k_parent_sink 0.00279 NA NA NA
## sigma 1.55616 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 1.00e+02 NA NA NA
## k__iore_parent_sink 9.44e-08 NA NA NA
## N_parent 3.31e+00 NA NA NA
## sigma 1.20e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.00e+02 NA NA NA
## k1 9.53e-03 NA NA NA
## k2 7.29e-12 NA NA NA
## g 3.98e-01 NA NA NA
## sigma 1.17e+00 NA NA NA
##
##
## 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 2.54e+10 2.46e+11 9.51e+10
##
## Representative half-life:
## [1] 6697.44
The slower rate constant reported by PestDF is negative, which is not physically realistic, and not possible in mkin. The other fits give the same results in mkin and PestDF.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 245.5248 135.0132 245.5248
##
## Critical sum of squares for checking the SFO model:
## [1] 165.9335
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 97.96751 NA NA NA
## k_parent_sink 0.00952 NA NA NA
## sigma 4.18778 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 95.874 NA NA NA
## k__iore_parent_sink 0.629 NA NA NA
## N_parent 0.000 NA NA NA
## sigma 3.105 NA NA NA
##
## $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
## sigma 4.18778 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 72.8 242 72.8
## IORE 76.3 137 41.3
## DFOP 72.8 242 72.8
##
## Representative half-life:
## [1] 41.33
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 106.91629 68.55574 106.91629
##
## Critical sum of squares for checking the SFO model:
## [1] 84.25618
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 1.01e+02 NA NA NA
## k_parent_sink 4.86e-03 NA NA NA
## sigma 2.76e+00 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 99.83 NA NA NA
## k__iore_parent_sink 0.38 NA NA NA
## N_parent 0.00 NA NA NA
## sigma 2.21 NA NA NA
##
## $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
## sigma 2.76e+00 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 143 474 143.0
## IORE 131 236 71.2
## DFOP 143 474 143.0
##
## Representative half-life:
## [1] 71.18
In mkin, only the IORE fit is affected (deemed unrealistic), as the fraction parameter of the DFOP model is restricted to the interval between 0 and 1 in mkin. The SFO fits give the same results for both mkin and PestDF.
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no
## covariance matrix
## 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
## Sums of squares:
## SFO IORE DFOP
## 3831.804 2062.008 1550.980
##
## Critical sum of squares for checking the SFO model:
## [1] 2247.348
##
## Parameters:
## $SFO
## Estimate Pr(>t) Lower Upper
## parent_0 71.953 NA NA NA
## k_parent_sink 0.159 NA NA NA
## sigma 11.302 NA NA NA
##
## $IORE
## Estimate Pr(>t) Lower Upper
## parent_0 8.74e+01 NA NA NA
## k__iore_parent_sink 4.55e-04 NA NA NA
## N_parent 2.70e+00 NA NA NA
## sigma 8.29e+00 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 88.5333 NA NA NA
## k1 18.5561 NA NA NA
## k2 0.0776 NA NA NA
## g 0.4733 NA NA NA
## sigma 7.1902 NA NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 4.35 14.4 4.35
## IORE 1.48 32.1 9.67
## DFOP 0.67 21.4 8.93
##
## Representative half-life:
## [1] 8.93
In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower \(\chi^2\) error level. As the half-life from the slower rate constant of the DFOP model is larger than the IORE derived half-life, the NAFTA recommendation obtained with mkin is to use the DFOP representative half-life of 8.9 days.
The results obtained with mkin deviate from the results obtained with PestDF either in cases where one of the interpretive rules would apply, i.e. the IORE parameter N is less than one or the DFOP k values obtained with PestDF are equal to the SFO k values, or in cases where the DFOP model did not converge, which often lead to negative rate constants returned by PestDF.
Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.