From e0bef15657df1d6cade99cc3f6d8b07fa35792fe Mon Sep 17 00:00:00 2001 From: Johannes Ranke Date: Mon, 8 Jul 2019 18:12:21 +0200 Subject: Adaptations for gmkin Address winbuilder check problems, update check log, update of static docs --- docs/articles/web_only/NAFTA_examples.html | 587 ++++++++++++++++------------- 1 file changed, 316 insertions(+), 271 deletions(-) (limited to 'docs/articles/web_only/NAFTA_examples.html') diff --git a/docs/articles/web_only/NAFTA_examples.html b/docs/articles/web_only/NAFTA_examples.html index c614166d..b8a5215d 100644 --- a/docs/articles/web_only/NAFTA_examples.html +++ b/docs/articles/web_only/NAFTA_examples.html @@ -88,7 +88,7 @@

Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance

Johannes Ranke

-

2019-07-05

+

2019-07-09

@@ -111,13 +111,11 @@

Example on page 5, upper panel

p5a <- nafta(NAFTA_SOP_Attachment[["p5a"]])
-
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## 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 
@@ -128,21 +126,24 @@
 ## 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       2.86e-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       2.86e-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:
@@ -152,19 +153,17 @@
 ## DFOP 55.5 4.42e+11 2.42e+11
 ## 
 ## Representative half-life:
-## [1] 321.5119
+## [1] 321.51

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 
@@ -175,21 +174,24 @@
 ## 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       1.16e-11 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       1.16e-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:
@@ -199,19 +201,17 @@
 ## DFOP 83.6 9.80e+10 5.98e+10
 ## 
 ## Representative half-life:
-## [1] 215.8655
+## [1] 215.87

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 
@@ -222,21 +222,24 @@
 ## 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 92.3478 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       4.90e-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       4.90e-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:
@@ -246,19 +249,17 @@
 ## DFOP 34.1 6.66e+09 1.41e+10
 ## 
 ## Representative half-life:
-## [1] 53.16582
+## [1] 53.17

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 
@@ -269,21 +270,24 @@
 ## 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       1.97e-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       1.97e-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:
@@ -293,7 +297,7 @@
 ## DFOP 96.4 6.97e+09 3.52e+09
 ## 
 ## Representative half-life:
-## [1] 454.5528
+## [1] 454.55
@@ -303,17 +307,12 @@

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))
-
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.
-
-## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.
+
p8 <- nafta(NAFTA_SOP_Attachment[["p8"]], parms.ini = c(k__iore_parent_sink = 1e-3))
## 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 
@@ -323,24 +322,25 @@
 ## 
 ## 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
+##               Estimate   Pr(>t)    Lower    Upper
+## parent_0      88.16549 6.53e-29 83.37344 92.95754
+## k_parent_sink  0.00803 1.67e-13  0.00674  0.00957
+## sigma          7.44786 4.17e-10  5.66209  9.23363
 ## 
 ## $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
-## 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
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 95.70619 8.99e-32 91.87941 99.53298
+## k1        0.02500 5.25e-04  0.01422  0.04394
+## k2        0.00273 6.84e-03  0.00125  0.00597
+## g         0.58835 2.84e-06  0.36595  0.77970
+## sigma     3.90001 6.94e-10  2.96260  4.83741
 ## 
 ## 
 ## DTx values:
@@ -350,7 +350,7 @@
 ## DFOP 55.6  517    253.0
 ## 
 ## Representative half-life:
-## [1] 201.0316
+## [1] 201.03
@@ -359,14 +359,12 @@

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 
@@ -377,21 +375,24 @@
 ## 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       6.02e-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:
@@ -401,20 +402,23 @@
 ## DFOP 10.5 2.07e+12 1.15e+12
 ## 
 ## Representative half-life:
-## [1] 101.4264
+## [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.

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 +428,25 @@
 ## 
 ## 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 1.43e-06  0.0312  0.0485
+## k2         0.0389 6.67e-03  0.0186  0.0812
+## g          0.7742      NaN      NA      NA
+## sigma      1.5957 2.50e-04  0.9135  2.2779
 ## 
 ## 
 ## DTx values:
@@ -449,20 +456,18 @@
 ## DFOP 17.8 59.2     17.8
 ## 
 ## Representative half-life:
-## [1] 14.80012
+## [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.

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 +478,24 @@
 ## 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 6.42e-04  0.0301   0.0814
+## k2         0.0495 1.66e-02  0.0200   0.1225
+## g          0.6634 5.00e-01  0.0000   1.0000
+## sigma      8.0152 2.50e-04  4.5886  11.4418
 ## 
 ## 
 ## DTx values:
@@ -497,7 +505,7 @@
 ## DFOP 14.0 46.5    14.00
 ## 
 ## Representative half-life:
-## [1] 8.862193
+## [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.

@@ -507,14 +515,12 @@

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 
@@ -525,21 +531,24 @@
 ## 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       7.25e-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:
@@ -560,14 +569,14 @@
 

 

 Example on page 12, upper panel

-
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

-
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.

+
p12a <- nafta(NAFTA_SOP_Attachment[["p12a"]])

+
## 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

-
plot(p12a)

+
plot(p12a)

 

-
print(p12a)

+
print(p12a)

 
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 695.4440 220.0685 695.4440 
@@ -578,21 +587,24 @@
 ## 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 5.74e-06  0.0958   0.161
+## k2          0.124 6.61e-02  0.0319   0.484
+## g           0.877 5.00e-01  0.0000   1.000
+## sigma       7.048 2.50e-04  4.0349  10.061
 ## 
 ## 
 ## DTx values:
@@ -602,19 +614,25 @@
 ## DFOP 5.58 18.5     5.58
 ## 
 ## Representative half-life:
-## [1] 3.987308

+## [1] 3.99

Example on page 12, lower panel

-
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
-
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.
+
p12b <- nafta(NAFTA_SOP_Attachment[["p12b"]])
+
## 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 +642,25 @@
 ## 
 ## 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          0.6902    NaN    NA    NA
+## sigma      3.4323    NaN   NaN   NaN
 ## 
 ## 
 ## DTx values:
@@ -649,19 +670,21 @@
 ## DFOP 11.8 39.1    11.80
 ## 
 ## Representative half-life:
-## [1] 9.461912
+## [1] 9.46

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"]])
+
## 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(p13)
+
plot(p13)

-
print(p13)
+
print(p13)
## Sums of squares:
 ##      SFO     IORE     DFOP 
 ## 174.5971 142.3951 174.5971 
@@ -671,22 +694,25 @@
 ## 
 ## 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 1.70e-08 3.92e+02
+## k2        0.00258 3.69e-08 2.20e-03 3.03e-03
+## g         0.00442 5.00e-01       NA       NA
+## sigma     3.41172 1.35e-04 2.02e+00 4.80e+00
 ## 
 ## 
 ## DTx values:
@@ -696,20 +722,22 @@
 ## DFOP  269  892      269
 ## 
 ## Representative half-life:
-## [1] 168.5123
+## [1] 168.51

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 
@@ -720,21 +748,24 @@
 ## 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       7.29e-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       7.29e-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:
@@ -744,20 +775,23 @@
 ## DFOP 2.54e+10 2.46e+11 9.51e+10
 ## 
 ## Representative half-life:
-## [1] 6697.437
+## [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.

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 +801,25 @@
 ## 
 ## 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
 ## 
 ## $DFOP
-##          Estimate Pr(>t) Lower Upper
-## parent_0 97.96752     NA    NA    NA
-## k1        0.00952     NA    NA    NA
-## k2        0.00952     NA    NA    NA
-## g         0.17247     NA    NA    NA
+##          Estimate   Pr(>t)    Lower    Upper
+## parent_0 97.96752 2.85e-13 94.21914 101.7159
+## k1        0.00952 6.80e-02  0.00277   0.0327
+## k2        0.00952 3.82e-06  0.00902   0.0100
+## g         0.17247      NaN       NA       NA
+## sigma     4.18778 2.50e-04  2.39747   5.9781
 ## 
 ## 
 ## DTx values:
@@ -792,15 +829,17 @@
 ## DFOP 72.8  242     72.8
 ## 
 ## Representative half-life:
-## [1] 41.32749
-
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
-
## Warning in summary.mkinfit(x): Could not estimate covariance matrix;
-## singular system.
+## [1] 41.33 +
p15b <- nafta(NAFTA_SOP_Attachment[["p15b"]])
+
## Warning in sqrt(diag(covar)): NaNs wurden erzeugt
+
## Warning in sqrt(1/diag(V)): NaNs wurden erzeugt
+
## Warning in cov2cor(ans$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(p15b)
+
plot(p15b)

-
print(p15b)
+
print(p15b)
## Sums of squares:
 ##       SFO      IORE      DFOP 
 ## 106.91629  68.55574 106.91629 
@@ -811,21 +850,24 @@
 ## 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 6.75e-04 3.49e-02
+## k2       4.86e-03     NA 3.37e-03 6.99e-03
+## g        1.50e-01     NA       NA       NA
+## sigma    2.76e+00     NA 1.58e+00 3.94e+00
 ## 
 ## 
 ## DTx values:
@@ -835,20 +877,20 @@
 ## DFOP  143  474    143.0
 ## 
 ## Representative half-life:
-## [1] 71.18014
+## [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.

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 +900,25 @@
 ## 
 ## 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        18.5561     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        18.5561 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:
@@ -883,7 +928,7 @@
 ## DFOP 0.67 21.4     8.93
 ## 
 ## Representative half-life:
-## [1] 8.932679
+## [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.

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