1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
|
<!DOCTYPE html>
<!-- Generated by pkgdown: do not edit by hand --><html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance • mkin</title>
<!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/css/bootstrap.min.css" integrity="sha256-bZLfwXAP04zRMK2BjiO8iu9pf4FbLqX6zitd+tIvLhE=" crossorigin="anonymous">
<script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../../bootstrap-toc.css">
<script src="../../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous">
<!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../../pkgdown.css" rel="stylesheet">
<script src="../../pkgdown.js"></script><meta property="og:title" content="Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance">
<meta property="og:description" content="mkin">
<!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
<![endif]-->
</head>
<body data-spy="scroll" data-target="#toc">
<div class="container template-article">
<header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar" aria-expanded="false">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<span class="navbar-brand">
<a class="navbar-link" href="../../index.html">mkin</a>
<span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="Released version">1.0.0</span>
</span>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="../../reference/index.html">Functions and data</a>
</li>
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-expanded="false">
Articles
<span class="caret"></span>
</a>
<ul class="dropdown-menu" role="menu">
<li>
<a href="../../articles/mkin.html">Introduction to mkin</a>
</li>
<li>
<a href="../../articles/FOCUS_D.html">Example evaluation of FOCUS Example Dataset D</a>
</li>
<li>
<a href="../../articles/FOCUS_L.html">Example evaluation of FOCUS Laboratory Data L1 to L3</a>
</li>
<li>
<a href="../../articles/web_only/FOCUS_Z.html">Example evaluation of FOCUS Example Dataset Z</a>
</li>
<li>
<a href="../../articles/web_only/compiled_models.html">Performance benefit by using compiled model definitions in mkin</a>
</li>
<li>
<a href="../../articles/twa.html">Calculation of time weighted average concentrations with mkin</a>
</li>
<li>
<a href="../../articles/web_only/NAFTA_examples.html">Example evaluation of NAFTA SOP Attachment examples</a>
</li>
<li>
<a href="../../articles/web_only/benchmarks.html">Some benchmark timings</a>
</li>
</ul>
</li>
<li>
<a href="../../news/index.html">News</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/jranke/mkin/">
<span class="fab fa-github fa-lg"></span>
</a>
</li>
</ul>
</div>
<!--/.nav-collapse -->
</div>
<!--/.container -->
</div>
<!--/.navbar -->
</header><div class="row">
<div class="col-md-9 contents">
<div class="page-header toc-ignore">
<h1 data-toc-skip>Evaluation of example datasets from Attachment 1 to the US EPA SOP for the NAFTA guidance</h1>
<h4 class="author">Johannes Ranke</h4>
<h4 class="date">2021-02-03</h4>
<small class="dont-index">Source: <a href="https://github.com/jranke/mkin/blob/master/vignettes/web_only/NAFTA_examples.rmd"><code>vignettes/web_only/NAFTA_examples.rmd</code></a></small>
<div class="hidden name"><code>NAFTA_examples.rmd</code></div>
</div>
<div id="introduction" class="section level1">
<h1 class="hasAnchor">
<a href="#introduction" class="anchor"></a>Introduction</h1>
<p>In this document, the example evaluations provided in Attachment 1 to the SOP of US EPA for using the NAFTA guidance <span class="citation">(US EPA 2015)</span> 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).</p>
<p>The datasets are now distributed with the mkin package.</p>
</div>
<div id="examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-dfop-did-not-converge-with-pestdf-0-8-4" class="anchor"></a>Examples where DFOP did not converge with PestDF 0.8.4</h1>
<p>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.</p>
<div id="example-on-page-5-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-5-upper-panel" class="anchor"></a>Example on page 5, upper panel</h2>
<div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p5a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb4"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5a-1.png" width="700"></p>
<div class="sourceCode" id="cb5"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p5a</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 4.67e-21 92.245 99.4357
## k_parent 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 NA 9.91e+01 1.02e+02
## k__iore_parent 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 1.41e-26 98.8116 101.0810
## k1 2.67e-02 5.05e-06 0.0243 0.0295
## k2 2.42e-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 5.22e+11 2.86e+11
##
## Representative half-life:
## [1] 321.51</code></pre>
</div>
<div id="example-on-page-5-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-5-lower-panel" class="anchor"></a>Example on page 5, lower panel</h2>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p5b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p5b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p5b-1.png" width="700"></p>
<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p5b</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 2.32e-24 94.85271 98.14155
## k_parent 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 1.17e-28 9.79e+01 9.92e+01
## k__iore_parent 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 1.24e-27 97.8078 98.9187
## k1 1.55e-02 4.10e-04 0.0143 0.0167
## k2 1.10e-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 1.03e+11 6.29e+10
##
## Representative half-life:
## [1] 215.87</code></pre>
</div>
<div id="example-on-page-6" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-6" class="anchor"></a>Example on page 6</h2>
<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p6</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p6"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p6-1.png" width="700"></p>
<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p6</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 7.29e-24 92.3478 97.2039
## k_parent 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 2.63e-26 95.62461 98.62431
## k__iore_parent 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 1.57e-25 95.3476 97.8979
## k1 2.55e-02 7.33e-06 0.0233 0.0278
## k2 3.60e-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 9.07e+09 1.93e+10
##
## Representative half-life:
## [1] 53.17</code></pre>
</div>
<div id="example-on-page-7" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-7" class="anchor"></a>Example on page 7</h2>
<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p7</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p7"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p7-1.png" width="700"></p>
<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p7</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 4.80e-53 93.32245 99.51347
## k_parent 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 NA 9.55e+01 1.03e+02
## k__iore_parent 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 9.44e-49 95.4640 102.2573
## k1 1.81e-02 1.75e-01 0.0116 0.0281
## k2 2.89e-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 4.75e+09 2.40e+09
##
## Representative half-life:
## [1] 454.55</code></pre>
</div>
</div>
<div id="examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-the-representative-half-life-deviates-from-the-observed-dt50" class="anchor"></a>Examples where the representative half-life deviates from the observed DT50</h1>
<div id="example-on-page-8" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-8" class="anchor"></a>Example on page 8</h2>
<p>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.</p>
<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p8</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p8"</span><span class="op">]</span><span class="op">]</span>, parms.ini <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span>k__iore_parent <span class="op">=</span> <span class="fl">1e-3</span><span class="op">)</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p8-1.png" width="700"></p>
<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p8</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 6.53e-29 83.37344 92.95754
## k_parent 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 7.03e-35 9.44e+01 1.01e+02
## k__iore_parent 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 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:
## 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</code></pre>
</div>
</div>
<div id="examples-where-sfo-was-not-selected-for-an-abiotic-study" class="section level1">
<h1 class="hasAnchor">
<a href="#examples-where-sfo-was-not-selected-for-an-abiotic-study" class="anchor"></a>Examples where SFO was not selected for an abiotic study</h1>
<div id="example-on-page-9-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-9-upper-panel" class="anchor"></a>Example on page 9, upper panel</h2>
<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p9a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9a-1.png" width="700"></p>
<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p9a</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 3.06e-12 79.9447 96.4419
## k_parent 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 1.12e-16 9.54e+01 1.02e+02
## k__iore_parent 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
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 9.85e+01 2.54e-20 97.390 99.672
## k1 1.38e-01 3.52e-05 0.131 0.146
## k2 9.03e-13 5.00e-01 0.000 Inf
## g 6.52e-01 8.13e-06 0.642 0.661
## sigma 7.88e-01 6.13e-02 0.481 1.095
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 16.9 5.63e+01 1.69e+01
## IORE 11.6 3.37e+02 1.01e+02
## DFOP 10.5 1.38e+12 7.67e+11
##
## Representative half-life:
## [1] 101.43</code></pre>
<p>In this example, the residuals of the SFO indicate a lack of fit of this model, so even if it was an abiotic experiment, the data do not suggest a simple exponential decline.</p>
</div>
<div id="example-on-page-9-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-9-lower-panel" class="anchor"></a>Example on page 9, lower panel</h2>
<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p9b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p9b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p9b-1.png" width="700"></p>
<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p9b</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 2.15e-19 93.178 96.2464
## k_parent 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 2.32e-18 92.4565 95.269
## k__iore_parent 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 93.1355 96.2891
## k1 0.0389 NA 0.0266 0.0569
## k2 0.0389 NA 0.0255 0.0592
## g 0.5256 NA NA NA
## sigma 1.5957 NA 0.9135 2.2779
##
##
## 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</code></pre>
<p>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.</p>
</div>
<div id="example-on-page-10" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-10" class="anchor"></a>Example on page 10</h2>
<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p10</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p10"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar_notrans)): NaNs produced</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p10-1.png" width="700"></p>
<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p10</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 6.42e-11 91.9259 111.5371
## k_parent 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 3.32e-12 90.848 102.863
## k__iore_parent 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 1.41e-09 91.6534 111.8097
## k1 0.0495 5.63e-03 0.0240 0.1020
## k2 0.0495 1.93e-03 0.0272 0.0903
## g 0.4487 NaN 0.0000 1.0000
## sigma 8.0152 2.50e-04 4.5886 11.4418
##
##
## 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</code></pre>
<p>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.</p>
</div>
</div>
<div id="the-dt50-was-not-observed-during-the-study" class="section level1">
<h1 class="hasAnchor">
<a href="#the-dt50-was-not-observed-during-the-study" class="anchor"></a>The DT50 was not observed during the study</h1>
<div id="example-on-page-11" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-11" class="anchor"></a>Example on page 11</h2>
<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p11</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p11"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb56"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p11-1.png" width="700"></p>
<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p11</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 4.83e-13 90.24934 1.02e+02
## k_parent 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 9.90e+01 1.10e+02
## k__iore_parent 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 9.47e-13 99.9990 109.1224
## k1 4.41e-02 5.95e-03 0.0296 0.0658
## k2 9.94e-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 3.07e+11 1.93e+12 6.97e+11
##
## Representative half-life:
## [1] 41148171</code></pre>
<p>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.</p>
</div>
</div>
<div id="n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="section level1">
<h1 class="hasAnchor">
<a href="#n-is-less-than-1-and-the-dfop-rate-constants-are-like-the-sfo-rate-constant" class="anchor"></a>N is less than 1 and the DFOP rate constants are like the SFO rate constant</h1>
<p>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.</p>
<div id="example-on-page-12-upper-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-upper-panel" class="anchor"></a>Example on page 12, upper panel</h2>
<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p12a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
## matrix
## Warning in summary.mkinfit(x): Could not calculate correlation; no covariance
## matrix</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12a-1.png" width="700"></p>
<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12a</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 8.75e-12 92.461 108.581
## k_parent 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 NA NA NA
## k__iore_parent 2.436 NA NA NA
## N_parent 0.263 NA NA NA
## sigma 3.965 NA NA NA
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 100.521 2.74e-10 NA NA
## k1 0.124 2.53e-05 NA NA
## k2 0.124 2.52e-02 NA NA
## g 0.793 5.00e-01 NA NA
## sigma 7.048 2.50e-04 NA NA
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 5.58 18.5 5.58
## IORE 6.49 13.2 3.99
## DFOP 5.58 18.5 5.58
##
## Representative half-life:
## [1] 3.99</code></pre>
</div>
<div id="example-on-page-12-lower-panel" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-12-lower-panel" class="anchor"></a>Example on page 12, lower panel</h2>
<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p12b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p12b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in qt(alpha/2, rdf): NaNs produced</code></pre>
<pre><code>## Warning in qt(1 - alpha/2, rdf): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p12b-1.png" width="700"></p>
<div class="sourceCode" id="cb75"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p12b</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 0.00039 85.9388 109.4292
## k_parent 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 0.0055 74.539157 116.51
## k__iore_parent 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
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 97.6840 NA NaN NaN
## k1 0.0589 NA NA NA
## k2 0.0589 NA NA NA
## g 0.6473 NA NA NA
## sigma 3.4323 NA NaN NaN
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 11.8 39.1 11.80
## IORE 12.9 31.4 9.46
## DFOP 11.8 39.1 11.80
##
## Representative half-life:
## [1] 9.46</code></pre>
</div>
<div id="example-on-page-13" class="section level2">
<h2 class="hasAnchor">
<a href="#example-on-page-13" class="anchor"></a>Example on page 13</h2>
<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p13</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p13"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p13-1.png" width="700"></p>
<div class="sourceCode" id="cb84"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p13</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 5.99e-17 89.61936 95.85065
## k_parent 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 6.34e-16 88.53086 94.672
## k__iore_parent 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
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 92.73500 NA 8.95e+01 95.92118
## k1 0.00258 NA 4.25e-04 0.01569
## k2 0.00258 NA 1.76e-03 0.00379
## g 0.16452 NA NA NA
## sigma 3.41172 NA 2.02e+00 4.79960
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 269 892 269
## IORE 261 560 169
## DFOP 269 892 269
##
## Representative half-life:
## [1] 168.51</code></pre>
</div>
</div>
<div id="dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="section level1">
<h1 class="hasAnchor">
<a href="#dt50-not-observed-in-the-study-and-dfop-problems-in-pestdf" class="anchor"></a>DT50 not observed in the study and DFOP problems in PestDF</h1>
<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p14</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p14"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb92"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p14-1.png" width="700"></p>
<div class="sourceCode" id="cb93"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p14</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 2.06e-30 98.42254 1.01e+02
## k_parent 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 NaN NaN
## k__iore_parent 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 2.96e-28 99.40280 101.2768
## k1 9.53e-03 1.20e-01 0.00638 0.0143
## k2 5.33e-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 3.48e+10 3.37e+11 1.30e+11
##
## Representative half-life:
## [1] 6697.44</code></pre>
<p>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.</p>
</div>
<div id="n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="section level1">
<h1 class="hasAnchor">
<a href="#n-is-less-than-1-and-dfop-fraction-parameter-is-below-zero" class="anchor"></a>N is less than 1 and DFOP fraction parameter is below zero</h1>
<div class="sourceCode" id="cb95"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p15a</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15a"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb98"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15a-1.png" width="700"></p>
<div class="sourceCode" id="cb99"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15a</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 2.00e-15 94.32049 101.615
## k_parent 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 2.94e-15 92.937 98.811
## k__iore_parent 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
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 97.96751 NA 94.21913 101.7159
## k1 0.00952 NA 0.00221 0.0411
## k2 0.00952 NA 0.00626 0.0145
## g 0.21241 NA 0.00000 1.0000
## sigma 4.18778 NA 2.39747 5.9781
##
##
## DTx values:
## DT50 DT90 DT50_rep
## SFO 72.8 242 72.8
## IORE 76.3 137 41.3
## DFOP 72.8 242 72.8
##
## Representative half-life:
## [1] 41.33</code></pre>
<div class="sourceCode" id="cb101"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p15b</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p15b"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## Warning in sqrt(diag(covar)): NaNs produced</code></pre>
<pre><code>## Warning in sqrt(1/diag(V)): NaNs produced</code></pre>
<pre><code>## Warning in cov2cor(ans$covar): diag(.) had 0 or NA entries; non-finite result is
## doubtful</code></pre>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The half-life obtained from the IORE model may be used</code></pre>
<div class="sourceCode" id="cb107"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p15b-1.png" width="700"></p>
<div class="sourceCode" id="cb108"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p15b</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 3.06e-17 98.31594 1.03e+02
## k_parent 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 1.81e-16 97.51348 102.14
## k__iore_parent 0.38 3.22e-01 0.00352 41.05
## N_parent 0.00 5.00e-01 -1.07696 1.08
## sigma 2.21 2.57e-04 1.23245 3.19
##
## $DFOP
## Estimate Pr(>t) Lower Upper
## parent_0 1.01e+02 NA 9.82e+01 1.04e+02
## k1 4.86e-03 NA 8.63e-04 2.73e-02
## k2 4.86e-03 NA 3.21e-03 7.35e-03
## g 1.88e-01 NA NA NA
## sigma 2.76e+00 NA 1.58e+00 3.94e+00
##
##
## 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</code></pre>
<p>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.</p>
</div>
<div id="the-dfop-fraction-parameter-is-greater-than-1" class="section level1">
<h1 class="hasAnchor">
<a href="#the-dfop-fraction-parameter-is-greater-than-1" class="anchor"></a>The DFOP fraction parameter is greater than 1</h1>
<div class="sourceCode" id="cb110"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="va">p16</span> <span class="op"><-</span> <span class="fu"><a href="../../reference/nafta.html">nafta</a></span><span class="op">(</span><span class="va">NAFTA_SOP_Attachment</span><span class="op">[[</span><span class="st">"p16"</span><span class="op">]</span><span class="op">]</span><span class="op">)</span></code></pre></div>
<pre><code>## The SFO model is rejected as S_SFO is equal or higher than the critical value S_c</code></pre>
<pre><code>## The representative half-life of the IORE model is longer than the one corresponding</code></pre>
<pre><code>## to the terminal degradation rate found with the DFOP model.</code></pre>
<pre><code>## The representative half-life obtained from the DFOP model may be used</code></pre>
<div class="sourceCode" id="cb115"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/graphics/plot.default.html">plot</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
<p><img src="NAFTA_examples_files/figure-html/p16-1.png" width="700"></p>
<div class="sourceCode" id="cb116"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span class="fu"><a href="https://rdrr.io/r/base/print.html">print</a></span><span class="op">(</span><span class="va">p16</span><span class="op">)</span></code></pre></div>
<pre><code>## 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 2.33e-13 60.509 83.40
## k_parent 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 2.48e-16 7.72e+01 97.52972
## k__iore_parent 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 7.40e-18 79.9836 97.083
## k1 18.8461 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:
## 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</code></pre>
<p>In PestDF, the DFOP fit seems to have stuck in a local minimum, as mkin finds a solution with a much lower <span class="math inline">\(\chi^2\)</span> 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.</p>
</div>
<div id="conclusions" class="section level1">
<h1 class="hasAnchor">
<a href="#conclusions" class="anchor"></a>Conclusions</h1>
<p>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.</p>
<p>Therefore, mkin appears to suitable for kinetic evaluations according to the NAFTA guidance.</p>
</div>
<div id="references" class="section level1 unnumbered">
<h1 class="hasAnchor">
<a href="#references" class="anchor"></a>References</h1>
<div id="refs" class="references">
<div id="ref-usepa2015">
<p>US EPA. 2015. “Standard Operating Procedure for Using the NAFTA Guidance to Calculate Representative Half-Life Values and Characterizing Pesticide Degradation.”</p>
</div>
</div>
</div>
</div>
<div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
<nav id="toc" data-toggle="toc"><h2 data-toc-skip>Contents</h2>
</nav>
</div>
</div>
<footer><div class="copyright">
<p>Developed by Johannes Ranke.</p>
</div>
<div class="pkgdown">
<p>Site built with <a href="https://pkgdown.r-lib.org/">pkgdown</a> 1.6.1.</p>
</div>
</footer>
</div>
</body>
</html>
|
