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
|
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
<title>Laboratory Data L1</title>
<script type="text/javascript">
window.onload = function() {
var imgs = document.getElementsByTagName('img'), i, img;
for (i = 0; i < imgs.length; i++) {
img = imgs[i];
// center an image if it is the only element of its parent
if (img.parentElement.childElementCount === 1)
img.parentElement.style.textAlign = 'center';
}
};
</script>
<!-- Styles for R syntax highlighter -->
<style type="text/css">
pre .operator,
pre .paren {
color: rgb(104, 118, 135)
}
pre .literal {
color: #990073
}
pre .number {
color: #099;
}
pre .comment {
color: #998;
font-style: italic
}
pre .keyword {
color: #900;
font-weight: bold
}
pre .identifier {
color: rgb(0, 0, 0);
}
pre .string {
color: #d14;
}
</style>
<!-- R syntax highlighter -->
<script type="text/javascript">
var hljs=new function(){function m(p){return p.replace(/&/gm,"&").replace(/</gm,"<")}function f(r,q,p){return RegExp(q,"m"+(r.cI?"i":"")+(p?"g":""))}function b(r){for(var p=0;p<r.childNodes.length;p++){var q=r.childNodes[p];if(q.nodeName=="CODE"){return q}if(!(q.nodeType==3&&q.nodeValue.match(/\s+/))){break}}}function h(t,s){var p="";for(var r=0;r<t.childNodes.length;r++){if(t.childNodes[r].nodeType==3){var q=t.childNodes[r].nodeValue;if(s){q=q.replace(/\n/g,"")}p+=q}else{if(t.childNodes[r].nodeName=="BR"){p+="\n"}else{p+=h(t.childNodes[r])}}}if(/MSIE [678]/.test(navigator.userAgent)){p=p.replace(/\r/g,"\n")}return p}function a(s){var r=s.className.split(/\s+/);r=r.concat(s.parentNode.className.split(/\s+/));for(var q=0;q<r.length;q++){var p=r[q].replace(/^language-/,"");if(e[p]){return p}}}function c(q){var p=[];(function(s,t){for(var r=0;r<s.childNodes.length;r++){if(s.childNodes[r].nodeType==3){t+=s.childNodes[r].nodeValue.length}else{if(s.childNodes[r].nodeName=="BR"){t+=1}else{if(s.childNodes[r].nodeType==1){p.push({event:"start",offset:t,node:s.childNodes[r]});t=arguments.callee(s.childNodes[r],t);p.push({event:"stop",offset:t,node:s.childNodes[r]})}}}}return t})(q,0);return p}function k(y,w,x){var q=0;var z="";var s=[];function u(){if(y.length&&w.length){if(y[0].offset!=w[0].offset){return(y[0].offset<w[0].offset)?y:w}else{return w[0].event=="start"?y:w}}else{return y.length?y:w}}function t(D){var A="<"+D.nodeName.toLowerCase();for(var B=0;B<D.attributes.length;B++){var C=D.attributes[B];A+=" "+C.nodeName.toLowerCase();if(C.value!==undefined&&C.value!==false&&C.value!==null){A+='="'+m(C.value)+'"'}}return A+">"}while(y.length||w.length){var v=u().splice(0,1)[0];z+=m(x.substr(q,v.offset-q));q=v.offset;if(v.event=="start"){z+=t(v.node);s.push(v.node)}else{if(v.event=="stop"){var p,r=s.length;do{r--;p=s[r];z+=("</"+p.nodeName.toLowerCase()+">")}while(p!=v.node);s.splice(r,1);while(r<s.length){z+=t(s[r]);r++}}}}return z+m(x.substr(q))}function j(){function q(x,y,v){if(x.compiled){return}var u;var s=[];if(x.k){x.lR=f(y,x.l||hljs.IR,true);for(var w in x.k){if(!x.k.hasOwnProperty(w)){continue}if(x.k[w] instanceof Object){u=x.k[w]}else{u=x.k;w="keyword"}for(var r in u){if(!u.hasOwnProperty(r)){continue}x.k[r]=[w,u[r]];s.push(r)}}}if(!v){if(x.bWK){x.b="\\b("+s.join("|")+")\\s"}x.bR=f(y,x.b?x.b:"\\B|\\b");if(!x.e&&!x.eW){x.e="\\B|\\b"}if(x.e){x.eR=f(y,x.e)}}if(x.i){x.iR=f(y,x.i)}if(x.r===undefined){x.r=1}if(!x.c){x.c=[]}x.compiled=true;for(var t=0;t<x.c.length;t++){if(x.c[t]=="self"){x.c[t]=x}q(x.c[t],y,false)}if(x.starts){q(x.starts,y,false)}}for(var p in e){if(!e.hasOwnProperty(p)){continue}q(e[p].dM,e[p],true)}}function d(B,C){if(!j.called){j();j.called=true}function q(r,M){for(var L=0;L<M.c.length;L++){if((M.c[L].bR.exec(r)||[null])[0]==r){return M.c[L]}}}function v(L,r){if(D[L].e&&D[L].eR.test(r)){return 1}if(D[L].eW){var M=v(L-1,r);return M?M+1:0}return 0}function w(r,L){return L.i&&L.iR.test(r)}function K(N,O){var M=[];for(var L=0;L<N.c.length;L++){M.push(N.c[L].b)}var r=D.length-1;do{if(D[r].e){M.push(D[r].e)}r--}while(D[r+1].eW);if(N.i){M.push(N.i)}return f(O,M.join("|"),true)}function p(M,L){var N=D[D.length-1];if(!N.t){N.t=K(N,E)}N.t.lastIndex=L;var r=N.t.exec(M);return r?[M.substr(L,r.index-L),r[0],false]:[M.substr(L),"",true]}function z(N,r){var L=E.cI?r[0].toLowerCase():r[0];var M=N.k[L];if(M&&M instanceof Array){return M}return false}function F(L,P){L=m(L);if(!P.k){return L}var r="";var O=0;P.lR.lastIndex=0;var M=P.lR.exec(L);while(M){r+=L.substr(O,M.index-O);var N=z(P,M);if(N){x+=N[1];r+='<span class="'+N[0]+'">'+M[0]+"</span>"}else{r+=M[0]}O=P.lR.lastIndex;M=P.lR.exec(L)}return r+L.substr(O,L.length-O)}function J(L,M){if(M.sL&&e[M.sL]){var r=d(M.sL,L);x+=r.keyword_count;return r.value}else{return F(L,M)}}function I(M,r){var L=M.cN?'<span class="'+M.cN+'">':"";if(M.rB){y+=L;M.buffer=""}else{if(M.eB){y+=m(r)+L;M.buffer=""}else{y+=L;M.buffer=r}}D.push(M);A+=M.r}function G(N,M,Q){var R=D[D.length-1];if(Q){y+=J(R.buffer+N,R);return false}var P=q(M,R);if(P){y+=J(R.buffer+N,R);I(P,M);return P.rB}var L=v(D.length-1,M);if(L){var O=R.cN?"</span>":"";if(R.rE){y+=J(R.buffer+N,R)+O}else{if(R.eE){y+=J(R.buffer+N,R)+O+m(M)}else{y+=J(R.buffer+N+M,R)+O}}while(L>1){O=D[D.length-2].cN?"</span>":"";y+=O;L--;D.length--}var r=D[D.length-1];D.length--;D[D.length-1].buffer="";if(r.starts){I(r.starts,"")}return R.rE}if(w(M,R)){throw"Illegal"}}var E=e[B];var D=[E.dM];var A=0;var x=0;var y="";try{var s,u=0;E.dM.buffer="";do{s=p(C,u);var t=G(s[0],s[1],s[2]);u+=s[0].length;if(!t){u+=s[1].length}}while(!s[2]);if(D.length>1){throw"Illegal"}return{r:A,keyword_count:x,value:y}}catch(H){if(H=="Illegal"){return{r:0,keyword_count:0,value:m(C)}}else{throw H}}}function g(t){var p={keyword_count:0,r:0,value:m(t)};var r=p;for(var q in e){if(!e.hasOwnProperty(q)){continue}var s=d(q,t);s.language=q;if(s.keyword_count+s.r>r.keyword_count+r.r){r=s}if(s.keyword_count+s.r>p.keyword_count+p.r){r=p;p=s}}if(r.language){p.second_best=r}return p}function i(r,q,p){if(q){r=r.replace(/^((<[^>]+>|\t)+)/gm,function(t,w,v,u){return w.replace(/\t/g,q)})}if(p){r=r.replace(/\n/g,"<br>")}return r}function n(t,w,r){var x=h(t,r);var v=a(t);var y,s;if(v){y=d(v,x)}else{return}var q=c(t);if(q.length){s=document.createElement("pre");s.innerHTML=y.value;y.value=k(q,c(s),x)}y.value=i(y.value,w,r);var u=t.className;if(!u.match("(\\s|^)(language-)?"+v+"(\\s|$)")){u=u?(u+" "+v):v}if(/MSIE [678]/.test(navigator.userAgent)&&t.tagName=="CODE"&&t.parentNode.tagName=="PRE"){s=t.parentNode;var p=document.createElement("div");p.innerHTML="<pre><code>"+y.value+"</code></pre>";t=p.firstChild.firstChild;p.firstChild.cN=s.cN;s.parentNode.replaceChild(p.firstChild,s)}else{t.innerHTML=y.value}t.className=u;t.result={language:v,kw:y.keyword_count,re:y.r};if(y.second_best){t.second_best={language:y.second_best.language,kw:y.second_best.keyword_count,re:y.second_best.r}}}function o(){if(o.called){return}o.called=true;var r=document.getElementsByTagName("pre");for(var p=0;p<r.length;p++){var q=b(r[p]);if(q){n(q,hljs.tabReplace)}}}function l(){if(window.addEventListener){window.addEventListener("DOMContentLoaded",o,false);window.addEventListener("load",o,false)}else{if(window.attachEvent){window.attachEvent("onload",o)}else{window.onload=o}}}var e={};this.LANGUAGES=e;this.highlight=d;this.highlightAuto=g;this.fixMarkup=i;this.highlightBlock=n;this.initHighlighting=o;this.initHighlightingOnLoad=l;this.IR="[a-zA-Z][a-zA-Z0-9_]*";this.UIR="[a-zA-Z_][a-zA-Z0-9_]*";this.NR="\\b\\d+(\\.\\d+)?";this.CNR="\\b(0[xX][a-fA-F0-9]+|(\\d+(\\.\\d*)?|\\.\\d+)([eE][-+]?\\d+)?)";this.BNR="\\b(0b[01]+)";this.RSR="!|!=|!==|%|%=|&|&&|&=|\\*|\\*=|\\+|\\+=|,|\\.|-|-=|/|/=|:|;|<|<<|<<=|<=|=|==|===|>|>=|>>|>>=|>>>|>>>=|\\?|\\[|\\{|\\(|\\^|\\^=|\\||\\|=|\\|\\||~";this.ER="(?![\\s\\S])";this.BE={b:"\\\\.",r:0};this.ASM={cN:"string",b:"'",e:"'",i:"\\n",c:[this.BE],r:0};this.QSM={cN:"string",b:'"',e:'"',i:"\\n",c:[this.BE],r:0};this.CLCM={cN:"comment",b:"//",e:"$"};this.CBLCLM={cN:"comment",b:"/\\*",e:"\\*/"};this.HCM={cN:"comment",b:"#",e:"$"};this.NM={cN:"number",b:this.NR,r:0};this.CNM={cN:"number",b:this.CNR,r:0};this.BNM={cN:"number",b:this.BNR,r:0};this.inherit=function(r,s){var p={};for(var q in r){p[q]=r[q]}if(s){for(var q in s){p[q]=s[q]}}return p}}();hljs.LANGUAGES.cpp=function(){var a={keyword:{"false":1,"int":1,"float":1,"while":1,"private":1,"char":1,"catch":1,"export":1,virtual:1,operator:2,sizeof:2,dynamic_cast:2,typedef:2,const_cast:2,"const":1,struct:1,"for":1,static_cast:2,union:1,namespace:1,unsigned:1,"long":1,"throw":1,"volatile":2,"static":1,"protected":1,bool:1,template:1,mutable:1,"if":1,"public":1,friend:2,"do":1,"return":1,"goto":1,auto:1,"void":2,"enum":1,"else":1,"break":1,"new":1,extern:1,using:1,"true":1,"class":1,asm:1,"case":1,typeid:1,"short":1,reinterpret_cast:2,"default":1,"double":1,register:1,explicit:1,signed:1,typename:1,"try":1,"this":1,"switch":1,"continue":1,wchar_t:1,inline:1,"delete":1,alignof:1,char16_t:1,char32_t:1,constexpr:1,decltype:1,noexcept:1,nullptr:1,static_assert:1,thread_local:1,restrict:1,_Bool:1,complex:1},built_in:{std:1,string:1,cin:1,cout:1,cerr:1,clog:1,stringstream:1,istringstream:1,ostringstream:1,auto_ptr:1,deque:1,list:1,queue:1,stack:1,vector:1,map:1,set:1,bitset:1,multiset:1,multimap:1,unordered_set:1,unordered_map:1,unordered_multiset:1,unordered_multimap:1,array:1,shared_ptr:1}};return{dM:{k:a,i:"</",c:[hljs.CLCM,hljs.CBLCLM,hljs.QSM,{cN:"string",b:"'\\\\?.",e:"'",i:"."},{cN:"number",b:"\\b(\\d+(\\.\\d*)?|\\.\\d+)(u|U|l|L|ul|UL|f|F)"},hljs.CNM,{cN:"preprocessor",b:"#",e:"$"},{cN:"stl_container",b:"\\b(deque|list|queue|stack|vector|map|set|bitset|multiset|multimap|unordered_map|unordered_set|unordered_multiset|unordered_multimap|array)\\s*<",e:">",k:a,r:10,c:["self"]}]}}}();hljs.LANGUAGES.r={dM:{c:[hljs.HCM,{cN:"number",b:"\\b0[xX][0-9a-fA-F]+[Li]?\\b",e:hljs.IMMEDIATE_RE,r:0},{cN:"number",b:"\\b\\d+(?:[eE][+\\-]?\\d*)?L\\b",e:hljs.IMMEDIATE_RE,r:0},{cN:"number",b:"\\b\\d+\\.(?!\\d)(?:i\\b)?",e:hljs.IMMEDIATE_RE,r:1},{cN:"number",b:"\\b\\d+(?:\\.\\d*)?(?:[eE][+\\-]?\\d*)?i?\\b",e:hljs.IMMEDIATE_RE,r:0},{cN:"number",b:"\\.\\d+(?:[eE][+\\-]?\\d*)?i?\\b",e:hljs.IMMEDIATE_RE,r:1},{cN:"keyword",b:"(?:tryCatch|library|setGeneric|setGroupGeneric)\\b",e:hljs.IMMEDIATE_RE,r:10},{cN:"keyword",b:"\\.\\.\\.",e:hljs.IMMEDIATE_RE,r:10},{cN:"keyword",b:"\\.\\.\\d+(?![\\w.])",e:hljs.IMMEDIATE_RE,r:10},{cN:"keyword",b:"\\b(?:function)",e:hljs.IMMEDIATE_RE,r:2},{cN:"keyword",b:"(?:if|in|break|next|repeat|else|for|return|switch|while|try|stop|warning|require|attach|detach|source|setMethod|setClass)\\b",e:hljs.IMMEDIATE_RE,r:1},{cN:"literal",b:"(?:NA|NA_integer_|NA_real_|NA_character_|NA_complex_)\\b",e:hljs.IMMEDIATE_RE,r:10},{cN:"literal",b:"(?:NULL|TRUE|FALSE|T|F|Inf|NaN)\\b",e:hljs.IMMEDIATE_RE,r:1},{cN:"identifier",b:"[a-zA-Z.][a-zA-Z0-9._]*\\b",e:hljs.IMMEDIATE_RE,r:0},{cN:"operator",b:"<\\-(?!\\s*\\d)",e:hljs.IMMEDIATE_RE,r:2},{cN:"operator",b:"\\->|<\\-",e:hljs.IMMEDIATE_RE,r:1},{cN:"operator",b:"%%|~",e:hljs.IMMEDIATE_RE},{cN:"operator",b:">=|<=|==|!=|\\|\\||&&|=|\\+|\\-|\\*|/|\\^|>|<|!|&|\\||\\$|:",e:hljs.IMMEDIATE_RE,r:0},{cN:"operator",b:"%",e:"%",i:"\\n",r:1},{cN:"identifier",b:"`",e:"`",r:0},{cN:"string",b:'"',e:'"',c:[hljs.BE],r:0},{cN:"string",b:"'",e:"'",c:[hljs.BE],r:0},{cN:"paren",b:"[[({\\])}]",e:hljs.IMMEDIATE_RE,r:0}]}};
hljs.initHighlightingOnLoad();
</script>
<!-- MathJax scripts -->
<script type="text/javascript" src="https://cdn.bootcss.com/mathjax/2.7.0/MathJax.js?config=TeX-MML-AM_CHTML">
</script>
<style type="text/css">
body, td {
font-family: sans-serif;
background-color: white;
font-size: 13px;
}
body {
max-width: 800px;
margin: auto;
padding: 1em;
line-height: 20px;
}
tt, code, pre {
font-family: 'DejaVu Sans Mono', 'Droid Sans Mono', 'Lucida Console', Consolas, Monaco, monospace;
}
h1 {
font-size:2.2em;
}
h2 {
font-size:1.8em;
}
h3 {
font-size:1.4em;
}
h4 {
font-size:1.0em;
}
h5 {
font-size:0.9em;
}
h6 {
font-size:0.8em;
}
a:visited {
color: rgb(50%, 0%, 50%);
}
pre, img {
max-width: 100%;
}
pre {
overflow-x: auto;
}
pre code {
display: block; padding: 0.5em;
}
code {
font-size: 92%;
border: 1px solid #ccc;
}
code[class] {
background-color: #F8F8F8;
}
table, td, th {
border: none;
}
blockquote {
color:#666666;
margin:0;
padding-left: 1em;
border-left: 0.5em #EEE solid;
}
hr {
height: 0px;
border-bottom: none;
border-top-width: thin;
border-top-style: dotted;
border-top-color: #999999;
}
@media print {
* {
background: transparent !important;
color: black !important;
filter:none !important;
-ms-filter: none !important;
}
body {
font-size:12pt;
max-width:100%;
}
a, a:visited {
text-decoration: underline;
}
hr {
visibility: hidden;
page-break-before: always;
}
pre, blockquote {
padding-right: 1em;
page-break-inside: avoid;
}
tr, img {
page-break-inside: avoid;
}
img {
max-width: 100% !important;
}
@page :left {
margin: 15mm 20mm 15mm 10mm;
}
@page :right {
margin: 15mm 10mm 15mm 20mm;
}
p, h2, h3 {
orphans: 3; widows: 3;
}
h2, h3 {
page-break-after: avoid;
}
}
</style>
</head>
<body>
<h1>Laboratory Data L1</h1>
<p>The following code defines example dataset L1 from the FOCUS kinetics
report, p. 284:</p>
<pre><code class="r">library("mkin", quietly = TRUE)
FOCUS_2006_L1 = data.frame(
t = rep(c(0, 1, 2, 3, 5, 7, 14, 21, 30), each = 2),
parent = c(88.3, 91.4, 85.6, 84.5, 78.9, 77.6,
72.0, 71.9, 50.3, 59.4, 47.0, 45.1,
27.7, 27.3, 10.0, 10.4, 2.9, 4.0))
FOCUS_2006_L1_mkin <- mkin_wide_to_long(FOCUS_2006_L1)
</code></pre>
<p>Here we use the assumptions of simple first order (SFO), the case of declining
rate constant over time (FOMC) and the case of two different phases of the
kinetics (DFOP). For a more detailed discussion of the models, please see the
FOCUS kinetics report.</p>
<p>Since mkin version 0.9-32 (July 2014), we can use shorthand notation like <code>"SFO"</code>
for parent only degradation models. The following two lines fit the model and
produce the summary report of the model fit. This covers the numerical analysis
given in the FOCUS report.</p>
<pre><code class="r">m.L1.SFO <- mkinfit("SFO", FOCUS_2006_L1_mkin, quiet = TRUE)
summary(m.L1.SFO)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:54 2018
## Date of summary: Thu Mar 1 14:24:54 2018
##
## Equations:
## d_parent/dt = - k_parent_sink * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 37 model solutions performed in 0.24 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 89.85 state
## k_parent_sink 0.10 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 89.850000 -Inf Inf
## log_k_parent_sink -2.302585 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 92.470 1.36800 89.570 95.370
## log_k_parent_sink -2.347 0.04057 -2.433 -2.261
##
## Parameter correlation:
## parent_0 log_k_parent_sink
## parent_0 1.0000 0.6248
## log_k_parent_sink 0.6248 1.0000
##
## Residual standard error: 2.948 on 16 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 92.47000 67.58 2.170e-21 89.57000 95.3700
## k_parent_sink 0.09561 24.65 1.867e-14 0.08773 0.1042
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 3.424 2 7
## parent 3.424 2 7
##
## Resulting formation fractions:
## ff
## parent_sink 1
##
## Estimated disappearance times:
## DT50 DT90
## parent 7.249 24.08
##
## Data:
## time variable observed predicted residual
## 0 parent 88.3 92.471 -4.1710
## 0 parent 91.4 92.471 -1.0710
## 1 parent 85.6 84.039 1.5610
## 1 parent 84.5 84.039 0.4610
## 2 parent 78.9 76.376 2.5241
## 2 parent 77.6 76.376 1.2241
## 3 parent 72.0 69.412 2.5884
## 3 parent 71.9 69.412 2.4884
## 5 parent 50.3 57.330 -7.0301
## 5 parent 59.4 57.330 2.0699
## 7 parent 47.0 47.352 -0.3515
## 7 parent 45.1 47.352 -2.2515
## 14 parent 27.7 24.247 3.4528
## 14 parent 27.3 24.247 3.0528
## 21 parent 10.0 12.416 -2.4163
## 21 parent 10.4 12.416 -2.0163
## 30 parent 2.9 5.251 -2.3513
## 30 parent 4.0 5.251 -1.2513
</code></pre>
<p>A plot of the fit is obtained with the plot function for mkinfit objects.</p>
<pre><code class="r">plot(m.L1.SFO, show_errmin = TRUE, main = "FOCUS L1 - SFO")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-4"/></p>
<p>The residual plot can be easily obtained by</p>
<pre><code class="r">mkinresplot(m.L1.SFO, ylab = "Observed", xlab = "Time")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-5"/></p>
<p>For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level
is checked.</p>
<pre><code class="r">m.L1.FOMC <- mkinfit("FOMC", FOCUS_2006_L1_mkin, quiet=TRUE)
plot(m.L1.FOMC, show_errmin = TRUE, main = "FOCUS L1 - FOMC")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-6"/></p>
<pre><code class="r">summary(m.L1.FOMC, data = FALSE)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:56 2018
## Date of summary: Thu Mar 1 14:24:57 2018
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 611 model solutions performed in 1.376 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 89.85 state
## alpha 1.00 deparm
## beta 10.00 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 89.850000 -Inf Inf
## log_alpha 0.000000 -Inf Inf
## log_beta 2.302585 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 92.47 1.482 89.31 95.63
## log_alpha 11.25 598.200 -1264.00 1286.00
## log_beta 13.60 598.200 -1261.00 1289.00
##
## Parameter correlation:
## parent_0 log_alpha log_beta
## parent_0 1.0000 -0.3016 -0.3016
## log_alpha -0.3016 1.0000 1.0000
## log_beta -0.3016 1.0000 1.0000
##
## Residual standard error: 3.045 on 15 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 92.47 64.45000 4.757e-20 89.31 95.63
## alpha 76830.00 0.02852 4.888e-01 0.00 Inf
## beta 803500.00 0.02852 4.888e-01 0.00 Inf
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 3.619 3 6
## parent 3.619 3 6
##
## Estimated disappearance times:
## DT50 DT90 DT50back
## parent 7.249 24.08 7.249
</code></pre>
<p>We get a warning that the default optimisation algorithm <code>Port</code> did not converge, which
is an indication that the model is overparameterised, <em>i.e.</em> contains too many
parameters that are ill-defined as a consequence.</p>
<p>And in fact, due to the higher number of parameters, and the lower number of
degrees of freedom of the fit, the \(\chi^2\) error level is actually higher for
the FOMC model (3.6%) than for the SFO model (3.4%). Additionally, the
parameters <code>log_alpha</code> and <code>log_beta</code> internally fitted in the model have
excessive confidence intervals, that span more than 25 orders of magnitude (!)
when backtransformed to the scale of <code>alpha</code> and <code>beta</code>. Also, the t-test
for significant difference from zero does not indicate such a significant difference,
with p-values greater than 0.1, and finally, the parameter correlation of <code>log_alpha</code>
and <code>log_beta</code> is 1.000, clearly indicating that the model is overparameterised.</p>
<p>The \(\chi^2\) error levels reported in Appendix 3 and Appendix 7 to the FOCUS
kinetics report are rounded to integer percentages and partly deviate by one
percentage point from the results calculated by mkin. The reason for
this is not known. However, mkin gives the same \(\chi^2\) error levels
as the kinfit package and the calculation routines of the kinfit package have
been extensively compared to the results obtained by the KinGUI
software, as documented in the kinfit package vignette. KinGUI was the first
widely used standard package in this field. Also, the calculation of
\(\chi^2\) error levels was compared with KinGUII, CAKE and DegKin manager in
a project sponsored by the German Umweltbundesamt [@ranke2014].</p>
<h1>Laboratory Data L2</h1>
<p>The following code defines example dataset L2 from the FOCUS kinetics
report, p. 287:</p>
<pre><code class="r">FOCUS_2006_L2 = data.frame(
t = rep(c(0, 1, 3, 7, 14, 28), each = 2),
parent = c(96.1, 91.8, 41.4, 38.7,
19.3, 22.3, 4.6, 4.6,
2.6, 1.2, 0.3, 0.6))
FOCUS_2006_L2_mkin <- mkin_wide_to_long(FOCUS_2006_L2)
</code></pre>
<h2>SFO fit for L2</h2>
<p>Again, the SFO model is fitted and the result is plotted. The residual plot
can be obtained simply by adding the argument <code>show_residuals</code> to the plot
command.</p>
<pre><code class="r">m.L2.SFO <- mkinfit("SFO", FOCUS_2006_L2_mkin, quiet=TRUE)
plot(m.L2.SFO, show_residuals = TRUE, show_errmin = TRUE,
main = "FOCUS L2 - SFO")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-8"/></p>
<p>The \(\chi^2\) error level of 14% suggests that the model does not fit very well.
This is also obvious from the plots of the fit, in which we have included
the residual plot.</p>
<p>In the FOCUS kinetics report, it is stated that there is no apparent systematic
error observed from the residual plot up to the measured DT90 (approximately at
day 5), and there is an underestimation beyond that point.</p>
<p>We may add that it is difficult to judge the random nature of the residuals just
from the three samplings at days 0, 1 and 3. Also, it is not clear <em>a
priori</em> why a consistent underestimation after the approximate DT90 should be
irrelevant. However, this can be rationalised by the fact that the FOCUS fate
models generally only implement SFO kinetics.</p>
<h2>FOMC fit for L2</h2>
<p>For comparison, the FOMC model is fitted as well, and the \(\chi^2\) error level
is checked.</p>
<pre><code class="r">m.L2.FOMC <- mkinfit("FOMC", FOCUS_2006_L2_mkin, quiet = TRUE)
plot(m.L2.FOMC, show_residuals = TRUE,
main = "FOCUS L2 - FOMC")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-9"/></p>
<pre><code class="r">summary(m.L2.FOMC, data = FALSE)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:57 2018
## Date of summary: Thu Mar 1 14:24:57 2018
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 81 model solutions performed in 0.169 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 93.95 state
## alpha 1.00 deparm
## beta 10.00 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 93.950000 -Inf Inf
## log_alpha 0.000000 -Inf Inf
## log_beta 2.302585 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 93.7700 1.8560 89.5700 97.9700
## log_alpha 0.3180 0.1867 -0.1044 0.7405
## log_beta 0.2102 0.2943 -0.4555 0.8759
##
## Parameter correlation:
## parent_0 log_alpha log_beta
## parent_0 1.00000 -0.09553 -0.1863
## log_alpha -0.09553 1.00000 0.9757
## log_beta -0.18628 0.97567 1.0000
##
## Residual standard error: 2.628 on 9 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 93.770 50.510 1.173e-12 89.5700 97.970
## alpha 1.374 5.355 2.296e-04 0.9009 2.097
## beta 1.234 3.398 3.949e-03 0.6341 2.401
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 6.205 3 3
## parent 6.205 3 3
##
## Estimated disappearance times:
## DT50 DT90 DT50back
## parent 0.8092 5.356 1.612
</code></pre>
<p>The error level at which the \(\chi^2\) test passes is much lower in this case.
Therefore, the FOMC model provides a better description of the data, as less
experimental error has to be assumed in order to explain the data.</p>
<h2>DFOP fit for L2</h2>
<p>Fitting the four parameter DFOP model further reduces the \(\chi^2\) error level.</p>
<pre><code class="r">m.L2.DFOP <- mkinfit("DFOP", FOCUS_2006_L2_mkin, quiet = TRUE)
plot(m.L2.DFOP, show_residuals = TRUE, show_errmin = TRUE,
main = "FOCUS L2 - DFOP")
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-10"/></p>
<pre><code class="r">summary(m.L2.DFOP, data = FALSE)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:58 2018
## Date of summary: Thu Mar 1 14:24:58 2018
##
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
## exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
## exp(-k2 * time))) * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 336 model solutions performed in 0.721 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 93.95 state
## k1 0.10 deparm
## k2 0.01 deparm
## g 0.50 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 93.950000 -Inf Inf
## log_k1 -2.302585 -Inf Inf
## log_k2 -4.605170 -Inf Inf
## g_ilr 0.000000 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 93.9500 NA NA NA
## log_k1 3.1370 NA NA NA
## log_k2 -1.0880 NA NA NA
## g_ilr -0.2821 NA NA NA
##
## Parameter correlation:
</code></pre>
<pre><code>## Warning in print.summary.mkinfit(x): Could not estimate covariance matrix; singular system:
</code></pre>
<pre><code>## Could not estimate covariance matrix; singular system:
##
## Residual standard error: 1.732 on 8 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 93.9500 NA NA NA NA
## k1 23.0400 NA NA NA NA
## k2 0.3369 NA NA NA NA
## g 0.4016 NA NA NA NA
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 2.53 4 2
## parent 2.53 4 2
##
## Estimated disappearance times:
## DT50 DT90 DT50_k1 DT50_k2
## parent 0.5335 5.311 0.03009 2.058
</code></pre>
<p>Here, the DFOP model is clearly the best-fit model for dataset L2 based on the
chi<sup>2</sup> error level criterion. However, the failure to calculate the covariance
matrix indicates that the parameter estimates correlate excessively. Therefore,
the FOMC model may be preferred for this dataset.</p>
<h1>Laboratory Data L3</h1>
<p>The following code defines example dataset L3 from the FOCUS kinetics report,
p. 290.</p>
<pre><code class="r">FOCUS_2006_L3 = data.frame(
t = c(0, 3, 7, 14, 30, 60, 91, 120),
parent = c(97.8, 60, 51, 43, 35, 22, 15, 12))
FOCUS_2006_L3_mkin <- mkin_wide_to_long(FOCUS_2006_L3)
</code></pre>
<h2>Fit multiple models</h2>
<p>As of mkin version 0.9-39 (June 2015), we can fit several models to
one or more datasets in one call to the function <code>mmkin</code>. The datasets
have to be passed in a list, in this case a named list holding only
the L3 dataset prepared above.</p>
<pre><code class="r"># Only use one core here, not to offend the CRAN checks
mm.L3 <- mmkin(c("SFO", "FOMC", "DFOP"), cores = 1,
list("FOCUS L3" = FOCUS_2006_L3_mkin), quiet = TRUE)
plot(mm.L3)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-12"/></p>
<p>The \(\chi^2\) error level of 21% as well as the plot suggest that the SFO model
does not fit very well. The FOMC model performs better, with an
error level at which the \(\chi^2\) test passes of 7%. Fitting the four
parameter DFOP model further reduces the \(\chi^2\) error level
considerably.</p>
<h2>Accessing mmkin objects</h2>
<p>The objects returned by mmkin are arranged like a matrix, with
models as a row index and datasets as a column index.</p>
<p>We can extract the summary and plot for <em>e.g.</em> the DFOP fit,
using square brackets for indexing which will result in the use of
the summary and plot functions working on mkinfit objects.</p>
<pre><code class="r">summary(mm.L3[["DFOP", 1]])
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:59 2018
## Date of summary: Thu Mar 1 14:24:59 2018
##
## Equations:
## d_parent/dt = - ((k1 * g * exp(-k1 * time) + k2 * (1 - g) *
## exp(-k2 * time)) / (g * exp(-k1 * time) + (1 - g) *
## exp(-k2 * time))) * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 137 model solutions performed in 0.283 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 97.80 state
## k1 0.10 deparm
## k2 0.01 deparm
## g 0.50 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 97.800000 -Inf Inf
## log_k1 -2.302585 -Inf Inf
## log_k2 -4.605170 -Inf Inf
## g_ilr 0.000000 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 97.7500 1.43800 93.7500 101.70000
## log_k1 -0.6612 0.13340 -1.0310 -0.29100
## log_k2 -4.2860 0.05902 -4.4500 -4.12200
## g_ilr -0.1229 0.05121 -0.2651 0.01925
##
## Parameter correlation:
## parent_0 log_k1 log_k2 g_ilr
## parent_0 1.00000 0.1640 0.01315 0.4253
## log_k1 0.16400 1.0000 0.46478 -0.5526
## log_k2 0.01315 0.4648 1.00000 -0.6631
## g_ilr 0.42526 -0.5526 -0.66310 1.0000
##
## Residual standard error: 1.439 on 4 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 97.75000 67.970 1.404e-07 93.75000 101.70000
## k1 0.51620 7.499 8.460e-04 0.35650 0.74750
## k2 0.01376 16.940 3.557e-05 0.01168 0.01621
## g 0.45660 25.410 7.121e-06 0.40730 0.50680
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 2.225 4 4
## parent 2.225 4 4
##
## Estimated disappearance times:
## DT50 DT90 DT50_k1 DT50_k2
## parent 7.464 123 1.343 50.37
##
## Data:
## time variable observed predicted residual
## 0 parent 97.8 97.75 0.05396
## 3 parent 60.0 60.45 -0.44933
## 7 parent 51.0 49.44 1.56338
## 14 parent 43.0 43.84 -0.83632
## 30 parent 35.0 35.15 -0.14707
## 60 parent 22.0 23.26 -1.25919
## 91 parent 15.0 15.18 -0.18181
## 120 parent 12.0 10.19 1.81395
</code></pre>
<pre><code class="r">plot(mm.L3[["DFOP", 1]], show_errmin = TRUE)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-13"/></p>
<p>Here, a look to the model plot, the confidence intervals of the parameters
and the correlation matrix suggest that the parameter estimates are reliable, and
the DFOP model can be used as the best-fit model based on the \(\chi^2\) error
level criterion for laboratory data L3.</p>
<p>This is also an example where the standard t-test for the parameter <code>g_ilr</code> is
misleading, as it tests for a significant difference from zero. In this case,
zero appears to be the correct value for this parameter, and the confidence
interval for the backtransformed parameter <code>g</code> is quite narrow.</p>
<h1>Laboratory Data L4</h1>
<p>The following code defines example dataset L4 from the FOCUS kinetics
report, p. 293:</p>
<pre><code class="r">FOCUS_2006_L4 = data.frame(
t = c(0, 3, 7, 14, 30, 60, 91, 120),
parent = c(96.6, 96.3, 94.3, 88.8, 74.9, 59.9, 53.5, 49.0))
FOCUS_2006_L4_mkin <- mkin_wide_to_long(FOCUS_2006_L4)
</code></pre>
<p>Fits of the SFO and FOMC models, plots and summaries are produced below:</p>
<pre><code class="r"># Only use one core here, not to offend the CRAN checks
mm.L4 <- mmkin(c("SFO", "FOMC"), cores = 1,
list("FOCUS L4" = FOCUS_2006_L4_mkin),
quiet = TRUE)
plot(mm.L4)
</code></pre>
<p><img src="data:image/png;base64,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" alt="plot of chunk unnamed-chunk-15"/></p>
<p>The \(\chi^2\) error level of 3.3% as well as the plot suggest that the SFO model
fits very well. The error level at which the \(\chi^2\) test passes is slightly
lower for the FOMC model. However, the difference appears negligible.</p>
<pre><code class="r">summary(mm.L4[["SFO", 1]], data = FALSE)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:59 2018
## Date of summary: Thu Mar 1 14:24:59 2018
##
## Equations:
## d_parent/dt = - k_parent_sink * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 46 model solutions performed in 0.098 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 96.6 state
## k_parent_sink 0.1 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 96.600000 -Inf Inf
## log_k_parent_sink -2.302585 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 96.44 1.94900 91.670 101.200
## log_k_parent_sink -5.03 0.07999 -5.225 -4.834
##
## Parameter correlation:
## parent_0 log_k_parent_sink
## parent_0 1.0000 0.5865
## log_k_parent_sink 0.5865 1.0000
##
## Residual standard error: 3.651 on 6 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 96.440000 49.49 2.283e-09 91.670000 1.012e+02
## k_parent_sink 0.006541 12.50 8.008e-06 0.005378 7.955e-03
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 3.287 2 6
## parent 3.287 2 6
##
## Resulting formation fractions:
## ff
## parent_sink 1
##
## Estimated disappearance times:
## DT50 DT90
## parent 106 352
</code></pre>
<pre><code class="r">summary(mm.L4[["FOMC", 1]], data = FALSE)
</code></pre>
<pre><code>## mkin version: 0.9.46.3
## R version: 3.4.3
## Date of fit: Thu Mar 1 14:24:59 2018
## Date of summary: Thu Mar 1 14:24:59 2018
##
## Equations:
## d_parent/dt = - (alpha/beta) * 1/((time/beta) + 1) * parent
##
## Model predictions using solution type analytical
##
## Fitted with method Port using 66 model solutions performed in 0.134 s
##
## Weighting: none
##
## Starting values for parameters to be optimised:
## value type
## parent_0 96.6 state
## alpha 1.0 deparm
## beta 10.0 deparm
##
## Starting values for the transformed parameters actually optimised:
## value lower upper
## parent_0 96.600000 -Inf Inf
## log_alpha 0.000000 -Inf Inf
## log_beta 2.302585 -Inf Inf
##
## Fixed parameter values:
## None
##
## Optimised, transformed parameters with symmetric confidence intervals:
## Estimate Std. Error Lower Upper
## parent_0 99.1400 1.6800 94.820 103.5000
## log_alpha -0.3506 0.3725 -1.308 0.6068
## log_beta 4.1740 0.5635 2.726 5.6230
##
## Parameter correlation:
## parent_0 log_alpha log_beta
## parent_0 1.0000 -0.5365 -0.6083
## log_alpha -0.5365 1.0000 0.9913
## log_beta -0.6083 0.9913 1.0000
##
## Residual standard error: 2.315 on 5 degrees of freedom
##
## Backtransformed parameters:
## Confidence intervals for internally transformed parameters are asymmetric.
## t-test (unrealistically) based on the assumption of normal distribution
## for estimators of untransformed parameters.
## Estimate t value Pr(>t) Lower Upper
## parent_0 99.1400 59.020 1.322e-08 94.8200 103.500
## alpha 0.7042 2.685 2.178e-02 0.2703 1.835
## beta 64.9800 1.775 6.807e-02 15.2600 276.600
##
## Chi2 error levels in percent:
## err.min n.optim df
## All data 2.029 3 5
## parent 2.029 3 5
##
## Estimated disappearance times:
## DT50 DT90 DT50back
## parent 108.9 1644 494.9
</code></pre>
<h1>References</h1>
</body>
</html>
|
