Bloque 2 Modelos más avanzados
Parte 1 Modelos de ocupación (site-occupancy models )
IREC, 14/05/2024
Javier Fernández-López, Valentin Lauret
\[~\] \[~\] \[~\] \[~\] \[~\] \[~\]
2024-05-15
En el menú…
Día 1:
Modelos Generalizados Lineales con R : Distribuciones de probabilidad, programación básica, simulaciones y modelos en ecología.
Intrducción al análisis Bayesiano con NIMBLE : Inferencia Bayesiana, NIMBLE y modelos en ecología
Día 2:
Modelos de ocupación : Detectabilidad imperfecta y probabilidad de presencia
Modelos N-mixture : Detectabilidad imperfecta y abundancia
Modelos de Captura-Recaptura espaciales (SCR)
Día 3:
Caso de estudio con Pepe Jiménez
Trabajo personal con datos propios
Ayer…
\[~\] Podemos crear un modelo para relacionar el número de excrementos de corzo con la temperatura en cada cuadrícula. ¿Qué distribución podría utilizar?
\[~\]
\[\begin{equation}
N_i \sim Poisson(\lambda_i)
\end{equation}\]
\[\begin{equation}
log(\lambda_i) = \beta_0 + \beta_1Temperatura_i
\end{equation}\]
En vez de contar excrementos, hoy vamos a anotar únicamente la presencia/ausencia de corzos en cada una de nuestras unidades muestrales, anotando la temperatura en cada una de ellas como variable predictora.
En vez de contar excrementos, hoy vamos a anotar únicamente la presencia/ausencia de corzos en cada una de nuestras unidades muestrales, anotando la temperatura en cada una de ellas como variable predictora.
\[~\]
\[\begin{equation}
Y_i \sim Bernoulli(p_i)
\end{equation}\]
\[\begin{equation}
p_i = \beta_0 + \beta_1Temperatura_i
\end{equation}\]
En vez de contar excrementos, hoy vamos a anotar únicamente la presencia/ausencia de corzos en cada una de nuestras unidades muestrales, anotando la temperatura en cada una de ellas como variable predictora.
\[\begin{equation}
Y_i \sim Bernoulli(p_i)
\end{equation}\]
\[\begin{equation}
logit(p_i) = \beta_0 + \beta_1Temperatura_i
\end{equation}\]
presencia temp
1 0 1.2
2 1 2.5
3 1 4.9
4 1 8.9
5 0 0.4
6 1 8.8
7 1 9.3
8 1 5.9
9 1 5.5
10 0 -1.3
11 0 0.5
12 0 0.1
13 1 6.2
14 0 2.6
15 1 7.2
16 1 4.0
17 1 6.6
18 1 9.9
19 1 2.6
20 1 7.3
21 1 9.2
22 0 0.5
23 1 5.8
24 0 -0.5
25 0 1.2
26 0 2.6
27 0 -1.8
28 1 2.6
29 1 8.4
30 1 2.1
31 1 3.8
32 1 5.2
33 1 3.9
34 0 0.2
35 1 7.9
36 1 6.0
37 1 7.5
38 0 -0.7
39 1 6.7
40 1 2.9
41 1 7.9
42 1 5.8
43 1 7.4
44 1 4.6
45 1 4.4
46 1 7.5
47 0 -1.7
48 1 3.7
49 1 6.8
50 1 6.3
51 1 3.7
52 1 8.3
53 1 3.3
54 0 0.9
55 0 -1.2
56 0 -0.8
57 0 1.8
58 1 4.2
59 1 5.9
60 1 2.9
61 1 9.0
62 1 1.5
63 1 3.5
64 0 2.0
65 1 5.8
66 0 1.1
67 1 3.7
68 1 7.2
69 0 -1.0
70 1 8.5
71 0 2.1
72 1 8.1
73 0 2.2
74 0 2.0
75 1 3.7
76 1 8.7
77 1 8.4
78 1 2.7
79 1 7.3
80 1 9.5
81 1 3.2
82 1 6.6
83 1 2.8
84 0 1.9
85 1 7.1
86 0 0.4
87 1 6.5
88 0 -0.5
89 0 0.9
90 0 -0.3
91 0 0.9
92 0 -1.3
93 1 5.7
94 1 8.5
95 1 7.3
96 1 7.6
97 1 3.5
98 1 2.9
99 1 7.7
100 1 5.3
101 1 5.9
102 0 2.2
103 0 1.2
104 1 9.9
105 1 5.6
106 0 0.6
107 0 -0.4
108 1 3.7
109 1 9.1
110 1 5.2
111 1 9.7
112 1 6.8
113 0 2.3
114 1 3.2
115 0 -0.2
116 0 -1.8
117 1 6.6
118 0 -0.8
119 1 3.4
120 1 5.7
121 1 9.9
122 1 3.9
123 1 3.8
124 0 0.1
125 1 7.1
126 0 3.4
127 1 4.1
128 0 0.5
129 0 0.7
130 1 5.1
131 1 4.9
132 0 -1.1
133 0 -1.6
134 1 5.7
135 1 9.1
136 1 5.2
137 1 4.7
138 1 4.3
139 1 9.8
140 1 4.1
141 1 6.2
142 1 5.2
143 0 0.9
144 0 1.1
145 1 6.8
146 1 3.4
147 0 0.1
148 1 7.0
149 0 -0.7
150 1 8.4
151 1 5.4
152 1 4.7
153 0 1.9
154 0 3.4
155 0 4.0
156 0 0.2
157 1 4.4
158 0 -1.1
159 0 1.3
160 0 0.6
161 0 1.4
162 1 8.7
163 1 3.4
164 1 7.4
165 1 8.6
166 1 3.0
167 0 -1.2
168 0 2.0
169 1 6.7
170 0 2.1
171 1 5.6
172 1 8.1
173 1 8.3
174 1 2.7
175 0 2.6
176 1 8.7
177 1 5.7
178 1 6.9
179 1 5.3
180 1 8.8
181 0 1.5
182 0 0.3
183 1 8.6
184 1 4.0
185 1 8.5
186 0 0.3
187 1 7.1
188 1 6.7
189 1 9.3
190 1 4.6
191 1 6.5
192 0 2.7
193 0 -0.8
194 1 9.1
195 0 1.4
196 1 5.1
197 0 -0.7
198 1 8.1
199 0 1.8
200 1 7.4
201 0 1.2
202 0 0.6
203 1 4.2
204 0 1.2
205 0 0.2
206 1 4.2
207 1 4.8
208 0 -0.5
209 0 1.1
210 1 6.6
211 1 9.5
212 0 -0.8
213 1 7.2
214 1 9.4
215 1 7.8
216 1 1.7
217 1 5.8
218 1 9.4
219 1 9.4
220 0 2.1
221 0 1.1
222 0 0.0
223 0 1.9
224 1 4.1
225 1 9.1
226 1 4.1
227 0 1.1
228 0 -1.4
229 0 3.0
230 1 8.2
231 0 2.2
232 0 -0.4
233 0 2.5
234 1 5.6
235 1 2.7
236 1 6.3
237 1 6.3
238 1 4.7
239 1 3.2
240 1 3.4
241 0 1.7
242 1 4.9
243 1 8.9
244 0 -0.3
245 0 3.0
246 0 0.5
247 0 3.1
248 0 -0.4
249 1 3.5
250 1 9.3
251 1 7.1
252 1 9.2
253 1 3.6
254 1 5.2
255 1 3.8
256 0 -0.7
257 0 1.0
258 1 4.0
259 1 2.5
260 1 9.2
261 1 4.3
262 0 1.8
263 0 1.3
264 1 7.5
265 1 6.4
266 0 0.0
267 0 -1.2
268 1 7.1
269 1 5.4
270 0 0.0
271 0 -1.3
272 0 -0.7
273 0 2.6
274 0 0.0
275 0 1.6
276 0 0.3
277 0 1.1
278 0 0.2
279 1 3.7
280 1 7.2
281 0 -1.7
282 1 4.3
283 1 8.6
284 1 2.5
285 0 -1.4
286 0 -0.3
287 0 1.9
288 0 -0.1
289 0 -0.4
290 0 0.7
291 0 0.7
292 0 -0.4
293 1 9.8
294 0 1.9
295 1 4.1
296 1 6.2
297 0 -0.8
298 0 -0.6
299 0 -1.4
300 1 9.2
301 1 6.1
302 0 -0.9
303 1 3.9
304 0 3.5
305 1 2.5
306 1 9.9
307 0 0.1
308 1 7.8
309 0 -1.2
310 1 2.8
311 0 -0.3
312 0 0.3
313 1 8.1
314 1 6.6
315 0 1.2
316 1 3.9
317 0 -1.0
318 0 2.2
319 1 9.6
320 1 5.5
321 1 6.0
322 0 1.7
323 0 2.9
324 1 10.0
325 1 8.3
326 1 9.4
327 1 7.7
328 1 7.4
329 0 1.2
330 1 7.1
331 1 9.8
332 0 1.5
333 1 2.8
334 1 7.7
335 0 -1.1
336 1 2.4
337 1 3.3
338 0 -0.1
339 1 5.0
340 1 9.6
341 1 9.9
342 0 0.1
343 1 4.5
344 1 2.6
345 1 6.1
346 0 1.2
347 1 3.6
348 0 0.1
349 1 2.4
350 1 6.7
351 1 3.8
352 0 -1.2
353 1 7.4
354 1 3.0
355 1 9.8
356 0 1.4
357 1 8.2
358 0 -1.0
359 1 8.6
360 0 3.7
361 0 -0.7
362 1 2.0
363 1 8.0
364 0 1.3
365 1 5.0
366 1 8.0
367 0 -1.1
368 1 6.4
369 1 6.4
370 1 3.6
371 1 3.2
372 1 4.7
373 1 9.1
374 0 0.8
375 0 0.7
376 0 3.0
377 1 2.0
378 1 8.4
379 0 0.1
380 1 3.9
381 0 3.2
382 1 4.8
383 1 5.9
384 1 9.7
385 0 0.8
386 0 0.9
387 1 7.6
388 1 8.0
389 0 -0.6
390 1 9.6
391 0 -0.2
392 0 -0.3
393 1 9.1
394 1 4.1
395 0 -0.1
396 0 2.2
397 1 5.9
398 1 1.7
399 0 2.2
400 0 -0.2
401 1 5.9
402 0 0.2
403 1 9.5
404 1 8.8
405 1 9.3
406 1 6.7
407 0 2.4
408 1 7.4
409 0 -1.9
410 1 9.3
411 1 9.9
412 0 2.3
413 1 7.0
414 1 7.5
415 1 6.5
416 1 3.7
417 1 3.9
418 0 1.7
419 1 6.3
420 1 7.9
421 0 3.2
422 1 4.2
423 1 6.0
424 0 -0.3
425 0 2.1
426 1 2.9
427 0 -1.0
428 1 9.2
429 1 8.1
430 1 8.6
431 1 9.2
432 0 -1.1
433 0 2.5
434 1 4.5
435 0 -0.7
436 1 7.6
437 1 6.9
438 0 -1.4
439 1 3.8
440 1 9.0
441 0 -1.5
442 0 1.5
443 1 4.0
444 1 5.3
445 1 1.2
446 1 3.1
447 0 2.4
448 1 9.3
449 0 -0.5
450 0 -1.2
451 1 9.6
452 1 3.3
453 0 2.4
454 0 0.0
455 0 -1.3
456 1 5.9
457 1 4.9
458 1 9.8
459 1 5.2
460 0 -1.2
461 0 -0.1
462 1 3.7
463 0 -2.0
464 1 3.3
465 0 1.1
466 1 9.3
467 1 6.6
468 0 0.0
469 1 3.7
470 1 6.3
471 1 3.5
472 1 9.5
473 1 6.6
474 1 2.8
475 0 -0.6
476 0 0.9
477 1 8.4
478 1 3.2
479 1 4.0
480 1 6.3
481 1 7.1
482 0 -0.1
483 1 8.2
484 1 9.4
485 1 5.1
486 1 4.0
487 0 0.3
488 0 -2.0
489 1 8.5
490 0 -0.4
491 0 -1.7
492 1 9.3
493 0 1.5
494 0 0.0
495 1 2.8
496 1 3.5
497 0 3.2
498 1 4.2
499 1 8.2
500 0 -1.3
501 1 4.7
502 1 6.3
503 1 5.9
504 1 6.0
505 1 3.7
506 1 9.6
507 0 2.8
508 1 8.2
509 1 7.1
510 1 4.4
511 1 8.5
512 1 3.6
513 0 -1.9
514 1 6.7
515 1 6.6
516 0 0.2
517 1 5.8
518 1 4.5
519 0 2.0
520 1 5.7
521 1 8.0
522 1 6.5
523 1 2.2
524 0 -0.5
525 1 2.7
526 1 9.1
527 1 7.7
528 1 7.1
529 1 9.5
530 1 9.9
531 1 5.3
532 0 -1.6
533 1 2.0
534 0 1.3
535 0 -0.6
536 0 -1.5
537 1 2.4
538 0 2.0
539 0 0.1
540 1 5.5
541 1 2.8
542 1 9.5
543 1 5.8
544 1 1.9
545 0 0.4
546 0 -0.6
547 1 10.0
548 1 2.6
549 1 4.7
550 1 6.8
551 1 8.4
552 1 4.9
553 0 -1.9
554 1 8.9
555 1 7.2
556 0 2.6
557 0 -0.9
558 0 -1.4
559 1 7.9
560 1 8.0
561 1 5.9
562 0 -0.4
563 1 2.1
564 1 6.8
565 1 8.9
566 1 6.4
567 0 0.9
568 1 5.7
569 0 1.4
570 1 9.5
571 0 -0.1
572 1 3.0
573 0 1.0
574 0 -0.9
575 1 7.9
576 0 4.3
577 1 6.0
578 1 2.9
579 1 8.1
580 1 6.8
581 0 2.2
582 1 9.4
583 1 5.8
584 0 -1.6
585 1 5.2
586 1 3.0
587 0 -1.1
588 1 4.3
589 1 9.5
590 1 6.5
591 1 4.6
592 0 0.9
593 1 7.3
594 1 5.8
595 1 8.0
596 1 5.8
597 1 3.8
598 1 3.9
599 0 2.6
600 1 3.4
601 1 7.8
602 1 9.1
603 0 -0.2
604 1 7.0
605 1 9.7
606 1 9.7
607 0 2.2
608 1 2.7
609 1 9.4
610 0 -0.7
611 1 9.2
612 1 2.2
613 1 4.4
614 1 4.5
615 1 6.6
616 0 2.9
617 0 -0.2
618 0 2.1
619 1 5.5
620 0 -1.3
621 1 8.2
622 0 0.6
623 1 4.5
624 0 -0.4
625 0 1.9
626 1 5.5
627 0 1.1
628 1 5.6
629 1 3.8
630 1 9.3
631 1 8.3
632 0 2.5
633 0 1.8
634 1 7.9
635 1 3.4
636 0 1.8
637 0 -0.8
638 0 -1.2
639 1 6.3
640 1 6.0
641 1 8.9
642 0 1.6
643 1 9.2
644 0 0.4
645 1 7.5
646 0 0.7
647 0 -1.6
648 1 8.3
649 1 6.2
650 1 9.3
651 1 6.1
652 1 8.1
653 0 2.3
654 1 2.7
655 0 4.8
656 0 -0.9
657 0 0.3
658 1 5.1
659 1 7.0
660 1 8.4
661 0 2.5
662 1 7.6
663 0 -1.3
664 1 5.5
665 1 2.3
666 1 5.1
667 1 9.0
668 0 0.4
669 1 2.4
670 1 6.1
671 1 7.2
672 1 4.3
673 1 7.9
674 1 4.3
675 1 4.0
676 1 3.0
677 0 2.3
678 0 -0.5
679 0 1.6
680 0 1.3
681 1 7.2
682 1 7.3
683 0 -0.3
684 1 4.2
685 0 5.2
686 1 4.1
687 1 2.6
688 0 3.1
689 0 -1.9
690 1 9.0
691 0 -1.0
692 1 4.1
693 1 7.8
694 1 5.2
695 1 3.1
696 1 4.7
697 1 7.5
698 0 0.0
699 1 9.6
700 1 3.7
701 1 9.2
702 1 8.8
703 1 7.0
704 1 6.1
705 1 5.8
706 0 -1.1
707 1 3.1
708 1 4.4
709 1 9.3
710 1 6.5
711 1 6.7
712 1 3.6
713 0 -0.6
714 1 7.4
715 1 3.3
716 0 3.2
717 0 -1.7
718 0 -0.2
719 1 3.1
720 1 7.2
721 0 -1.9
722 1 5.2
723 1 8.9
724 1 6.5
725 0 1.2
726 1 8.2
727 0 2.0
728 1 4.9
729 1 3.2
730 0 -1.4
731 1 6.8
732 1 4.6
733 1 7.0
734 0 -1.4
735 1 6.6
736 0 1.6
737 0 1.4
738 1 8.0
739 0 -1.0
740 0 -1.5
741 1 2.2
742 0 4.5
743 1 5.3
744 0 1.3
745 0 0.5
746 1 2.6
747 1 3.7
748 1 8.0
749 0 -0.5
750 1 6.1
751 1 4.0
752 1 8.8
753 1 4.6
754 0 -0.5
755 1 3.3
756 0 0.3
757 1 3.2
758 0 0.7
759 1 9.5
760 1 3.4
761 1 7.3
762 0 -0.1
763 1 8.4
764 0 0.5
765 0 0.1
766 0 0.0
767 1 4.8
768 1 6.7
769 1 8.5
770 1 6.5
771 0 3.7
772 1 7.8
773 0 -1.8
774 1 10.0
775 1 5.6
776 1 3.1
777 0 -1.7
778 1 7.0
779 0 0.5
780 1 10.0
781 1 8.9
782 1 6.5
783 1 6.8
784 1 3.7
785 1 8.4
786 0 0.0
787 1 5.4
788 0 1.5
789 1 3.5
790 0 -1.5
791 0 0.1
792 0 -1.3
793 1 9.3
794 0 2.1
795 1 4.2
796 1 5.5
797 0 0.8
798 1 4.2
799 1 7.7
800 0 2.2
801 1 8.3
802 0 -1.6
803 1 9.7
804 1 6.9
805 0 1.3
806 1 6.1
807 0 2.2
808 1 9.4
809 1 2.1
810 0 -1.6
811 0 2.2
812 1 2.6
813 1 2.3
814 1 9.5
815 0 2.6
816 1 4.6
817 1 9.1
818 1 9.0
819 0 0.9
820 1 6.6
821 0 2.2
822 1 4.7
823 1 6.9
824 1 7.8
825 1 8.4
826 0 -1.6
827 0 0.6
828 0 2.4
829 1 1.7
830 1 6.7
831 1 6.4
832 1 8.9
833 1 8.1
834 1 7.3
835 0 2.8
836 1 4.9
837 0 -1.1
838 1 8.5
839 1 9.5
840 1 4.1
841 1 9.1
842 0 -0.4
843 1 0.9
844 0 3.9
845 1 3.7
846 1 3.2
847 0 -1.5
848 1 5.7
849 1 6.6
850 0 2.2
851 1 9.4
852 1 6.9
853 0 -1.4
854 1 9.8
855 0 0.6
856 0 -1.6
857 0 1.1
858 1 6.6
859 0 1.0
860 0 0.8
861 0 -1.7
862 0 1.2
863 1 6.3
864 0 -1.6
865 0 -1.2
866 1 2.8
867 1 3.9
868 1 5.6
869 1 6.7
870 0 -1.1
871 0 3.1
872 1 9.7
873 1 7.8
874 0 0.7
875 1 3.9
876 0 -1.9
877 0 1.1
878 1 3.5
879 1 6.9
880 1 9.9
881 0 2.0
882 1 9.3
883 1 9.5
884 1 8.8
885 1 3.9
886 1 7.4
887 1 7.6
888 1 6.1
889 1 5.0
890 0 2.0
891 0 -2.0
892 0 -1.2
893 0 -1.0
894 0 -1.8
895 1 2.0
896 0 -0.6
897 1 5.1
898 0 -1.6
899 0 -1.9
900 0 -0.1
901 1 8.0
902 1 7.2
903 0 1.3
904 0 0.3
905 0 0.7
906 0 -1.3
907 0 -1.3
908 0 -0.2
909 0 -1.1
910 0 -1.5
911 1 4.3
912 1 7.5
913 1 6.3
914 0 -1.2
915 0 -1.8
916 1 3.3
917 0 -0.1
918 1 6.6
919 1 6.4
920 1 8.6
921 0 1.9
922 1 9.7
923 1 9.8
924 0 -1.5
925 1 8.7
926 1 7.9
927 1 6.7
928 0 1.5
929 1 4.0
930 0 3.1
931 1 5.3
932 1 9.1
933 0 0.9
934 0 1.3
935 1 6.8
936 1 7.0
937 1 9.2
938 1 3.6
939 1 8.3
940 0 1.7
941 0 0.5
942 1 9.0
943 0 -1.4
944 1 2.9
945 1 3.5
946 1 3.0
947 1 6.0
948 1 7.1
949 1 8.9
950 1 7.8
951 0 -0.9
952 0 0.1
953 1 5.7
954 1 8.5
955 1 5.1
956 0 1.1
957 1 8.6
958 0 0.3
959 1 3.9
960 0 -1.9
961 1 2.3
962 1 3.3
963 0 -0.5
964 1 5.5
965 0 1.6
966 0 0.9
967 1 2.3
968 1 8.7
969 1 9.9
970 1 6.8
971 1 9.9
972 1 4.5
973 1 3.2
974 1 9.6
975 0 -0.2
976 0 -1.2
977 0 -1.7
978 1 5.3
979 1 6.4
980 1 7.6
981 0 -0.3
982 0 -0.1
983 1 9.9
984 1 2.8
985 0 0.3
986 1 3.7
987 1 4.5
988 0 1.9
989 1 10.0
990 1 4.3
991 0 -0.4
992 1 3.3
993 1 5.4
994 0 0.4
995 0 -0.4
996 1 7.3
997 1 5.6
998 0 1.4
999 0 0.3
1000 0 1.2
En vez de contar excrementos, hoy vamos a anotar únicamente la presencia/ausencia de corzos en cada una de nuestras unidades muestrales, anotando la temperatura en cada una de ellas como variable predictora.
\[\begin{equation}
Y_i \sim Bernoulli(p_i)
\end{equation}\]
\[\begin{equation}
logit(p_i) = \beta_0 + \beta_1Temperatura_i
\end{equation}\]
m1 <- glm (presencia ~ temp, family = binomial (link = "logit" ), data = df)
Estimate Std. Error z value Pr(>|z|)
(Intercept) -5.030253 0.4553153 -11.04785 2.245344e-28
temp 1.956012 0.1658162 11.79627 4.080023e-32
En vez de contar excrementos, hoy vamos a anotar únicamente la presencia/ausencia de corzos en cada una de nuestras unidades muestrales, anotando la temperatura en cada una de ellas como variable predictora.
\[\begin{equation}
Y_i \sim Bernoulli(p_i)
\end{equation}\]
\[\begin{equation}
logit(p_i) = \beta_0 + \beta_1Temperatura_i
\end{equation}\]
Ahora, en vez de muestrear una vez cada una de nuestras celdas, las muestreamos en 4 ocasiones, anotando si hemos detectado o no la especie de estudio
presencia temp o1 o2 o3 o4
1 0 1.2 0 0 0 0
2 1 2.5 1 1 1 0
3 1 4.9 0 0 0 0
4 1 8.9 0 0 0 0
5 0 0.4 0 0 0 0
6 1 8.8 1 0 0 0
7 1 9.3 0 0 1 0
8 1 5.9 0 1 0 0
9 1 5.5 0 1 0 0
10 0 -1.3 0 0 0 0
11 0 0.5 0 0 0 0
12 0 0.1 0 0 0 0
13 1 6.2 1 0 0 0
14 0 2.6 0 0 0 0
15 1 7.2 0 1 0 0
16 1 4.0 0 1 1 0
17 1 6.6 0 0 1 0
18 1 9.9 1 0 1 0
19 1 2.6 1 1 0 1
20 1 7.3 0 0 1 0
21 1 9.2 0 0 1 0
22 0 0.5 0 0 0 0
23 1 5.8 0 0 0 1
24 0 -0.5 0 0 0 0
25 0 1.2 0 0 0 0
26 0 2.6 0 0 0 0
27 0 -1.8 0 0 0 0
28 1 2.6 0 0 0 0
29 1 8.4 1 0 1 1
30 1 2.1 0 1 1 0
31 1 3.8 1 0 0 0
32 1 5.2 1 0 1 0
33 1 3.9 0 1 0 0
34 0 0.2 0 0 0 0
35 1 7.9 1 0 1 1
36 1 6.0 1 0 0 0
37 1 7.5 1 1 0 0
38 0 -0.7 0 0 0 0
39 1 6.7 0 1 0 0
40 1 2.9 0 1 1 0
41 1 7.9 1 1 0 0
42 1 5.8 1 1 0 0
43 1 7.4 1 1 0 1
44 1 4.6 0 0 1 0
45 1 4.4 1 1 0 0
46 1 7.5 0 1 0 1
47 0 -1.7 0 0 0 0
48 1 3.7 0 1 0 0
49 1 6.8 0 1 0 0
50 1 6.3 1 0 0 0
51 1 3.7 0 0 1 0
52 1 8.3 1 0 0 0
53 1 3.3 0 0 0 0
54 0 0.9 0 0 0 0
55 0 -1.2 0 0 0 0
56 0 -0.8 0 0 0 0
57 0 1.8 0 0 0 0
58 1 4.2 1 0 0 0
59 1 5.9 1 1 0 0
60 1 2.9 1 1 0 0
61 1 9.0 0 0 0 0
62 1 1.5 1 0 0 0
63 1 3.5 1 0 0 1
64 0 2.0 0 0 0 0
65 1 5.8 1 1 1 0
66 0 1.1 0 0 0 0
67 1 3.7 0 1 0 0
68 1 7.2 0 0 0 1
69 0 -1.0 0 0 0 0
70 1 8.5 1 1 1 0
71 0 2.1 0 0 0 0
72 1 8.1 0 1 1 0
73 0 2.2 0 0 0 0
74 0 2.0 0 0 0 0
75 1 3.7 0 1 0 0
76 1 8.7 1 0 0 0
77 1 8.4 0 0 1 1
78 1 2.7 0 0 0 1
79 1 7.3 0 0 1 0
80 1 9.5 0 0 1 0
81 1 3.2 1 0 1 0
82 1 6.6 0 1 1 0
83 1 2.8 0 0 0 1
84 0 1.9 0 0 0 0
85 1 7.1 0 0 0 1
86 0 0.4 0 0 0 0
87 1 6.5 0 0 0 0
88 0 -0.5 0 0 0 0
89 0 0.9 0 0 0 0
90 0 -0.3 0 0 0 0
91 0 0.9 0 0 0 0
92 0 -1.3 0 0 0 0
93 1 5.7 0 0 0 0
94 1 8.5 1 1 0 1
95 1 7.3 0 0 0 0
96 1 7.6 0 0 0 1
97 1 3.5 1 0 0 0
98 1 2.9 0 0 0 1
99 1 7.7 0 1 1 1
100 1 5.3 0 0 0 1
101 1 5.9 1 0 0 1
102 0 2.2 0 0 0 0
103 0 1.2 0 0 0 0
104 1 9.9 1 1 1 0
105 1 5.6 0 1 1 0
106 0 0.6 0 0 0 0
107 0 -0.4 0 0 0 0
108 1 3.7 1 0 0 0
109 1 9.1 0 0 0 0
110 1 5.2 1 0 0 1
111 1 9.7 0 1 0 1
112 1 6.8 1 0 0 1
113 0 2.3 0 0 0 0
114 1 3.2 0 1 0 0
115 0 -0.2 0 0 0 0
116 0 -1.8 0 0 0 0
117 1 6.6 0 0 0 0
118 0 -0.8 0 0 0 0
119 1 3.4 0 0 0 1
120 1 5.7 0 1 1 0
121 1 9.9 0 0 0 1
122 1 3.9 0 1 0 0
123 1 3.8 1 0 0 1
124 0 0.1 0 0 0 0
125 1 7.1 0 0 0 1
126 0 3.4 0 0 0 0
127 1 4.1 0 0 0 1
128 0 0.5 0 0 0 0
129 0 0.7 0 0 0 0
130 1 5.1 1 1 1 1
131 1 4.9 1 1 1 1
132 0 -1.1 0 0 0 0
133 0 -1.6 0 0 0 0
134 1 5.7 0 1 1 0
135 1 9.1 0 1 0 0
136 1 5.2 1 0 0 0
137 1 4.7 0 1 0 1
138 1 4.3 1 1 1 0
139 1 9.8 1 0 0 0
140 1 4.1 1 1 0 0
141 1 6.2 1 1 0 1
142 1 5.2 0 1 1 0
143 0 0.9 0 0 0 0
144 0 1.1 0 0 0 0
145 1 6.8 0 0 0 1
146 1 3.4 0 0 0 0
147 0 0.1 0 0 0 0
148 1 7.0 0 0 0 0
149 0 -0.7 0 0 0 0
150 1 8.4 0 0 1 1
151 1 5.4 0 0 0 1
152 1 4.7 1 0 1 1
153 0 1.9 0 0 0 0
154 0 3.4 0 0 0 0
155 0 4.0 0 0 0 0
156 0 0.2 0 0 0 0
157 1 4.4 0 1 0 0
158 0 -1.1 0 0 0 0
159 0 1.3 0 0 0 0
160 0 0.6 0 0 0 0
161 0 1.4 0 0 0 0
162 1 8.7 1 1 1 1
163 1 3.4 0 1 1 1
164 1 7.4 0 0 0 0
165 1 8.6 1 0 1 1
166 1 3.0 1 0 0 1
167 0 -1.2 0 0 0 0
168 0 2.0 0 0 0 0
169 1 6.7 1 0 1 1
170 0 2.1 0 0 0 0
171 1 5.6 0 0 1 0
172 1 8.1 0 1 0 1
173 1 8.3 1 0 1 1
174 1 2.7 0 1 0 0
175 0 2.6 0 0 0 0
176 1 8.7 1 1 0 0
177 1 5.7 0 0 1 0
178 1 6.9 1 0 0 1
179 1 5.3 0 0 1 0
180 1 8.8 0 0 1 0
181 0 1.5 0 0 0 0
182 0 0.3 0 0 0 0
183 1 8.6 0 0 0 0
184 1 4.0 0 0 1 0
185 1 8.5 0 1 0 0
186 0 0.3 0 0 0 0
187 1 7.1 0 1 0 0
188 1 6.7 1 0 0 1
189 1 9.3 0 1 0 0
190 1 4.6 0 0 1 0
191 1 6.5 1 0 1 0
192 0 2.7 0 0 0 0
193 0 -0.8 0 0 0 0
194 1 9.1 0 0 0 0
195 0 1.4 0 0 0 0
196 1 5.1 1 1 0 0
197 0 -0.7 0 0 0 0
198 1 8.1 1 1 0 1
199 0 1.8 0 0 0 0
200 1 7.4 0 0 0 0
201 0 1.2 0 0 0 0
202 0 0.6 0 0 0 0
203 1 4.2 0 1 0 1
204 0 1.2 0 0 0 0
205 0 0.2 0 0 0 0
206 1 4.2 0 1 0 0
207 1 4.8 1 0 0 1
208 0 -0.5 0 0 0 0
209 0 1.1 0 0 0 0
210 1 6.6 0 1 1 0
211 1 9.5 1 0 1 0
212 0 -0.8 0 0 0 0
213 1 7.2 1 1 0 0
214 1 9.4 1 0 1 0
215 1 7.8 1 1 1 1
216 1 1.7 0 1 0 0
217 1 5.8 0 0 1 0
218 1 9.4 1 1 1 0
219 1 9.4 0 0 0 0
220 0 2.1 0 0 0 0
221 0 1.1 0 0 0 0
222 0 0.0 0 0 0 0
223 0 1.9 0 0 0 0
224 1 4.1 0 0 1 1
225 1 9.1 1 1 1 0
226 1 4.1 1 1 0 1
227 0 1.1 0 0 0 0
228 0 -1.4 0 0 0 0
229 0 3.0 0 0 0 0
230 1 8.2 1 1 1 1
231 0 2.2 0 0 0 0
232 0 -0.4 0 0 0 0
233 0 2.5 0 0 0 0
234 1 5.6 1 0 0 0
235 1 2.7 0 0 1 1
236 1 6.3 0 0 1 1
237 1 6.3 1 0 1 0
238 1 4.7 0 1 0 0
239 1 3.2 1 0 0 1
240 1 3.4 0 0 0 0
241 0 1.7 0 0 0 0
242 1 4.9 0 0 1 0
243 1 8.9 0 0 1 0
244 0 -0.3 0 0 0 0
245 0 3.0 0 0 0 0
246 0 0.5 0 0 0 0
247 0 3.1 0 0 0 0
248 0 -0.4 0 0 0 0
249 1 3.5 0 0 0 0
250 1 9.3 0 0 0 1
251 1 7.1 0 0 1 0
252 1 9.2 0 0 1 1
253 1 3.6 0 0 1 0
254 1 5.2 0 1 0 0
255 1 3.8 1 0 0 0
256 0 -0.7 0 0 0 0
257 0 1.0 0 0 0 0
258 1 4.0 1 0 0 0
259 1 2.5 0 0 0 0
260 1 9.2 0 0 0 0
261 1 4.3 0 1 0 1
262 0 1.8 0 0 0 0
263 0 1.3 0 0 0 0
264 1 7.5 0 1 1 1
265 1 6.4 0 0 1 0
266 0 0.0 0 0 0 0
267 0 -1.2 0 0 0 0
268 1 7.1 0 0 0 1
269 1 5.4 0 0 0 0
270 0 0.0 0 0 0 0
271 0 -1.3 0 0 0 0
272 0 -0.7 0 0 0 0
273 0 2.6 0 0 0 0
274 0 0.0 0 0 0 0
275 0 1.6 0 0 0 0
276 0 0.3 0 0 0 0
277 0 1.1 0 0 0 0
278 0 0.2 0 0 0 0
279 1 3.7 0 1 1 0
280 1 7.2 1 0 1 0
281 0 -1.7 0 0 0 0
282 1 4.3 0 0 0 1
283 1 8.6 0 0 0 1
284 1 2.5 0 1 1 0
285 0 -1.4 0 0 0 0
286 0 -0.3 0 0 0 0
287 0 1.9 0 0 0 0
288 0 -0.1 0 0 0 0
289 0 -0.4 0 0 0 0
290 0 0.7 0 0 0 0
291 0 0.7 0 0 0 0
292 0 -0.4 0 0 0 0
293 1 9.8 0 0 1 1
294 0 1.9 0 0 0 0
295 1 4.1 0 0 0 0
296 1 6.2 0 0 0 0
297 0 -0.8 0 0 0 0
298 0 -0.6 0 0 0 0
299 0 -1.4 0 0 0 0
300 1 9.2 0 1 0 0
301 1 6.1 0 1 0 0
302 0 -0.9 0 0 0 0
303 1 3.9 0 1 0 1
304 0 3.5 0 0 0 0
305 1 2.5 1 1 0 1
306 1 9.9 0 0 0 0
307 0 0.1 0 0 0 0
308 1 7.8 0 1 0 0
309 0 -1.2 0 0 0 0
310 1 2.8 0 1 0 0
311 0 -0.3 0 0 0 0
312 0 0.3 0 0 0 0
313 1 8.1 1 0 1 0
314 1 6.6 1 0 0 1
315 0 1.2 0 0 0 0
316 1 3.9 1 0 0 0
317 0 -1.0 0 0 0 0
318 0 2.2 0 0 0 0
319 1 9.6 1 0 0 0
320 1 5.5 0 0 0 0
321 1 6.0 0 1 0 1
322 0 1.7 0 0 0 0
323 0 2.9 0 0 0 0
324 1 10.0 1 0 0 0
325 1 8.3 0 0 0 0
326 1 9.4 1 0 0 1
327 1 7.7 0 0 0 1
328 1 7.4 0 1 1 0
329 0 1.2 0 0 0 0
330 1 7.1 0 0 0 1
331 1 9.8 0 0 1 0
332 0 1.5 0 0 0 0
333 1 2.8 0 1 1 0
334 1 7.7 1 0 0 0
335 0 -1.1 0 0 0 0
336 1 2.4 0 1 0 0
337 1 3.3 0 0 0 0
338 0 -0.1 0 0 0 0
339 1 5.0 1 1 0 0
340 1 9.6 0 0 0 0
341 1 9.9 1 0 0 0
342 0 0.1 0 0 0 0
343 1 4.5 0 1 1 1
344 1 2.6 0 0 0 1
345 1 6.1 0 0 1 0
346 0 1.2 0 0 0 0
347 1 3.6 1 1 1 1
348 0 0.1 0 0 0 0
349 1 2.4 1 0 1 0
350 1 6.7 1 0 1 1
351 1 3.8 1 1 0 1
352 0 -1.2 0 0 0 0
353 1 7.4 0 0 0 0
354 1 3.0 0 0 1 0
355 1 9.8 0 0 1 0
356 0 1.4 0 0 0 0
357 1 8.2 1 1 1 0
358 0 -1.0 0 0 0 0
359 1 8.6 1 0 0 1
360 0 3.7 0 0 0 0
361 0 -0.7 0 0 0 0
362 1 2.0 1 0 0 0
363 1 8.0 1 0 1 0
364 0 1.3 0 0 0 0
365 1 5.0 0 1 0 1
366 1 8.0 0 0 1 1
367 0 -1.1 0 0 0 0
368 1 6.4 0 0 0 1
369 1 6.4 1 0 0 1
370 1 3.6 0 1 0 1
371 1 3.2 0 0 0 0
372 1 4.7 0 0 0 1
373 1 9.1 0 1 0 0
374 0 0.8 0 0 0 0
375 0 0.7 0 0 0 0
376 0 3.0 0 0 0 0
377 1 2.0 1 0 1 1
378 1 8.4 1 0 1 1
379 0 0.1 0 0 0 0
380 1 3.9 0 0 1 1
381 0 3.2 0 0 0 0
382 1 4.8 1 1 0 0
383 1 5.9 0 0 1 1
384 1 9.7 0 0 1 0
385 0 0.8 0 0 0 0
386 0 0.9 0 0 0 0
387 1 7.6 0 0 0 1
388 1 8.0 0 1 0 1
389 0 -0.6 0 0 0 0
390 1 9.6 0 0 0 1
391 0 -0.2 0 0 0 0
392 0 -0.3 0 0 0 0
393 1 9.1 1 1 0 1
394 1 4.1 1 0 0 1
395 0 -0.1 0 0 0 0
396 0 2.2 0 0 0 0
397 1 5.9 0 0 0 0
398 1 1.7 0 1 0 1
399 0 2.2 0 0 0 0
400 0 -0.2 0 0 0 0
401 1 5.9 0 1 0 0
402 0 0.2 0 0 0 0
403 1 9.5 1 0 1 0
404 1 8.8 1 1 0 1
405 1 9.3 0 0 1 0
406 1 6.7 1 0 0 1
407 0 2.4 0 0 0 0
408 1 7.4 0 0 1 0
409 0 -1.9 0 0 0 0
410 1 9.3 1 1 0 0
411 1 9.9 0 0 1 0
412 0 2.3 0 0 0 0
413 1 7.0 0 0 0 0
414 1 7.5 1 0 0 0
415 1 6.5 1 1 0 0
416 1 3.7 1 1 0 0
417 1 3.9 1 1 1 1
418 0 1.7 0 0 0 0
419 1 6.3 0 0 1 1
420 1 7.9 0 0 0 0
421 0 3.2 0 0 0 0
422 1 4.2 0 0 0 0
423 1 6.0 0 0 0 0
424 0 -0.3 0 0 0 0
425 0 2.1 0 0 0 0
426 1 2.9 0 0 1 0
427 0 -1.0 0 0 0 0
428 1 9.2 0 0 1 0
429 1 8.1 0 0 1 0
430 1 8.6 1 0 0 0
431 1 9.2 0 1 0 0
432 0 -1.1 0 0 0 0
433 0 2.5 0 0 0 0
434 1 4.5 0 0 0 0
435 0 -0.7 0 0 0 0
436 1 7.6 0 0 1 0
437 1 6.9 0 1 1 1
438 0 -1.4 0 0 0 0
439 1 3.8 0 0 1 0
440 1 9.0 1 1 0 0
441 0 -1.5 0 0 0 0
442 0 1.5 0 0 0 0
443 1 4.0 0 1 1 1
444 1 5.3 0 1 1 1
445 1 1.2 1 0 0 1
446 1 3.1 0 1 0 1
447 0 2.4 0 0 0 0
448 1 9.3 0 0 0 1
449 0 -0.5 0 0 0 0
450 0 -1.2 0 0 0 0
451 1 9.6 1 1 0 0
452 1 3.3 1 0 1 1
453 0 2.4 0 0 0 0
454 0 0.0 0 0 0 0
455 0 -1.3 0 0 0 0
456 1 5.9 0 0 0 0
457 1 4.9 1 0 1 0
458 1 9.8 1 1 1 0
459 1 5.2 1 0 0 0
460 0 -1.2 0 0 0 0
461 0 -0.1 0 0 0 0
462 1 3.7 0 1 0 1
463 0 -2.0 0 0 0 0
464 1 3.3 0 0 0 0
465 0 1.1 0 0 0 0
466 1 9.3 0 0 1 1
467 1 6.6 0 1 0 1
468 0 0.0 0 0 0 0
469 1 3.7 1 1 1 0
470 1 6.3 1 1 0 1
471 1 3.5 0 0 0 1
472 1 9.5 1 0 1 1
473 1 6.6 0 0 0 0
474 1 2.8 1 1 1 1
475 0 -0.6 0 0 0 0
476 0 0.9 0 0 0 0
477 1 8.4 0 0 1 0
478 1 3.2 0 0 1 1
479 1 4.0 0 0 0 0
480 1 6.3 1 1 1 0
481 1 7.1 0 0 1 1
482 0 -0.1 0 0 0 0
483 1 8.2 1 0 0 1
484 1 9.4 0 1 0 0
485 1 5.1 0 0 1 0
486 1 4.0 0 0 0 1
487 0 0.3 0 0 0 0
488 0 -2.0 0 0 0 0
489 1 8.5 1 1 0 1
490 0 -0.4 0 0 0 0
491 0 -1.7 0 0 0 0
492 1 9.3 0 1 0 0
493 0 1.5 0 0 0 0
494 0 0.0 0 0 0 0
495 1 2.8 1 1 0 1
496 1 3.5 0 0 1 0
497 0 3.2 0 0 0 0
498 1 4.2 0 1 1 0
499 1 8.2 1 0 1 0
500 0 -1.3 0 0 0 0
501 1 4.7 1 0 1 1
502 1 6.3 1 1 0 0
503 1 5.9 1 1 0 1
504 1 6.0 1 1 1 0
505 1 3.7 0 1 0 0
506 1 9.6 0 0 1 0
507 0 2.8 0 0 0 0
508 1 8.2 0 1 0 0
509 1 7.1 0 0 0 0
510 1 4.4 0 1 0 0
511 1 8.5 1 0 0 0
512 1 3.6 0 0 0 0
513 0 -1.9 0 0 0 0
514 1 6.7 0 0 0 0
515 1 6.6 1 0 0 1
516 0 0.2 0 0 0 0
517 1 5.8 0 1 1 0
518 1 4.5 1 0 0 1
519 0 2.0 0 0 0 0
520 1 5.7 0 0 0 0
521 1 8.0 1 0 1 1
522 1 6.5 0 0 1 1
523 1 2.2 1 1 0 1
524 0 -0.5 0 0 0 0
525 1 2.7 1 0 0 1
526 1 9.1 1 1 1 1
527 1 7.7 0 0 0 0
528 1 7.1 0 1 0 1
529 1 9.5 0 1 1 1
530 1 9.9 0 1 0 1
531 1 5.3 0 1 1 1
532 0 -1.6 0 0 0 0
533 1 2.0 1 1 0 1
534 0 1.3 0 0 0 0
535 0 -0.6 0 0 0 0
536 0 -1.5 0 0 0 0
537 1 2.4 0 0 1 0
538 0 2.0 0 0 0 0
539 0 0.1 0 0 0 0
540 1 5.5 0 0 0 1
541 1 2.8 0 0 0 0
542 1 9.5 1 1 1 0
543 1 5.8 0 0 1 0
544 1 1.9 0 0 0 1
545 0 0.4 0 0 0 0
546 0 -0.6 0 0 0 0
547 1 10.0 0 0 0 1
548 1 2.6 0 0 1 0
549 1 4.7 1 1 1 0
550 1 6.8 0 1 1 1
551 1 8.4 1 1 1 0
552 1 4.9 0 1 1 0
553 0 -1.9 0 0 0 0
554 1 8.9 0 0 0 0
555 1 7.2 1 0 0 0
556 0 2.6 0 0 0 0
557 0 -0.9 0 0 0 0
558 0 -1.4 0 0 0 0
559 1 7.9 0 0 0 0
560 1 8.0 0 1 1 0
561 1 5.9 0 0 0 1
562 0 -0.4 0 0 0 0
563 1 2.1 0 0 0 0
564 1 6.8 1 0 0 1
565 1 8.9 1 0 0 1
566 1 6.4 0 1 1 0
567 0 0.9 0 0 0 0
568 1 5.7 0 1 0 0
569 0 1.4 0 0 0 0
570 1 9.5 0 1 0 0
571 0 -0.1 0 0 0 0
572 1 3.0 0 1 0 0
573 0 1.0 0 0 0 0
574 0 -0.9 0 0 0 0
575 1 7.9 1 1 0 0
576 0 4.3 0 0 0 0
577 1 6.0 1 1 1 1
578 1 2.9 0 0 0 1
579 1 8.1 0 1 1 0
580 1 6.8 0 0 0 0
581 0 2.2 0 0 0 0
582 1 9.4 0 1 1 0
583 1 5.8 1 0 0 1
584 0 -1.6 0 0 0 0
585 1 5.2 0 1 0 1
586 1 3.0 1 1 1 1
587 0 -1.1 0 0 0 0
588 1 4.3 0 1 1 0
589 1 9.5 1 0 0 0
590 1 6.5 0 0 1 0
591 1 4.6 1 1 0 0
592 0 0.9 0 0 0 0
593 1 7.3 1 0 0 0
594 1 5.8 0 0 1 1
595 1 8.0 1 0 1 1
596 1 5.8 0 1 1 1
597 1 3.8 1 0 0 0
598 1 3.9 0 1 1 0
599 0 2.6 0 0 0 0
600 1 3.4 0 0 0 0
601 1 7.8 0 1 0 0
602 1 9.1 0 1 0 0
603 0 -0.2 0 0 0 0
604 1 7.0 1 1 1 0
605 1 9.7 0 0 0 0
606 1 9.7 0 1 1 0
607 0 2.2 0 0 0 0
608 1 2.7 0 0 1 1
609 1 9.4 0 0 0 1
610 0 -0.7 0 0 0 0
611 1 9.2 1 1 0 1
612 1 2.2 1 1 1 0
613 1 4.4 0 1 1 1
614 1 4.5 0 0 0 1
615 1 6.6 0 1 1 0
616 0 2.9 0 0 0 0
617 0 -0.2 0 0 0 0
618 0 2.1 0 0 0 0
619 1 5.5 1 0 0 1
620 0 -1.3 0 0 0 0
621 1 8.2 0 0 0 1
622 0 0.6 0 0 0 0
623 1 4.5 0 1 0 1
624 0 -0.4 0 0 0 0
625 0 1.9 0 0 0 0
626 1 5.5 0 0 0 0
627 0 1.1 0 0 0 0
628 1 5.6 0 1 0 0
629 1 3.8 0 0 1 0
630 1 9.3 0 0 1 0
631 1 8.3 0 0 0 0
632 0 2.5 0 0 0 0
633 0 1.8 0 0 0 0
634 1 7.9 0 1 0 0
635 1 3.4 0 0 1 0
636 0 1.8 0 0 0 0
637 0 -0.8 0 0 0 0
638 0 -1.2 0 0 0 0
639 1 6.3 0 1 1 1
640 1 6.0 0 0 1 0
641 1 8.9 1 0 0 0
642 0 1.6 0 0 0 0
643 1 9.2 1 0 1 0
644 0 0.4 0 0 0 0
645 1 7.5 0 1 1 0
646 0 0.7 0 0 0 0
647 0 -1.6 0 0 0 0
648 1 8.3 0 0 1 0
649 1 6.2 0 1 1 0
650 1 9.3 0 0 1 0
651 1 6.1 0 1 0 0
652 1 8.1 0 1 1 1
653 0 2.3 0 0 0 0
654 1 2.7 0 0 1 1
655 0 4.8 0 0 0 0
656 0 -0.9 0 0 0 0
657 0 0.3 0 0 0 0
658 1 5.1 0 0 0 1
659 1 7.0 0 0 0 0
660 1 8.4 0 0 1 0
661 0 2.5 0 0 0 0
662 1 7.6 1 1 1 0
663 0 -1.3 0 0 0 0
664 1 5.5 1 0 1 1
665 1 2.3 0 0 1 0
666 1 5.1 0 1 0 1
667 1 9.0 0 0 0 0
668 0 0.4 0 0 0 0
669 1 2.4 0 0 1 1
670 1 6.1 0 0 1 1
671 1 7.2 1 1 0 1
672 1 4.3 1 0 0 0
673 1 7.9 1 1 0 1
674 1 4.3 1 0 1 1
675 1 4.0 1 1 1 1
676 1 3.0 1 0 1 0
677 0 2.3 0 0 0 0
678 0 -0.5 0 0 0 0
679 0 1.6 0 0 0 0
680 0 1.3 0 0 0 0
681 1 7.2 0 0 1 1
682 1 7.3 0 0 1 1
683 0 -0.3 0 0 0 0
684 1 4.2 1 0 1 0
685 0 5.2 0 0 0 0
686 1 4.1 0 1 0 1
687 1 2.6 0 0 0 0
688 0 3.1 0 0 0 0
689 0 -1.9 0 0 0 0
690 1 9.0 0 0 1 0
691 0 -1.0 0 0 0 0
692 1 4.1 0 1 0 1
693 1 7.8 1 0 0 1
694 1 5.2 0 0 1 1
695 1 3.1 1 1 0 1
696 1 4.7 0 0 0 0
697 1 7.5 0 0 0 0
698 0 0.0 0 0 0 0
699 1 9.6 0 1 0 0
700 1 3.7 0 0 0 0
701 1 9.2 0 0 0 0
702 1 8.8 0 1 1 0
703 1 7.0 0 1 0 1
704 1 6.1 1 1 0 0
705 1 5.8 0 0 1 0
706 0 -1.1 0 0 0 0
707 1 3.1 0 0 1 0
708 1 4.4 1 1 0 0
709 1 9.3 0 0 1 1
710 1 6.5 0 0 0 0
711 1 6.7 0 1 1 1
712 1 3.6 0 0 1 0
713 0 -0.6 0 0 0 0
714 1 7.4 0 1 1 1
715 1 3.3 0 1 1 0
716 0 3.2 0 0 0 0
717 0 -1.7 0 0 0 0
718 0 -0.2 0 0 0 0
719 1 3.1 1 0 0 1
720 1 7.2 0 0 0 1
721 0 -1.9 0 0 0 0
722 1 5.2 0 0 1 1
723 1 8.9 0 0 0 1
724 1 6.5 1 0 0 1
725 0 1.2 0 0 0 0
726 1 8.2 0 0 0 0
727 0 2.0 0 0 0 0
728 1 4.9 1 1 0 1
729 1 3.2 0 1 0 0
730 0 -1.4 0 0 0 0
731 1 6.8 0 0 0 1
732 1 4.6 1 0 0 0
733 1 7.0 0 0 1 0
734 0 -1.4 0 0 0 0
735 1 6.6 0 1 1 0
736 0 1.6 0 0 0 0
737 0 1.4 0 0 0 0
738 1 8.0 0 1 0 1
739 0 -1.0 0 0 0 0
740 0 -1.5 0 0 0 0
741 1 2.2 0 0 0 0
742 0 4.5 0 0 0 0
743 1 5.3 1 0 0 1
744 0 1.3 0 0 0 0
745 0 0.5 0 0 0 0
746 1 2.6 1 0 0 0
747 1 3.7 0 1 0 0
748 1 8.0 1 0 1 0
749 0 -0.5 0 0 0 0
750 1 6.1 1 0 1 0
751 1 4.0 0 0 1 0
752 1 8.8 0 0 1 1
753 1 4.6 0 0 0 0
754 0 -0.5 0 0 0 0
755 1 3.3 0 0 0 0
756 0 0.3 0 0 0 0
757 1 3.2 1 0 0 0
758 0 0.7 0 0 0 0
759 1 9.5 0 1 0 0
760 1 3.4 0 1 0 0
761 1 7.3 0 0 0 0
762 0 -0.1 0 0 0 0
763 1 8.4 1 1 1 0
764 0 0.5 0 0 0 0
765 0 0.1 0 0 0 0
766 0 0.0 0 0 0 0
767 1 4.8 1 1 1 0
768 1 6.7 0 0 1 0
769 1 8.5 0 0 1 0
770 1 6.5 0 0 1 1
771 0 3.7 0 0 0 0
772 1 7.8 0 0 1 0
773 0 -1.8 0 0 0 0
774 1 10.0 0 1 1 0
775 1 5.6 0 0 0 0
776 1 3.1 1 0 0 1
777 0 -1.7 0 0 0 0
778 1 7.0 0 1 0 0
779 0 0.5 0 0 0 0
780 1 10.0 1 0 0 0
781 1 8.9 1 1 0 1
782 1 6.5 0 0 0 0
783 1 6.8 0 1 0 0
784 1 3.7 0 0 1 0
785 1 8.4 0 0 1 0
786 0 0.0 0 0 0 0
787 1 5.4 1 1 1 0
788 0 1.5 0 0 0 0
789 1 3.5 1 0 1 1
790 0 -1.5 0 0 0 0
791 0 0.1 0 0 0 0
792 0 -1.3 0 0 0 0
793 1 9.3 1 0 0 0
794 0 2.1 0 0 0 0
795 1 4.2 1 0 0 0
796 1 5.5 1 0 0 0
797 0 0.8 0 0 0 0
798 1 4.2 1 0 0 1
799 1 7.7 0 0 0 0
800 0 2.2 0 0 0 0
801 1 8.3 1 0 1 1
802 0 -1.6 0 0 0 0
803 1 9.7 0 0 1 0
804 1 6.9 0 1 0 0
805 0 1.3 0 0 0 0
806 1 6.1 0 0 0 0
807 0 2.2 0 0 0 0
808 1 9.4 0 0 0 0
809 1 2.1 1 1 0 1
810 0 -1.6 0 0 0 0
811 0 2.2 0 0 0 0
812 1 2.6 1 1 1 1
813 1 2.3 0 1 0 0
814 1 9.5 0 0 1 0
815 0 2.6 0 0 0 0
816 1 4.6 0 0 0 0
817 1 9.1 0 1 1 1
818 1 9.0 1 1 0 0
819 0 0.9 0 0 0 0
820 1 6.6 0 0 0 1
821 0 2.2 0 0 0 0
822 1 4.7 0 0 1 0
823 1 6.9 0 1 0 1
824 1 7.8 0 0 0 0
825 1 8.4 1 0 1 1
826 0 -1.6 0 0 0 0
827 0 0.6 0 0 0 0
828 0 2.4 0 0 0 0
829 1 1.7 1 0 0 0
830 1 6.7 0 1 1 0
831 1 6.4 0 0 1 0
832 1 8.9 0 1 0 0
833 1 8.1 0 0 1 1
834 1 7.3 0 0 1 1
835 0 2.8 0 0 0 0
836 1 4.9 1 1 1 1
837 0 -1.1 0 0 0 0
838 1 8.5 1 1 0 0
839 1 9.5 0 1 0 0
840 1 4.1 0 0 0 0
841 1 9.1 0 1 0 1
842 0 -0.4 0 0 0 0
843 1 0.9 1 0 0 0
844 0 3.9 0 0 0 0
845 1 3.7 1 1 0 0
846 1 3.2 0 0 0 0
847 0 -1.5 0 0 0 0
848 1 5.7 0 1 0 0
849 1 6.6 0 0 1 0
850 0 2.2 0 0 0 0
851 1 9.4 0 1 1 0
852 1 6.9 1 1 0 1
853 0 -1.4 0 0 0 0
854 1 9.8 0 1 0 0
855 0 0.6 0 0 0 0
856 0 -1.6 0 0 0 0
857 0 1.1 0 0 0 0
858 1 6.6 0 0 1 1
859 0 1.0 0 0 0 0
860 0 0.8 0 0 0 0
861 0 -1.7 0 0 0 0
862 0 1.2 0 0 0 0
863 1 6.3 0 0 1 1
864 0 -1.6 0 0 0 0
865 0 -1.2 0 0 0 0
866 1 2.8 1 1 1 1
867 1 3.9 0 1 0 1
868 1 5.6 1 0 0 1
869 1 6.7 1 0 0 0
870 0 -1.1 0 0 0 0
871 0 3.1 0 0 0 0
872 1 9.7 0 0 0 0
873 1 7.8 0 0 0 1
874 0 0.7 0 0 0 0
875 1 3.9 0 1 0 1
876 0 -1.9 0 0 0 0
877 0 1.1 0 0 0 0
878 1 3.5 0 0 0 0
879 1 6.9 0 0 0 1
880 1 9.9 1 0 0 0
881 0 2.0 0 0 0 0
882 1 9.3 0 1 0 1
883 1 9.5 0 0 0 1
884 1 8.8 1 0 1 0
885 1 3.9 0 1 0 1
886 1 7.4 1 1 0 1
887 1 7.6 0 0 0 0
888 1 6.1 0 0 1 1
889 1 5.0 1 0 1 0
890 0 2.0 0 0 0 0
891 0 -2.0 0 0 0 0
892 0 -1.2 0 0 0 0
893 0 -1.0 0 0 0 0
894 0 -1.8 0 0 0 0
895 1 2.0 0 1 0 1
896 0 -0.6 0 0 0 0
897 1 5.1 1 0 0 0
898 0 -1.6 0 0 0 0
899 0 -1.9 0 0 0 0
900 0 -0.1 0 0 0 0
901 1 8.0 0 0 0 1
902 1 7.2 0 0 0 1
903 0 1.3 0 0 0 0
904 0 0.3 0 0 0 0
905 0 0.7 0 0 0 0
906 0 -1.3 0 0 0 0
907 0 -1.3 0 0 0 0
908 0 -0.2 0 0 0 0
909 0 -1.1 0 0 0 0
910 0 -1.5 0 0 0 0
911 1 4.3 1 0 1 1
912 1 7.5 1 0 0 0
913 1 6.3 0 0 1 0
914 0 -1.2 0 0 0 0
915 0 -1.8 0 0 0 0
916 1 3.3 0 0 1 0
917 0 -0.1 0 0 0 0
918 1 6.6 0 1 0 1
919 1 6.4 0 0 0 0
920 1 8.6 1 1 0 0
921 0 1.9 0 0 0 0
922 1 9.7 0 1 0 0
923 1 9.8 0 0 0 0
924 0 -1.5 0 0 0 0
925 1 8.7 0 0 0 1
926 1 7.9 1 1 1 0
927 1 6.7 1 1 0 1
928 0 1.5 0 0 0 0
929 1 4.0 1 0 1 0
930 0 3.1 0 0 0 0
931 1 5.3 0 0 0 0
932 1 9.1 0 0 1 1
933 0 0.9 0 0 0 0
934 0 1.3 0 0 0 0
935 1 6.8 0 0 1 1
936 1 7.0 1 0 0 0
937 1 9.2 0 0 0 0
938 1 3.6 0 0 0 1
939 1 8.3 0 1 0 0
940 0 1.7 0 0 0 0
941 0 0.5 0 0 0 0
942 1 9.0 0 0 1 1
943 0 -1.4 0 0 0 0
944 1 2.9 0 1 0 1
945 1 3.5 1 0 0 0
946 1 3.0 1 0 0 1
947 1 6.0 1 1 0 0
948 1 7.1 0 0 1 0
949 1 8.9 0 1 1 0
950 1 7.8 0 0 1 1
951 0 -0.9 0 0 0 0
952 0 0.1 0 0 0 0
953 1 5.7 1 0 0 0
954 1 8.5 0 0 1 1
955 1 5.1 0 0 0 1
956 0 1.1 0 0 0 0
957 1 8.6 1 1 1 0
958 0 0.3 0 0 0 0
959 1 3.9 0 0 0 0
960 0 -1.9 0 0 0 0
961 1 2.3 0 0 0 1
962 1 3.3 1 1 1 0
963 0 -0.5 0 0 0 0
964 1 5.5 0 1 0 0
965 0 1.6 0 0 0 0
966 0 0.9 0 0 0 0
967 1 2.3 1 0 1 1
968 1 8.7 1 1 1 0
969 1 9.9 0 0 1 0
970 1 6.8 1 0 1 1
971 1 9.9 0 1 0 1
972 1 4.5 0 0 1 1
973 1 3.2 0 1 0 0
974 1 9.6 0 0 0 0
975 0 -0.2 0 0 0 0
976 0 -1.2 0 0 0 0
977 0 -1.7 0 0 0 0
978 1 5.3 0 0 0 0
979 1 6.4 0 0 0 1
980 1 7.6 1 0 0 1
981 0 -0.3 0 0 0 0
982 0 -0.1 0 0 0 0
983 1 9.9 0 1 0 0
984 1 2.8 0 0 1 1
985 0 0.3 0 0 0 0
986 1 3.7 1 0 0 1
987 1 4.5 0 1 1 0
988 0 1.9 0 0 0 0
989 1 10.0 1 1 0 1
990 1 4.3 0 0 1 0
991 0 -0.4 0 0 0 0
992 1 3.3 0 0 0 0
993 1 5.4 1 0 0 0
994 0 0.4 0 0 0 0
995 0 -0.4 0 0 0 0
996 1 7.3 0 0 0 0
997 1 5.6 1 1 0 0
998 0 1.4 0 0 0 0
999 0 0.3 0 0 0 0
1000 0 1.2 0 0 0 0
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1X1_i
\end{equation}\]
\[~\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1X2_{ij}
\end{equation}\]
\[~\] \(h_{ij}\) = detección / no detección de la especie en la celda \(i\) en la ocasión \(j\)
\(p_{ij}\) = probabilidad de detección en la celda en la celda \(i\) en la ocasión \(j\)
\[~\]
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1X1_i
\end{equation}\]
\[~\]
\(i\) = sitios de muestreo (celdas)
\(Y_{i}\) = Presencia/ausencia de la especie en la celda \(i\) (0/1)
\(\Psi_{i}\) = probabilidad de presencia de la espeice en la celda \(i\)
\(\beta_0\) y \(\beta_1\) = coeficientes para la \(\Psi_i\)
\(X1_i\) = Variables predictoras para la probabilidad de presencia de la especie
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1X1_i
\end{equation}\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1X2_{ij}
\end{equation}\]
\[~\]
\(j\) = ocasiones de muestreo
\(h_{ij}\) = Detección/no detección de la especie en la celda \(i\) en la ocasión \(j\)
\(p_{ij}\) = probabilidad de detección de la espeice en la celda \(i\) en la ocasión \(j\)
\(\alpha_0\) y \(\alpha_1\) = coeficientes para la \(p_{ij}\)
\(X2_{ij}\) = Variables predictoras para la probabilidad de detección de la especie en la celda \(i\) en la ocasión \(j\)
Asunciones del modelo
La ocupación de un sitio no varía durante el periodo de muestreo (población cerrada, no hay colonización ni extinción)
Las detecciones / no detecciones son independientes
No hay falsos positivos
No existe heterogeneidad no modelada
A modelizar!
Caso práctico
Queremos modelizar la ocupación (probabilidad de presencia) de una especie a partir de datos de cámaras trampa . Nuestro área de estudio es una zona montañosa dividida en una malla de 50x50 celdas . Sabemos que nuestra especie utiliza mayormente el hábitat de matorral de los fondos de valle de nuestro área de estudio. Disponemos de un total de 100 cámaras de fototrampeo que hemos dispuesto aleatoriamente en nuestro área de estudio que han estado activas durante 7 noches utilizando una lata de sardinas como atrayente. De las 100 cámaras, 47 de ellas son de la marca A y 53 de la marca B .
# Instalamos y cargamos las librerías que vamos a utilizar.
#install.packages("terra")
library (terra)
library (nimble)
library (MCMCvis)
library (tidyverse)
# Leemos nuestros datos en formato CVS
datos <- read.csv ("https://raw.githubusercontent.com/jabiologo/web/master/tutorials/tallerSECEM_files/occuDatos.csv" )
# Le pedimos a R que nos muestre nuestros datos.
datos
id marca o1 o2 o3 o4 o5 o6 o7 dia1 dia2 dia3 dia4 dia5 dia6 dia7
1 593 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
2 1942 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
3 1945 A 0 0 0 1 0 0 0 1 2 3 4 5 6 7
4 253 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
5 2152 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
6 1528 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
7 408 B 0 0 0 1 0 0 0 1 2 3 4 5 6 7
8 1798 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
9 616 B 1 1 0 0 1 0 0 1 2 3 4 5 6 7
10 378 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
11 1050 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
12 769 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
13 1712 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
14 514 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
15 1777 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
16 1465 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
17 1585 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
18 1533 A 0 0 1 0 0 0 0 1 2 3 4 5 6 7
19 1172 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
20 73 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
21 2332 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
22 1686 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
23 1128 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
24 166 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
25 1233 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
26 971 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
27 1661 B 1 0 0 0 0 0 1 1 2 3 4 5 6 7
28 2192 B 0 1 1 1 1 1 0 1 2 3 4 5 6 7
29 2155 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
30 2422 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
31 176 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
32 1836 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
33 2389 A 1 1 1 0 1 0 0 1 2 3 4 5 6 7
34 64 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
35 1444 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
36 612 B 0 0 0 1 0 0 0 1 2 3 4 5 6 7
37 1192 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
38 11 B 1 1 1 0 1 1 0 1 2 3 4 5 6 7
39 1316 B 0 1 0 0 0 0 0 1 2 3 4 5 6 7
40 1161 B 1 1 0 0 0 1 0 1 2 3 4 5 6 7
41 459 A 0 0 0 1 0 0 0 1 2 3 4 5 6 7
42 1238 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
43 1170 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
44 579 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
45 2248 B 1 1 0 0 0 0 0 1 2 3 4 5 6 7
46 81 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
47 1756 A 1 0 0 0 0 0 0 1 2 3 4 5 6 7
48 737 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
49 1536 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
50 2345 B 1 0 0 0 0 0 0 1 2 3 4 5 6 7
51 1610 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
52 1240 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
53 1788 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
54 648 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
55 1002 B 1 0 0 0 0 0 0 1 2 3 4 5 6 7
56 1124 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
57 827 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
58 965 A 1 0 1 1 0 1 0 1 2 3 4 5 6 7
59 555 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
60 2374 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
61 2329 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
62 964 B 0 1 1 0 0 0 0 1 2 3 4 5 6 7
63 1514 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
64 2478 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
65 248 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
66 1096 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
67 2209 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
68 2427 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
69 471 A 0 0 0 1 0 0 0 1 2 3 4 5 6 7
70 911 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
71 1293 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
72 1280 B 1 1 1 0 0 0 0 1 2 3 4 5 6 7
73 1980 B 1 0 0 0 0 0 1 1 2 3 4 5 6 7
74 1200 A 1 0 0 0 0 0 0 1 2 3 4 5 6 7
75 1782 B 0 0 1 1 0 1 0 1 2 3 4 5 6 7
76 1415 A 0 0 1 0 1 0 0 1 2 3 4 5 6 7
77 351 B 1 1 1 0 0 0 0 1 2 3 4 5 6 7
78 249 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
79 2431 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
80 1271 B 1 1 1 1 0 0 0 1 2 3 4 5 6 7
81 1572 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
82 1102 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
83 273 B 1 0 0 0 0 0 0 1 2 3 4 5 6 7
84 481 B 1 0 0 1 0 0 0 1 2 3 4 5 6 7
85 865 A 1 0 1 0 1 0 0 1 2 3 4 5 6 7
86 452 B 1 1 1 0 0 1 0 1 2 3 4 5 6 7
87 2225 A 1 0 1 0 0 0 0 1 2 3 4 5 6 7
88 934 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
89 1424 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
90 1143 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
91 2303 B 1 1 0 0 0 0 0 1 2 3 4 5 6 7
92 304 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
93 703 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
94 2175 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
95 1391 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
96 2020 B 1 0 0 0 0 0 0 1 2 3 4 5 6 7
97 296 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
98 2439 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
99 212 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
100 687 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
# Cargamos las capas raster correspondientes a nuestras covariables predictoras,
# en este caso elevación y porcentaje de vegetación arbustiva.
elev <- rast ("https://github.com/jabiologo/web/raw/master/tutorials/tallerSECEM_files/elev.tif" )
arbu <- rast ("https://github.com/jabiologo/web/raw/master/tutorials/tallerSECEM_files/arbu.tif" )
names (elev) <- "elev"
names (arbu) <- "arbu"
# Vamos a graficar estas capas para hacernos una idea de cómo son. Además,
# colocaremos encima las localizaciones de nuestros dos modelos de cámaras.
par (mfrow = c (1 ,2 ))
plot (elev, main = "Elevación" )
points (xyFromCell (elev, datos$ id[datos$ marca == "A" ]), col = "darkred" , pch = 19 )
points (xyFromCell (elev, datos$ id[datos$ marca == "B" ]), col = "darkblue" , pch = 19 )
plot (arbu, main = "Porcentaje arbusto" )
# En este paso estandarizaremos nuestras variables para que su media sea 0 y su
# desviación estándar 1. Esta es una práctica habitual en modelización que ayuda
# a ajustar los modelos de forma más efectiva. La fórmula es:
# valor escalado = (valor de la cov - valor medio de la cov)/ SD de la cov
datos$ elev <- scale (elev[datos$ id])[1 : 100 ]
datos$ arbu <- scale (arbu[datos$ id])[1 : 100 ]
# Inspeccionamos las primeras filas de nuestro juego de datos.
head (datos)
id marca o1 o2 o3 o4 o5 o6 o7 dia1 dia2 dia3 dia4 dia5 dia6 dia7
1 593 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
2 1942 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
3 1945 A 0 0 0 1 0 0 0 1 2 3 4 5 6 7
4 253 B 0 0 0 0 0 0 0 1 2 3 4 5 6 7
5 2152 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
6 1528 A 0 0 0 0 0 0 0 1 2 3 4 5 6 7
elev arbu
1 0.55262104 1.4229936
2 0.37677981 -0.4942135
3 0.03575438 0.7839246
4 -0.80082361 0.9685444
5 0.29685197 0.3578785
6 0.35546572 -1.5735298
Vamos a pensar un poco sobre el posible modelo…
Sabemos que nuestra especie utiliza mayormente el hábitat de matorral de los fondos de valle de nuestro área de estudio. Disponemos de un total de 100 cámaras de fototrampeo que hemos dispuesto aleatoriamente en nuestro área de estudio que han estado activas durante 7 noches utilizando una lata de sardinas como atrayente. De las 100 cámaras, 47 de ellas son de la marca A y 53 de la marca B
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1X1_i
\end{equation}\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1X2_{ij}
\end{equation}\]
Vamos a pensar un poco más sobre el posible modelo…
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1X1_i
\end{equation}\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1X2_{ij}
\end{equation}\]
Vamos a pensar un poco más sobre el posible modelo…
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1Elev_i + \beta_2Arbu_i
\end{equation}\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1Marca_{i} + \alpha_2Arbu_i + \alpha_3Dia_{ij}
\end{equation}\]
Traducción a Nimble
\[\begin{equation}
Y_i \sim Bernoulli(\Psi_i)
\end{equation}\]
\[\begin{equation}
logit(\Psi_i) = \beta_0 + \beta_1Elev_i + \beta_2Arbu_i
\end{equation}\]
\[\begin{equation}
h_{ij}|Y_i \sim Bernoulli(Y_ip_{ij})
\end{equation}\]
\[\begin{equation}
logit(p_{ij}) = \alpha_0 + \alpha_1Marca_{i} + \alpha_2Arbu_i + \alpha_3Dia_{ij}
\end{equation}\]
# Likelihood
for (i in 1 : nsitios) {
Y[i] ~ dbern (psi[i])
logit (psi[i]) <- b0 + b1* elev[i] + b2* arbu[i]
for (j in 1 : nocasiones) {
hdet[i,j] ~ dbern (Y[i] * p[i,j])
logit (p[i,j]) <- a0 + a1* marca[i] + a2* arbu[i] + a3* dia[i,j]
}
}
Preparamos nuestros datos para dárselos a Nimble
my.data <- list (hdet = datos[,3 : 9 ])
my.constants <- list (elev = datos$ elev,
arbu = datos$ arbu,
marca = as.numeric (datos$ marca == "A" ),
dia = datos[,10 : 16 ],
nsitios = 100 ,
nocasiones = 7 )
my.data$ hdet
o1 o2 o3 o4 o5 o6 o7
1 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0
3 0 0 0 1 0 0 0
4 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0
6 0 0 0 0 0 0 0
7 0 0 0 1 0 0 0
8 0 0 0 0 0 0 0
9 1 1 0 0 1 0 0
10 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0
14 0 0 0 0 0 0 0
15 0 0 0 0 0 0 0
16 0 0 0 0 0 0 0
17 0 0 0 0 0 0 0
18 0 0 1 0 0 0 0
19 0 0 0 0 0 0 0
20 0 0 0 0 0 0 0
21 0 0 0 0 0 0 0
22 0 0 0 0 0 0 0
23 0 0 0 0 0 0 0
24 0 0 0 0 0 0 0
25 0 0 0 0 0 0 0
26 0 0 0 0 0 0 0
27 1 0 0 0 0 0 1
28 0 1 1 1 1 1 0
29 0 0 0 0 0 0 0
30 0 0 0 0 0 0 0
31 0 0 0 0 0 0 0
32 0 0 0 0 0 0 0
33 1 1 1 0 1 0 0
34 0 0 0 0 0 0 0
35 0 0 0 0 0 0 0
36 0 0 0 1 0 0 0
37 0 0 0 0 0 0 0
38 1 1 1 0 1 1 0
39 0 1 0 0 0 0 0
40 1 1 0 0 0 1 0
41 0 0 0 1 0 0 0
42 0 0 0 0 0 0 0
43 0 0 0 0 0 0 0
44 0 0 0 0 0 0 0
45 1 1 0 0 0 0 0
46 0 0 0 0 0 0 0
47 1 0 0 0 0 0 0
48 0 0 0 0 0 0 0
49 0 0 0 0 0 0 0
50 1 0 0 0 0 0 0
51 0 0 0 0 0 0 0
52 0 0 0 0 0 0 0
53 0 0 0 0 0 0 0
54 0 0 0 0 0 0 0
55 1 0 0 0 0 0 0
56 0 0 0 0 0 0 0
57 0 0 0 0 0 0 0
58 1 0 1 1 0 1 0
59 0 0 0 0 0 0 0
60 0 0 0 0 0 0 0
61 0 0 0 0 0 0 0
62 0 1 1 0 0 0 0
63 0 0 0 0 0 0 0
64 0 0 0 0 0 0 0
65 0 0 0 0 0 0 0
66 0 0 0 0 0 0 0
67 0 0 0 0 0 0 0
68 0 0 0 0 0 0 0
69 0 0 0 1 0 0 0
70 0 0 0 0 0 0 0
71 0 0 0 0 0 0 0
72 1 1 1 0 0 0 0
73 1 0 0 0 0 0 1
74 1 0 0 0 0 0 0
75 0 0 1 1 0 1 0
76 0 0 1 0 1 0 0
77 1 1 1 0 0 0 0
78 0 0 0 0 0 0 0
79 0 0 0 0 0 0 0
80 1 1 1 1 0 0 0
81 0 0 0 0 0 0 0
82 0 0 0 0 0 0 0
83 1 0 0 0 0 0 0
84 1 0 0 1 0 0 0
85 1 0 1 0 1 0 0
86 1 1 1 0 0 1 0
87 1 0 1 0 0 0 0
88 0 0 0 0 0 0 0
89 0 0 0 0 0 0 0
90 0 0 0 0 0 0 0
91 1 1 0 0 0 0 0
92 0 0 0 0 0 0 0
93 0 0 0 0 0 0 0
94 0 0 0 0 0 0 0
95 0 0 0 0 0 0 0
96 1 0 0 0 0 0 0
97 0 0 0 0 0 0 0
98 0 0 0 0 0 0 0
99 0 0 0 0 0 0 0
100 0 0 0 0 0 0 0
Preparamos nuestros datos para dárselos a Nimble
my.data <- list (hdet = datos[,3 : 9 ])
my.constants <- list (elev = datos$ elev,
arbu = datos$ arbu,
marca = as.numeric (datos$ marca == "A" ),
dia = datos[,10 : 16 ],
nsitios = 100 ,
nocasiones = 7 )
my.constants$ elev
[1] 0.552621041 0.376779807 0.035754384 -0.800823606 0.296851974
[6] 0.355465718 -2.340766531 -1.253747996 -0.614325328 -0.086801627
[11] -0.795495084 -0.491769317 1.277300064 -1.498860019 -0.198700594
[16] -0.177386505 0.675177052 0.499335818 0.408750940 -1.045935629
[21] 0.536635474 0.307509018 0.701819663 -0.843451784 1.303942675
[26] -0.406512961 0.851018286 0.216924140 1.085473264 1.506426520
[31] -0.832794740 0.163638918 0.190281529 -1.003307451 0.302180496
[36] -1.408275141 1.074816219 -1.184477207 -1.973098497 -1.530831152
[41] -1.909156230 1.810152287 -0.353227739 -0.204029116 0.307509018
[46] -0.630310895 -0.294613994 1.170729620 1.224014842 0.291523451
[51] 0.270209362 1.549054698 0.440722074 0.541963996 -0.704910206
[56] 0.680505574 -0.001545271 -1.552145241 -0.635639417 0.973574297
[61] 0.856346808 -1.759957608 0.430065029 0.270209362 0.856346808
[66] 0.270209362 1.335913809 0.536635474 -0.891408484 -1.706672386
[71] 0.648534441 0.264880840 0.270209362 -0.822137695 0.057068473
[76] -0.912722573 -1.131191985 0.685834096 0.334151629 -0.880751440
[81] 1.751538543 -0.465126706 -0.225343205 -0.603668284 -1.530831152
[86] -1.184477207 1.186715186 0.824375674 0.653862963 0.925617597
[91] -0.422498528 -0.593011239 -1.392289574 1.266643020 1.309271198
[96] 1.682267754 1.085473264 0.462036163 -2.378066187 1.730224454
Preparamos nuestros datos para dárselos a Nimble
my.data <- list (hdet = datos[,3 : 9 ])
my.constants <- list (elev = datos$ elev,
arbu = datos$ arbu,
marca = as.numeric (datos$ marca == "A" ),
dia = datos[,10 : 16 ],
nsitios = 100 ,
nocasiones = 7 )
my.constants$ arbu
[1] 1.422993573 -0.494213483 0.783924555 0.968544385 0.357878542
[6] -1.573529831 0.684513710 2.488109146 -0.337996287 -0.366399462
[11] -0.238585984 -1.928568175 0.684513710 -0.465810307 -0.835049968
[16] 0.670312393 1.593412087 1.110559722 0.499893880 0.201661888
[21] -0.636228820 2.260883739 0.897536716 -1.829157330 -0.068167470
[26] -1.104879326 0.712916886 -1.885963682 0.400483035 -0.962863988
[31] -1.261095980 1.991054923 -1.332103649 -0.551019293 0.826529048
[36] 0.783924555 -0.480011624 1.366187763 0.301072732 -1.743948344
[41] 0.940141751 -0.337996287 -0.536817976 -0.636228820 1.948450430
[46] -2.169994357 -0.281190477 -0.579422469 1.593412087 0.386281718
[51] 0.045444691 -0.238585984 0.783924555 0.059646550 0.585103407
[56] 1.124761581 0.059646550 -0.096570646 -0.153376456 -0.011361119
[61] 1.011149420 -0.465810307 0.613506041 0.045444691 -0.096570646
[66] 0.329475366 0.002840198 -1.601933007 -0.337996287 -0.380601321
[71] 0.783924555 -0.366399462 -1.218491487 -0.451608990 0.073847867
[76] -0.124973280 -0.437407131 -0.238585984 0.783924555 -1.332103649
[81] 0.272669556 -1.914366858 0.272669556 -1.289499156 -1.857560506
[86] -0.252787301 -0.195980949 -0.252787301 -1.005468481 -0.011361119
[91] 0.570901548 1.309381412 0.073847867 0.343677225 1.153164757
[96] 0.386281718 1.877442762 -1.772351520 -0.011361119 0.315274049
Preparamos nuestros datos para dárselos a Nimble
my.data <- list (hdet = datos[,3 : 9 ])
my.constants <- list (elev = datos$ elev,
arbu = datos$ arbu,
marca = as.numeric (datos$ marca == "A" ),
dia = datos[,10 : 16 ],
nsitios = 100 ,
nocasiones = 7 )
my.constants$ marca
[1] 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 1 0 0
[38] 0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 1
[75] 0 1 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1
Preparamos nuestros datos para dárselos a Nimble
my.data <- list (hdet = datos[,3 : 9 ])
my.constants <- list (elev = datos$ elev,
arbu = datos$ arbu,
marca = as.numeric (datos$ marca == "A" ),
dia = datos[,10 : 16 ],
nsitios = 100 ,
nocasiones = 7 )
my.constants$ dia
dia1 dia2 dia3 dia4 dia5 dia6 dia7
1 1 2 3 4 5 6 7
2 1 2 3 4 5 6 7
3 1 2 3 4 5 6 7
4 1 2 3 4 5 6 7
5 1 2 3 4 5 6 7
6 1 2 3 4 5 6 7
7 1 2 3 4 5 6 7
8 1 2 3 4 5 6 7
9 1 2 3 4 5 6 7
10 1 2 3 4 5 6 7
11 1 2 3 4 5 6 7
12 1 2 3 4 5 6 7
13 1 2 3 4 5 6 7
14 1 2 3 4 5 6 7
15 1 2 3 4 5 6 7
16 1 2 3 4 5 6 7
17 1 2 3 4 5 6 7
18 1 2 3 4 5 6 7
19 1 2 3 4 5 6 7
20 1 2 3 4 5 6 7
21 1 2 3 4 5 6 7
22 1 2 3 4 5 6 7
23 1 2 3 4 5 6 7
24 1 2 3 4 5 6 7
25 1 2 3 4 5 6 7
26 1 2 3 4 5 6 7
27 1 2 3 4 5 6 7
28 1 2 3 4 5 6 7
29 1 2 3 4 5 6 7
30 1 2 3 4 5 6 7
31 1 2 3 4 5 6 7
32 1 2 3 4 5 6 7
33 1 2 3 4 5 6 7
34 1 2 3 4 5 6 7
35 1 2 3 4 5 6 7
36 1 2 3 4 5 6 7
37 1 2 3 4 5 6 7
38 1 2 3 4 5 6 7
39 1 2 3 4 5 6 7
40 1 2 3 4 5 6 7
41 1 2 3 4 5 6 7
42 1 2 3 4 5 6 7
43 1 2 3 4 5 6 7
44 1 2 3 4 5 6 7
45 1 2 3 4 5 6 7
46 1 2 3 4 5 6 7
47 1 2 3 4 5 6 7
48 1 2 3 4 5 6 7
49 1 2 3 4 5 6 7
50 1 2 3 4 5 6 7
51 1 2 3 4 5 6 7
52 1 2 3 4 5 6 7
53 1 2 3 4 5 6 7
54 1 2 3 4 5 6 7
55 1 2 3 4 5 6 7
56 1 2 3 4 5 6 7
57 1 2 3 4 5 6 7
58 1 2 3 4 5 6 7
59 1 2 3 4 5 6 7
60 1 2 3 4 5 6 7
61 1 2 3 4 5 6 7
62 1 2 3 4 5 6 7
63 1 2 3 4 5 6 7
64 1 2 3 4 5 6 7
65 1 2 3 4 5 6 7
66 1 2 3 4 5 6 7
67 1 2 3 4 5 6 7
68 1 2 3 4 5 6 7
69 1 2 3 4 5 6 7
70 1 2 3 4 5 6 7
71 1 2 3 4 5 6 7
72 1 2 3 4 5 6 7
73 1 2 3 4 5 6 7
74 1 2 3 4 5 6 7
75 1 2 3 4 5 6 7
76 1 2 3 4 5 6 7
77 1 2 3 4 5 6 7
78 1 2 3 4 5 6 7
79 1 2 3 4 5 6 7
80 1 2 3 4 5 6 7
81 1 2 3 4 5 6 7
82 1 2 3 4 5 6 7
83 1 2 3 4 5 6 7
84 1 2 3 4 5 6 7
85 1 2 3 4 5 6 7
86 1 2 3 4 5 6 7
87 1 2 3 4 5 6 7
88 1 2 3 4 5 6 7
89 1 2 3 4 5 6 7
90 1 2 3 4 5 6 7
91 1 2 3 4 5 6 7
92 1 2 3 4 5 6 7
93 1 2 3 4 5 6 7
94 1 2 3 4 5 6 7
95 1 2 3 4 5 6 7
96 1 2 3 4 5 6 7
97 1 2 3 4 5 6 7
98 1 2 3 4 5 6 7
99 1 2 3 4 5 6 7
100 1 2 3 4 5 6 7
Escribimos el modelo
occu.mod <- nimbleCode ({
# Priors
b0 ~ dnorm (mean = 0 , sd = 1 )
b1 ~ dnorm (mean = 0 , sd = 1 )
b2 ~ dnorm (mean = 0 , sd = 1 )
a0 ~ dnorm (mean = 0 , sd = 1 )
a1 ~ dnorm (mean = 0 , sd = 1 )
a2 ~ dnorm (mean = 0 , sd = 1 )
a3 ~ dnorm (mean = 0 , sd = 1 )
# Likelihood
for (i in 1 : nsitios) {
Y[i] ~ dbern (psi[i]) # True occupancy status
logit (psi[i]) <- b0 + b1* elev[i] + b2* arbu[i]
for (j in 1 : nocasiones) {
hdet[i,j] ~ dbern (Y[i] * p[i,j]) # Observed data
logit (p[i,j]) <- a0 + a1* marca[i] + a2* arbu[i] + a3* dia[i,j]
}
}
})
Definimos el resto de elementos que nos faltan
initial.values <- list (b0 = rnorm (1 ,0 ,1 ),
b1 = rnorm (1 , 0 , 1 ),
b2 = rnorm (1 , 0 , 1 ),
a0 = rnorm (1 ,0 ,1 ),
a1 = rnorm (1 ,0 ,1 ),
a2 = rnorm (1 ,0 ,1 ),
a3 = rnorm (1 ,0 ,1 ),
Y = as.numeric (rowSums (my.data$ hdet) > 0 ))
parameters.to.save <- c ("b0" , "b1" , "b2" , "a0" , "a1" , "a2" , "a3" )
n.iter <- 3000
n.burnin <- 200
n.chains <- 3
n.thin <- 1
Corremos nuestro MCMC
mcmc.output <- nimbleMCMC (code = occu.mod,
data = my.data,
constants = my.constants,
inits = initial.values,
monitors = parameters.to.save,
thin = n.thin,
niter = n.iter,
nburnin = n.burnin,
nchains = n.chains)
|-------------|-------------|-------------|-------------|
|-------------------------------------------------------|
|-------------|-------------|-------------|-------------|
|-------------------------------------------------------|
|-------------|-------------|-------------|-------------|
|-------------------------------------------------------|
Inspeccionamos los traceplots
MCMCtrace (mcmc.output, pdf = F, params = c ("a0" , "a1" , "a2" , "a3" ))
Inspeccionamos los traceplots
MCMCtrace (mcmc.output, pdf = F, params = c ("b0" , "b1" , "b2" ))
Inspeccionamos el resumen del modelo
MCMCsummary (mcmc.output, round = 2 )
mean sd 2.5% 50% 97.5% Rhat n.eff
a0 0.70 0.35 0.02 0.70 1.38 1.01 238
a1 -0.65 0.35 -1.34 -0.64 0.01 1.01 854
a2 -0.63 0.18 -0.98 -0.63 -0.25 1.01 1138
a3 -0.44 0.08 -0.62 -0.44 -0.29 1.01 269
b0 -0.40 0.30 -0.96 -0.41 0.22 1.00 882
b1 -1.03 0.32 -1.73 -1.01 -0.46 1.00 1028
b2 0.31 0.30 -0.23 0.30 0.95 1.01 827
\[~\]
# Likelihood
for (i in 1 : nsitios) {
Y[i] ~ dbern (psi[i])
logit (psi[i]) <- b0 + b1* elev[i] + b2* arbu[i]
for (j in 1 : nocasiones) {
hdet[i,j] ~ dbern (Y[i] * p[i,j])
logit (p[i,j]) <- a0 + a1* marca[i] + a2* arbu[i] + a3* dia[i,j]
}
}
Una vez hemos inspeccionado los traceplots y nos hemos asegurado que las cadenas convergen, podemos juntarlas y empezar a hacer predicciones.
mcmc.bind <- rbind (mcmc.output$ chain1, mcmc.output$ chain2, mcmc.output$ chain3)
\[~\] Vamos a hacer la predicción de la detectabilidad en función de los días que lleve instalada la cámara. Para ello fijaremos el resto de variables a su media (porcentaje de arbustos = 0; cámara marca B).
pred.dia <- seq (from = 1 , to = 7 , by = 1 )
pred.p <- matrix (NA , nrow = nrow (mcmc.bind), ncol = length (pred.dia))
for (i in 1 : nrow (pred.p)){
pred.p[i,] <- plogis (mcmc.bind[i,"a0" ] +
mcmc.bind[i,"a1" ] * 0 +
mcmc.bind[i,"a2" ] * pred.dia +
mcmc.bind[i,"a3" ] * 0 )
}
mean.p <- apply (pred.p, 2 , mean) # extract mean
sd.p <- apply (pred.p, 2 , sd) # extract sd
ci <- apply (pred.p, 2 , quantile, c (0.1 , 0.9 )) # 80% CI
pred.p.results <- tibble (dia = pred.dia,
mean = mean.p,
sd = sd.p,
cinf = ci[1 ,],
csup = ci[2 ,])
plot (pred.p.results$ dia, pred.p.results$ mean, type = "l" , lwd = 3 , col = "darkred" ,
xlab = "Días desde que se instaló la cámara" , ylab = "Probabilidad de detección" )
lines (pred.p.results$ dia, pred.p.results$ cinf, lty = 2 , col = "darkblue" )
lines (pred.p.results$ dia, pred.p.results$ csup, lty = 2 , col = "darkblue" )
Predicciones sobre el mapa
Tenemos que tener en cuenta que hemos estandarizado nuestras variables (media 0 sd 1) para correr estos modelos. Por lo tanto, antes de realizar las predicciones sobre el mapa debemos estandarizar también nuestros rásters de la misma forma que lo hicimos con nuestros datosanteriormente
elevS <- (elev - 958.29 ) / 187.6693
arbuS <- (arbu - 49.78 ) / 7.041493
Predicciones sobre el mapa
Vamos a hacer una predicción sólo sobre la media (no propagaremos la incertidumbre!). Para ello utilizaremos las medias de las distribuciones a posteriori obtenidas con MCMCsummary
. Recordad que hay que hacer la inversa de logit
!
prediccion <- exp (- 0.41 - 1.01 * elevS + 0.29 * arbuS)/ (1 + exp (- 0.41 - 1.01 * elevS + 0.29 * arbuS))
par (mfrow = c (1 ,3 ))
plot (elev, main = "Elevacion" )
plot (arbu, main = "Arbusto" )
plot (prediccion, main = "Probabilidad de ocupación media predicha" )