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Model Selection and Multi-Model Inference
X Lake.ID Name treatment shorline sizehectars elevation UTM.zone northing easting BUBO.breeding BUBO.breeding2 PSRE.breeding.Y.N RACA.y.n veg.extent X..of.transects.with.veg bank.slope silt.0.1. silt.total X10cm.area vegetated.area RACA.1K lakes.1k dist.ave ls raca.basin fish.basin lakes.basin co.lakes.basin ls2 woody herbacious unveg total woodyprop herbprop unvegprop logveg archerb arcsilt
1 1 531 Mill Creek 0 377.96 0.713 2008.9368 10 518882 4565085 y 1 n y 0.691 0.682 0.308095216 0.6818 0.71212 111.5 261.17 3 4 0.5538 0.75 3 0 3 0 1 6082255.229 54367.17182 1399749.194 7536371.595 0.807053521 0.007213972 0.185732508 2.41692328905509 0.0850375574910141 1.00445938904933
2 2 533 East Boulder 1 1356.4 11.4 2034.8448 10 518069 4564441 y 1 y y 2.28 0.292 0.092475736 0.376 0.3472 980.56 3092.59 5 10 0.8268 0.5 4 4 8 2 0.5 5699686.549 1302747.189 1470012.242 8472445.979 0.67273212 0.15376282 0.173505059 3.49032234724526 0.402941577234993 0.630113907491124
3 3 534 Mosquito 1 555.65 2.221 2017 10 520565 4564620 y 1 y y 0.425 0.292 0.067204288 0.375 0.6806 289.4 236.15 0 2 0.52 0 0 0 1 0 0 5048929.965 89795.82505 188674.0617 5327399.852 0.947728743 0.016855469 0.035415788 2.37318794991272 0.13019612877964 0.970175389664562
4 4 537 Upper Boulder 1 530.48 2.009 1927 10 518185 4563757 y 1 y y 1.17 0.875 0.068711911 0.875 0.9306 244.02 620.66 4 9 0.8312 0.444444444 4 4 8 2 0.5 5699686.549 1302747.189 1470012.242 8472445.979 0.67273212 0.15376282 0.173505059 2.7928537570834 0.402941577234993 1.30421113262519
5 5 539 Big Marshy 1 667.29 2.813 1911 10 519781 4563423 y 1 y y 0.517 0.826 0.331579018 0.83333 0.5278 153.48 344.99 2 4 0.563 0.5 3 1 4 1 0.75 4163162.351 365814.0766 381401.5985 4910378.026 0.847829297 0.07449815 0.077672553 2.53780650664498 0.276451377067193 0.81321250666084
6 6 543 Little Marshy 1 339.29 0.661 1875 10 518185 4563757 y 1 y y 0.27 0.875 0.233320289 1 1 61.07 91.61 3 4 0.5114 0.75 3 1 4 1 0.75 5699686.549 1302747.189 1470012.242 8472445.979 0.67273212 0.15376282 0.173505059 1.96194288314139 0.402941577234993 1.5707963267949
7 7 544 Middle Boulder 1 604.369 2.493 1984.8576 10 516709 4562826 y 1 n y 2.48 0.636 0.08493805 0.6364 0.81818 197.79 1498.84 3 7 0.9013 0.428571429 1 2 5 0 0.2 9431012.702 1523636.031 939040.9555 11893689.69 0.792942556 0.128104572 0.078952872 3.17575527472565 0.366036145019016 1.13028330677218
8 8 553 Fox Creek 1 661.25 2.791 2003 10 512651 4562132 n 0 y y 2.16 0.542 0.091902485 0.8333 0.90278 304.17 1428.3 3 4 0.7386 0.75 0 0 0 0 0 4236206.422 67803.93366 165571.6861 4469582.042 0.947785807 0.015170084 0.037044109 3.15481943619417 0.123480448832674 1.25370815685985
9 9 554 Telephone 1 534.796 1.493 2098.8528 10 516391 4562228 y 1 y y 0.292 0.291 0.254833499 0.3333 0.29167 178.27 156.16 4 5 0.4198 0.8 2 1 4 0 0.5 9431012.702 1523636.031 939040.9555 11893689.69 0.792942556 0.128104572 0.078952872 2.19356980032262 0.366036145019016 0.57051411453301
10 10 555 Mavis 0 502.95 1.721 2048 10 513531 4562062 n 0 y y 1.8 0.565 0.153416601 0.4782 0.6956 186.09 905.31 2 2 0.6144 1 1 0 1 0 1 4236206.422 67803.93366 165571.6861 4469582.042 0.947785807 0.015170084 0.037044109 2.95679731758781 0.123480448832674 0.986365736642058
11 11 556 West Boulder 0 552.5 2.053 2122.3224 10 515248 4562118 y 1 y n 0.2 0.25 0.398011014 0.1667 0.1691 138.12 110.5 2 2 0.5504 1 3 1 4 1 0.75 9431012.702 1523636.031 939040.9555 11893689.69 0.792942556 0.128104572 0.078952872 2.04336227802113 0.366036145019016 0.42378953989023
12 12 561 Virginia 1 453.892 1.43 2008.0224 10 511931 4561555 n 0 n y 1.2 0.708 0.136797022 0.9167 0.8472 151.3 544.67 0 1 0.4821 0 0 0 0 0 0 4236206.422 67803.93366 165571.6861 4469582.042 0.947785807 0.015170084 0.037044109 2.73613345532957 0.123480448832674 1.16919104136446
13 13 563 Tangle Blue 0 870.27 4.534 1751 10 521440 4561693 y 1 y y 2.08 0.833 0.218926013 0.9583 0.8889 311.56 1810.16 0 0 0.5399 0 0 0 0 0 0 3753234.847 44885.39707 75559.57374 3873679.818 0.968906834 0.011587276 0.01950589 3.25771696384489 0.107853185609941 1.23097709539702
14 14 573 Twin 1 1 261.673 0.415 1967.1792 10 501982 4560450 y 1 y y 4.43 0.857 0.043439116 1 1 314.01 1159.21 1 5 0.44 0.2 1 0 4 0 0.25 9712469.841 360952.0095 248307.4167 10321729.27 0.940973125 0.03497011 0.024056765 3.0641621189487 0.188110404256456 1.5707963267949
15 15 574 Fish 1 525.934 1.558 1821.18 10 503200 4560208 y 1 n y 6.36 1 0.07240347 1 1 306.79 3344.94 1 2 1.0843 0.5 0 0 1 0 0 9712469.841 360952.0095 248307.4167 10321729.27 0.940973125 0.03497011 0.024056765 3.52438833199843 0.188110404256456 1.5707963267949
16 16 576 Long Gulch 0 1021.974 7.362 1952.5488 10 506779 4560018 y 1 n n 0.9125 0.667 0.293120249 0.583 0.513 374.72 932.55 0 0 0.1676 0 0 0 0 0 0 5716789.474 233236.0196 110030.7652 6060056.259 0.943355842 0.038487435 0.018156723 2.96967212642384 0.197462879973287 0.798399628509846
17 17 588 Trail Gulch 0 983.875 6.777 1961.6928 10 505299 4558959 y 1 n n 0.45 0.4583 0.316543667 0.54166 0.4167 323.86 442.74 0 0 0.6774 0 0 0 0 0 0 8347010.724 404047.8247 242744.5556 8993803.104 0.928084663 0.044925136 0.026990201 2.64614876072859 0.213575495220347 0.701707929764643
18 18 593 Granite 0 594.77 2.297 1964.7408 10 515026 4558535 n 0 n n 0 0 0.347121369 0.79167 0.875 131.35 0 0 0 0.5445 0 0 0 0 0 0 18498420.42 271590.7421 23218.44076 18793229.6 0.984313011 0.01445152 0.001235468 0 0.12050592131947 1.20942920288819
19 19 601 Doe 0 543.717 1.672 2131.1616 10 516656 4557435 y 1 n n 0 0 0.286799343 0.7917 0.69444 92.88 0 0 0 0.5531 0 0 0 0 0 0 3190128.038 381502.0769 47387.58457 3619017.7 0.881490035 0.105415919 0.013094046 0 0.330671452276355 0.985105959166056
20 20 609 Rush Creek 1 453.08 1.311 2013 10 503126 4555571 y 1 y y 1.45 0.9583 0.13807655 1 0.97222 244.67 656.97 0 0 0 0 0 0 0 0 0 7946383.765 302516.9945 33472.87659 8282373.636 0.959433142 0.036525398 0.004041459 2.81754553830875 0.192299171321275 1.40334148647253
21 21 611 Stoddard 0 1349.484 12.69 1777.5936 10 520514 4555666 n 0 y y 0.492 0.7917 0.21156318 0.333 0.5278 635.38 663.95 2 6 0.2882 0.333333333 2 1 6 1 0.333333333 19632617.35 67978.76418 564830.9595 20265427.07 0.968773926 0.003354421 0.027871653 2.82213537523894 0.0579497923899455 0.81321250666084
22 22 612 McDonald 1 714.23 2.77 1797 10 520526 4555169 n 0 y y 2.54 0.8333 0.165445662 0.875 0.8611 521.39 1814.15 1 6 0.1235 0.166666667 1 1 6 0 0.166666667 19632617.35 67978.76418 564830.9595 20265427.07 0.968773926 0.003354421 0.027871653 3.25867319313149 0.0579497923899455 1.18888701447886
23 23 666 Sugar Pine 0 638.939 2.474 2005.2792 10 512280 4545701 n 0 n n 0.192 0.0833 0.337661923 0.4583 0.5139 141.1 122.68 1 2 0.1666 0.5 1 0 2 0 0.5 7555078.376 113440.309 52741.99409 7721260.679 0.97847731 0.014691941 0.006830749 2.08877376731045 0.121509099295068 0.799299954433068
24 24 681 Boulder Lake, Big 1 654.43 2.642 1850 10 516147 4544203 y 1 y y 0.895 0.571 0.094854622 0.857 0.9206 164.92 585.72 3 7 0.5311 0.428571429 0 1 2 0 0 8350347.637 0 152571.0462 8502918.683 0.982056626 0 0.017943374 2.76769005370415 NA 1.28514748977933
25 25 682 Conway 1 217.701 0.283 2078.736 10 512971 4543896 n 0 n y 1.426 0.842 0.105423578 0.8421 0.8596 137.59 310.44 1 16 0.0902 0.0625 1 0 5 0 0.2 2076327.642 7606.052788 846148.431 2930082.125 0.708624384 0.00259585 0.288779766 2.49197767476417 0.050971553445267 1.18672327659261
26 26 683 Foster 0 680.13 2.662 2208.276 10 512130 4543849 n 0 n y 0 0 0.183714243 0.125 0.4028 246.55 0 1 13 0.1753 0.076923077 2 0 8 0 0.25 2076327.642 7606.052788 846148.431 2930082.125 0.708624384 0.00259585 0.288779766 0 0.050971553445267 0.687575291481972
27 27 684 Lion 0 471.651 1.544 2132.3808 10 512738 4543894 n 0 n y 0.129 0.5417 0.527896107 0.625 0.444 68.78 60.84 2 18 0.1694 0.111111111 0 0 0 0 0 2076327.642 7606.052788 846148.431 2930082.125 0.708624384 0.00259585 0.288779766 1.78418920538096 0.050971553445267 0.729280420208908
28 28 686 Little Boulder 0 531.091 1.897 1925.7264 10 517098 4543954 n 0 n n 1.181 0.857 0.362842014 0.619 0.571 116.33 627.22 1 3 0.4532 0.333333333 0 0 0 0 0 8350347.637 0 152571.0462 8502918.683 0.982056626 0 0.017943374 2.79741989813167 NA 0.856638962154039
29 29 688 Union 1 666.691 1.49 1837.3344 10 509757 4543557 n 0 y y 0.654 0.583 0.05 0.7083 0.8056 500 436.02 2 4 1.091 0.5 1 0 2 0 0.5 4919748.419 212619.5512 807694.3279 5940062.299 0.828231788 0.035794162 0.13597405 2.6395064105769 0.190340698379716 1.11418609301515
30 30 700 Lilypad 0 349.108 0.846 1915.3632 10 516110 4541932 y 1 n n 1.65 0.789 0.076035504 1 1 246.21 576.03 1 6 0.25 0.166666667 1 0 6 0 0.166666667 5727944.441 54893.59787 565948.948 6348786.987 0.90221084 0.008646313 0.089142847 2.76044510233845 0.0931200737336209 1.5707963267949
31 31 722 Salmon 1 490.09 0.658 2179 10 506610 4538422 y 1 y y 1.29 0.895 0.265192487 0.9474 0.8567 284.25 632.21 1 11 0.1394 0.090909091 1 0 7 0 0.142857143 6906710.501 45810.99035 2443042.424 9395563.915 0.735103349 0.004875811 0.26002084 2.80086136102345 0.0698838764161109 1.1825672632676
32 32 727 Twin 2 0 238.123 0.319 1549.908 10 515239 4538020 n 0 y y 0.281 0.25 0.080434362 1 1 17.86 66.91 1 4 0.34 0.25 1 0 1 0 1 5531792.832 39381.26629 35177.95804 5606352.056 0.986700938 0.007024401 0.006274661 1.82549102987943 0.0839101322872417 1.5707963267949
33 33 732 El 1 1071.03 2.259 1990 10 498828 4536778 y 1 y y 0.22 0.2 0.141795358 0.9 0.867 524.8 235.63 0 4 0.2779 0 2 2 4 0 0.5 5415736.971 61073.43835 20011021.59 25487832 0.212483234 0.00239618 0.785120586 2.37223058325011 0.0489703618786081 1.19749470193976
34 34 760 Luella 0 357 0.942 2110.1304 10 508239 4533457 y 1 y y 0.025 0.0833 0.480850091 0.5417 0.36111 23.8 8.92 2 7 0.16 0.285714286 0 0 1 0 0 2679851.035 667032.256 2904220.614 6251103.905 0.428700446 0.106706314 0.46459324 0.950364854376123 0.332766831063272 0.644656970151775
35 35 765 Forbidden 1 0 453.246 0.773 1869.948 10 496236 4532552 n 0 y n 2.38 0.6 0.162730513 0.6 0.63333 292.34 1078.73 6 10 0.5672 0.6 6 3 10 1 0.6 4633981.257 0 10146766.69 14780747.95 0.313514666 0 0.686485334 3.032912756839 NA 0.92036110274514
36 36 767 Forbidden 2 0 272.539 0.355 1875.1296 10 496065 4532439 n 0 n y 0.141 0.3182 0.529263988 0.4545 0.363636 50.79 38.43 4 7 0.54 0.571428571 6 3 10 1 0.6 4633981.257 0 10146766.69 14780747.95 0.313514666 0 0.686485334 1.58467038446435 NA 0.647284470051139
37 37 770 Deer 0 440.21 1.314 2176 10 508977 4532528 y 1 n n 0.48 0.625 0.369188018 0.875 0.75 127.66 211.3 1 4 0.3665 0.25 0 0 0 0 0 2679851.035 667032.256 2904220.614 6251103.905 0.428700446 0.106706314 0.46459324 2.32489949705231 0.332766831063272 1.0471975511966
38 38 771 Diamond 0 372.57 0.949 2200 10 507990 4532496 n 0 n n 0.7 0.217 0.546235472 0.8696 0.8116 7.45 260.8 1 6 0.33 0.166666667 1 1 3 0 0.333333333 4235026.041 0 2696724.247 6931750.288 0.61096056 0 0.38903944 2.41630758705988 NA 1.12181206841725
39 39 773 Summit 0 738.19 3.636 2300.0208 10 508669 4531974 n 0 n n 0 0 0.379639963 0 0 147.64 0 2 4 0.428 0.5 0 0 0 0 0 4235026.041 0 2696724.247 6931750.288 0.61096056 0 0.38903944 0 NA NA
40 40 26177 South Fork 1 0 529.882 1.823 2041.5504 10 508345 4561374 n 0 n n 0.191 0.45833 0.167922684 0.4583 0.5556 317.93 101.21 0 4 0 0 0 1 2 0 0 7868924.145 372358.9597 334835.4841 8576118.589 0.917539102 0.043418122 0.039042777 2.00522342485814 0.209908241391098 0.841113392151149
41 41 26184 U Boulder Pond 1 0 243.28 0.441 2072.64 10 518345 4563869 n 0 n y 0.742 0.917 0.250498382 0.9167 0.8889 107.45 180.51 5 10 0.5 0.5 5 4 8 3 0.625 5699686.549 1302747.189 1470012.242 8472445.979 0.67273212 0.15376282 0.173505059 2.25650126621132 0.402941577234993 1.23097709539702
42 42 26187 M Boulder Pond 1 0 234.927 0.375 2133.6 10 517432 4562568 n 0 n y 0.575 1 0.302735107 1 0.8056 35.24 135.08 2 5 0.482 0.4 2 2 5 1 0.4 9431012.702 1523636.031 939040.9555 11893689.69 0.792942556 0.128104572 0.078952872 2.13059105196337 0.366036145019016 1.11418609301515
destinatio wild fish hike escape photo climb friends relax other size lake stocked management ID amps fishyn cows herp.rich fish.rich rich visitors logsize
1 Adams 1 0 3 1 2 1 1 2 1 NA y n Amps 624 BUBO, HYRE, RACA, THSP n n 4 0 4 4 NA
2 alpine 6 4 11 7 7 2 5 9 4 5.23 y n Amps 768 RACA, THSP y n 1 1 2 12 0.718501688867274
3 anna 6 3 13 10 6 1 7 9 2 1.573 y n NA 781 HYRE y n 0 1 1 13 0.196728722623287
4 B_marshy 4 4 4 3 2 0 4 4 0 2.813 y n Stocked Lake 539 BUBO, HYRE, RACA, THSP y n 4 1 5 4 0.449169732165201
5 BBD 1 0 2 1 1 0 0 1 1 NA y n Amps 26065 AMMA, HYRE, RACA n n 2 0 2 2 NA
6 bear basin 7 4 17 12 5 1 11 8 10 NA n n NA NA NA NA NA 0 0 0 19 NA
7 bear_wallow 1 0 1 1 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
8 bee_tree 0 0 3 3 2 0 3 1 3 NA n n NA NA NA NA NA 0 0 0 3 NA
9 big flat 0 0 2 2 0 0 0 0 0 NA n n NA NA NA NA NA 0 0 0 2 NA
10 bingham 1 0 1 1 1 0 1 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
11 black_basin 0 0 1 1 0 0 1 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
12 boulder 23 21 41 30 20 4 33 23 8 2.642 y n Stocked Lake 681 BUBO, HYRE, RACA, THSP y n 4 2 6 42 0.421932813278508
13 boulder cr 7 5 15 13 8 0 9 13 3 0.451 y n Amps 762 HYRE, RACA, THSP y n 3 1 4 16 -0.345823458122039
14 bowerman mdw 11 0 21 15 11 1 14 13 8 NA n n NA NA NA NA NA 0 0 0 21 NA
15 browns mdw 1 0 1 0 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
16 bullards basin 0 0 0 0 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
17 caribou 34 10 67 52 33 12 39 37 17 30.515 y n NA 702 BUBO, RACA y n 1 2 3 72 1.48451337429261
18 caribou mt 1 0 1 1 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 2 NA
19 CC 7 2 11 5 5 1 4 7 1 NA n y NA NA NA NA NA 0 0 0 12 NA
20 CC falls 0 1 6 3 2 0 3 4 0 NA n y NA NA NA NA NA 0 0 0 6 NA
21 CCL 30 14 49 43 21 2 33 35 11 6.702 y y Stocked Lake 742 THSP y n 1 3 4 51 0.826204423499253
22 CCM 1 1 4 4 4 0 3 3 0 NA n y NA NA NA NA NA 0 0 0 4 NA
23 ceasar pk 0 0 1 1 1 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
24 ceaser pk 1 0 1 1 1 1 1 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
25 cherry flat 2 1 2 1 0 0 2 1 1 NA n n NA NA NA NA NA 0 0 0 3 NA
26 china_garden 1 1 1 0 1 0 0 1 0 NA n n NA NA NA NA NA 0 0 0 1 NA
27 cold springs 2 0 2 2 2 0 2 2 2 NA n n NA NA NA NA NA 0 0 0 2 NA
28 conway 1 0 1 1 0 1 1 1 1 NA y n Amps 682 BUBO, HYRE, RACA, THSP y n 3 0 3 1 NA
29 deer 21 5 38 30 21 4 22 18 7 1.314 y y Stocked Lake 770 BUBO, HYRE, RACA, THSP y n 2 1 3 38 0.118595365223762
30 deer_creek 1 0 2 2 1 0 2 2 0 NA n n NA NA NA y n 0 0 0 2 NA
31 deer_creek_camp 1 1 2 2 1 0 1 1 1 NA n n NA NA NA y n 0 0 0 2 NA
32 deer_flat 0 0 2 1 0 0 1 1 0 NA n n NA NA NA y n 0 0 0 2 NA
33 diamond 20 4 31 26 21 4 20 16 6 0.949 y y Stocked Lake 771 HYRE, THSP y n 0 1 1 31 -0.0227337875727074
34 dorleska_mine 2 0 3 2 1 0 1 2 1 NA n n NA NA NA NA NA 0 0 0 3 NA
35 eagle pk 1 0 1 0 1 0 0 0 0 NA n n NA NA NA NA NA 0 0 0 1 NA
36 east_boulder 15 11 16 14 12 1 16 15 3 11.44 y n Stocked Lake 533 BUBO, HYRE, RACA, THSP y n 4 1 5 20 1.05842602445701
37 east_weaver 0 1 1 0 0 0 0 0 0 0.22 y y NA 852 HYRE NA NA 1 1 2 1 -0.657577319177794
38 echo 5 0 6 5 4 0 3 3 2 1.303 y n Amps 786 AMMA, HYRE, RACA, THSP y n 4 1 5 6 0.114944415712585
39 El 5 0 7 7 5 0 6 6 4 2.259 y n Amps 732 BUBO, HYRE, RACA y n 3 1 4 7 0.353916230920363
40 eleanor 1 0 4 2 2 0 3 1 0 NA y n NA NA NA n n 0 0 0 4 NA
41 emerald 34 17 46 30 30 2 22 27 12 9.695 y y Stocked Lake 711 THSP NA NA 1 1 2 46 0.986547813414724
42 fish 0 0 1 0 0 0 0 0 1 NA y n Amps 574 BUBO, RACA y y 2 0 2 1 NA
43 forbidden 3 1 4 4 3 0 4 4 1 0.773 y n NA 765 HYRE, RACA y n 0 1 1 4 -0.111820506081675
44 foster 3 2 6 6 3 3 4 5 1 2.662 y n Stocked Lake 683 HYRE, RACA y n 0 2 2 6 0.425208051138656
45 foster's_cabin 2 0 3 2 0 0 3 3 0 NA n n NA NA NA NA NA 0 0 0 3 NA
46 found 3 2 3 3 2 0 3 1 0 NA y n Amps 690 AMMA, HYRE, RACA, THSP n n 4 0 4 3 NA
47 fox_creek 0 3 5 1 2 0 2 2 2 2.791 y n Amps 553 BUBO, HYRE, RACA, THSP y n 3 3 6 5 0.445759836488631
48 gibson pk 0 0 1 1 1 0 0 0 0 NA n n NA NA NA NA NA 0 0 0 1 NA
49 gibson_mdw 0 1 1 0 1 0 0 0 0 NA n n NA NA NA NA NA 0 0 0 1 NA
50 granite 35 15 73 55 37 5 47 42 15 10.122 y y Stocked Lake 759 BUBO, THSP y n 2 1 3 75 1.00526633297277
51 granite_cr 1 0 4 4 0 0 1 1 0 NA n n NA NA NA NA NA 0 0 0 4 NA
52 granite_pk 0 0 2 2 1 0 2 1 0 NA n n NA NA NA NA NA 0 0 0 2 NA
53 grizzly 9 6 19 14 11 3 11 8 5 16.747 y n Stocked Lake 708 RACA y n 1 1 2 19 1.22393702031998
54 grizzly_mdw 1 2 2 2 2 0 1 1 0 NA n n NA NA NA NA NA 0 0 0 2 NA
55 hidden 15 8 25 17 11 4 16 13 9 NA y n Amps 551 BUBO, HYRE, THSP n y 2 0 2 27 NA
56 horseshoe 8 2 10 10 6 2 7 8 2 1.932 y n Stocked Lake 726 BUBO, HYRE, THSP y n 2 2 4 10 0.286007122079475
57 kalmia 1 0 1 1 0 0 1 1 1 NA y n NA 729 BUBO, RACA, THSP NA n 2 0 2 1 NA
58 l_boulder 5 1 8 4 4 2 4 5 1 1.897 y y Stocked Lake 686 BUBO, HYRE y n 0 1 1 9 0.278067330888663
59 l_marshy 1 0 1 1 1 0 0 1 0 0.661 y n Stocked Lake 543 BUBO, HYRE, RACA, THSP NA NA 4 1 5 1 -0.17979854051436
60 L_south_fork 0 0 1 1 0 0 0 1 1 3.383 y n NA 704 RACA NA NA 1 1 2 1 0.529301997787981
61 landers 3 0 4 4 2 0 0 2 0 NA y n Stocked Lake 692 BUBO n n 1 0 1 4 NA
62 lion 2 3 7 5 4 3 5 5 1 1.544 y y Stocked Lake 684 RACA y n 0 1 1 7 0.188647295999717
63 little_caribou 1 0 3 2 0 0 3 3 1 1.018 y n Amps 685 BUBO, HYRE, RACA y n 1 1 2 4 0.00774777800073995
64 long_canyon 3 1 19 7 6 0 6 7 5 NA n n NA NA NA NA NA 0 0 0 20 NA
65 long_gulch 4 4 9 6 3 0 6 6 3 7.362 y n Amps 576 BUBO, RACA y y 1 2 3 10 0.866995813110648
66 luella 16 3 24 20 14 3 16 11 6 0.942 y y Stocked Lake 760 BUBO, HYRE, RACA y n 2 1 3 24 -0.0259490972071227
67 mavis 0 3 4 0 1 0 1 1 2 1.721 y n Stocked Lake 555 HYRE, RACA y n 1 1 2 4 0.23578087032756
68 middle_boulder 5 1 7 5 3 1 5 5 0 2.493 y n Amps 544 BUBO, HYRE, RACA, THSP y y 4 1 5 7 0.396722278503773
69 mill_creek 1 0 1 1 1 0 0 1 0 0.713 y n Stocked Lake 531 BUBO, RACA, THSP y y 2 1 3 1 -0.146910470148134
70 mirror 4 0 6 5 3 2 4 3 1 5.629 y n NA 719 BUBO NA n 0 1 1 6 0.750431248660202
71 morris 1 1 3 2 1 0 1 1 0 1.819 y n Amps 744 BUBO, RACA NA n 2 1 3 3 0.259832699063484
72 morris mdw 13 0 16 14 6 0 14 15 6 NA n n NA NA NA NA NA 0 0 0 17 NA
73 mumford_mdw 12 1 16 16 11 2 15 10 4 NA n n NA NA NA NA NA 0 0 0 16 NA
74 north fork coffee creek 1 0 1 0 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
75 packers pk 0 0 0 1 1 0 0 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
76 papoose 6 3 11 10 6 1 6 9 1 10.955 y n Stocked Lake 737 RACA y n 0 2 2 12 1.03961238189672
77 parker_cr 1 0 2 2 1 0 2 1 2 NA n n NA NA NA NA NA 0 0 0 2 NA
78 parker_mdw 0 1 3 2 1 1 1 1 0 NA n n NA NA NA NA NA 0 0 0 3 NA
79 PCT 6 0 17 7 6 0 3 3 5 NA n n NA NA NA NA NA 0 0 0 18 NA
80 PCT_through 3 0 17 7 5 0 3 3 8 NA n n NA NA NA NA NA 0 0 0 19 NA
81 poison_canyon 1 0 1 1 1 0 1 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
82 Preachers_pk 1 0 1 1 1 1 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
83 rattlesnake 1 1 2 1 1 0 1 2 0 NA n n NA NA NA NA NA 0 0 0 2 NA
84 saloon creek 0 0 0 0 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
85 salt_creek 1 1 1 1 1 1 1 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
86 sapphire 18 4 24 22 13 2 15 19 12 19.41 y n Stocked Lake 716 HYRE, THSP y n 2 2 4 24 1.28802553538836
87 sawtooth_mt 1 0 1 1 1 0 1 1 0 NA n n NA NA NA NA NA 0 0 0 1 NA
88 sawtooth_ridge 4 1 6 2 4 0 3 3 2 NA n n NA NA NA NA NA 0 0 0 7 NA
89 schlomberg cabin 0 0 0 0 0 0 0 0 1 NA n n NA NA NA NA NA 0 0 0 1 NA
90 Scott summit 0 0 3 2 1 0 1 2 0 NA n n NA NA NA NA NA 0 0 0 3 NA
91 seven_up_pk 2 1 4 4 2 1 3 3 2 NA n n NA NA NA NA NA 0 0 0 5 NA
92 shimmy 1 0 1 1 1 0 1 1 1 NA y n Amps 713 HYRE, RACA, THSP n n 3 0 3 1 NA
93 siligo_mdw 6 0 7 7 4 0 3 3 2 NA n n NA NA NA NA NA 0 0 0 7 NA
94 siligo_pk 1 0 2 2 1 1 1 0 0 NA n n NA NA NA NA NA 0 0 0 2 NA
95 sinks 1 0 1 1 1 0 1 0 0 NA n n NA NA NA NA NA 0 0 0 1 NA
96 smith 1 2 4 3 1 1 1 1 0 7.866 y n Amps 746 RACA NA n 0 2 2 4 0.895753942073728
97 snowslide 1 0 2 1 2 0 1 1 1 3.545 y n Amps 695 BUBO y n 1 3 4 2 0.549616239519085
98 south fork 9 2 16 15 11 2 11 13 4 NA y n Amps 567 THSP n n 1 0 1 19 NA
99 steavale mdw 0 0 1 1 0 0 0 1 0 NA n n NA NA NA NA NA 0 0 0 1 NA
100 stoddard 0 0 3 1 1 0 0 1 2 12.69 y n Amps 611 BUBO, HYRE, RACA, THSP NA NA 3 2 5 3 1.1034616220947
101 stuart fork 5 4 10 9 1 0 5 6 4 NA n y NA NA NA NA NA 0 0 0 12 NA
102 sugar_pine 0 1 1 1 1 1 0 1 0 2.474 y n Stocked Lake 666 THSP NA NA 1 2 3 1 0.393399695293102
103 summit 17 4 29 24 15 3 18 15 7 3.636 y n Stocked Lake 773 NA y n 1 1 2 29 0.56062387454993
104 sunrise pass 0 0 1 0 0 0 1 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
105 swift creek 3 5 14 6 4 0 9 6 1 NA n n NA NA NA NA NA 0 0 0 15 NA
106 tangle_blue 5 4 8 4 5 1 4 6 2 4.534 y n Stocked Lake 563 BUBO, HYRE, RACA, THSP NA NA 3 2 5 8 0.656481515790499
107 Tapie 2 0 2 1 0 0 1 1 0 NA y n Amps 687 AMMA, BUBO, HYRE, RACA n n 3 0 3 2 NA
108 telephone 1 1 1 1 0 0 1 1 0 1.493 y n Stocked Lake 554 BUBO, HYRE, RACA, THSP y y 4 1 5 1 0.174059807725025
109 thompson pk 2 0 5 5 3 4 3 3 1 NA n n NA NA NA NA NA 0 0 0 5 NA
110 thumb_rock 1 1 1 1 1 1 1 1 0 NA n n NA NA NA NA NA 0 0 0 1 NA
111 trail gulch 12 5 24 19 6 0 16 17 6 6.777 y n Stocked Lake 588 BUBO, HYRE, RACA, THSP y y 3 2 5 28 0.831037485640025
112 tri forest pass 1 1 1 1 1 0 1 1 0 NA n n NA NA NA NA NA 0 0 0 1 NA
113 u_boulder 2 0 2 2 2 0 2 2 0 2.009 y n Amps 537 BUBO, HYRE, RACA, THSP y y 4 2 6 2 0.302979936748249
114 union 7 2 8 6 4 1 5 6 2 1.49 y n Stocked Lake 688 BUBO, HYRE, RACA, THSP y n 3 2 5 8 0.173186268412274
115 valley_loop 0 0 1 1 0 0 0 1 1 NA n n NA NA NA NA NA 0 0 0 1 NA
116 virginia 0 3 4 0 1 0 1 1 2 1.43 y n Stocked Lake 561 BUBO, HYRE, RACA y n 2 2 4 4 0.155336037465062
117 ward 7 5 12 12 6 2 7 9 2 2.385 y n Stocked Lake 715 BUBO, HYRE, THSP y n 3 2 5 12 0.377488383376133
118 west_boulder 1 1 1 1 0 0 1 1 0 2.053 y n Stocked Lake 556 BUBO y y 1 2 3 1 0.312388949370592
119 yellow_rose_mine 0 0 1 0 1 0 1 0 0 NA n n NA NA NA NA NA 0 0 0 1 NA
# Model selection and multi-model inference
# A not-particularly good introduction by Rosemary Hartman
# (yes, I am just doing this for the flying monkey)
# So, let's say you want to find out where things are
# and why they are there.
# But there are a lot of reasons someone might be somewhere
# Let's say these things are fishermen,
# And we aren't sure what the reasons are yet.
# Start by making some good guesses. Maybe they all go to the
# big lakes. Maybe they all go to the lakes that CDFW stocks with fish.
# Maybe they go to the lakes with lots of frogs (not likely, but hey, why not try?)
# Once you have all your guesses, you need to figure out which one is right.
# There are two basic methods to use (or two that I have been exploring)
# Method #1: The kitchen sink
# load package "glmulti"
library(glmulti)
# create a model that has all the predictor variables you would like to test
global.model <- glm(fish~ # number of fishermen
stocked+ # CDFW fish stocking y/n
cows+ # cattle grazing in area y/n
herp.rich+ # amphibian species richness
fish.rich+ # fish species richness
visitors+ # total number of visitors
logsize, # log of the area
data=lakes.df2) # data frame we got this from
# Now we will use the "glmulti" function to find the best model;
# this goes through every possible model and finds the best one.
fish.model <- glmulti(global.model, # use the model with built as a starting point
level = 1, # just look at main effects
crit="aicc") # use AICc because it works better than AIC for small sample sizes
summary(fish.model)
# That showed us the best model, now lets look at some of the others
weightable(fish.model)
# So this is the best model
f <- glm(fish~1+cows+herp.rich+visitors+logsize, data=lakes.df2)
summary(f)
# I hate trying to interpret models based on tables of coeficients.
# Let's look at some graphs
library(visreg)
visreg(f)
# But according to theory, models with AIC within two points of each other are basically
# equal. So what about the other models? Should we totally throw them out? Looking
# at the table of aicc weights, there is a pretty big jump between model 8 and model 9.
# So lets try averaging the top 8 models if we want to use this to make predictions,
# evaluate variable importance, etc.
library(MuMIn)
# run the top 8 models
f2 <- glm(fish ~ 1 + cows + herp.rich + fish.rich + visitors + logsize, data=lakes.df2)
f3 <- glm(fish ~ 1 + stocked + cows + herp.rich + visitors + logsize, data=lakes.df2)
f4 <- glm(fish ~ 1 + cows + visitors + logsize, data=lakes.df2)
f5 <- glm(fish ~ 1 + cows + fish.rich + visitors + logsize, data=lakes.df2)
f6 <- glm(fish ~ 1 + stocked + cows + visitors + logsize, data=lakes.df2)
f7 <- glm(fish ~ 1 + stocked + cows + herp.rich + fish.rich + visitors + logsize, data=lakes.df2)
f8 <- glm(fish ~ 1 + stocked + cows + fish.rich + visitors + logsize, data=lakes.df2)
# average the models together
f.ave <- model.avg(f, f2, f3, f4, f5, f6, f7, f8)
summary(f.ave)
# Now we know the relative variable importance, all of the avereged coefficents,
# etc, and can use the "predict" funciton to predict how many fishermen will
# be at the next lake. Graphing these are more difficult, so we'll skip this for now.
# Ask me later if you really want to know.
# Model selection method #2: Use your brain
# We often can discard (or choose) some models a priori based on our knowlege of
# the system. It's usually better to do it this way if you have several hundered
# possible combination of variables, or want to put in some interaction terms.
# I used this method for my frog data.
# load package bbmle
library(bbmle)
# Decide on which set of models you want to use. This is hard. A statistician
# who knows a lot more than I do told me so. I spent a long time playing around
# with different transformations, predictor variables, and combinations
# before I came up with a set of hypotheses (models) that I was happy with.
m1 <- glm(treatment ~ 1+ logveg + bank.slope, family=binomial("logit"), data= fishlakes)
m2 <- glm(treatment ~ 1+ logveg + silt.total +bank.slope, family=binomial("logit"), data= fishlakes)
m3 <- glm(treatment ~ 1+ raca.basin + logveg + bank.slope, family=binomial("logit"), data= fishlakes)
m4 <- glm(treatment ~ 1+ BUBO.breeding + logveg + bank.slope, family=binomial("logit"), data= fishlakes)
m5 <- glm(treatment ~ 1+ BUBO.breeding + logveg + bank.slope + raca.basin, family=binomial("logit"), data= fishlakes)
m6 <- glm(treatment ~ 1+ raca.basin*BUBO.breeding, family=binomial("logit"), data= fishlakes)
m7 <- glm(treatment ~ 1+ herbacious + raca.basin + lakes.basin, family=binomial("logit"), data= fishlakes)
m8 <- glm(treatment ~ 1+ BUBO.breeding, family=binomial("logit"), data= fishlakes)
m9 <- glm(treatment ~ BUBO.breeding + herbacious + bank.slope + logveg, family=binomial("logit"), data= fishlakes)
m10 <- glm(treatment ~ BUBO.breeding*raca.basin + herbacious+ lakes.basin, family=binomial("logit"), data= fishlakes)
m11 <- glm(treatment ~ 1 + bank.slope + logveg + BUBO.breeding:raca.basin, family = binomial("logit"), data = fishlakes)
# Now let's rank them via AICc
AICctab(m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11, base=T, weights=T, nobs=length(fishlakes))
# Model m11 comes out ahead by quite a bit, but we'll average the top two models, just to show
# you how its done.
m.ave <- model.avg(m4, m11)
summary(m.ave)
#OK, there is a predictive model, but how good is it?
# Let's try cross-validation first. If this was a single model, we could try using
# the cv.glm function from the "boot" library like this:
library("boot")
cost <- function(r, pi = 0) mean(abs(r-pi) > 0.5) ## cost function necessary for binomial data
m11.cv <- cv.glm(data=fishlakes, m11, cost, K=42) # use leave-one-out cross validation (can use K-fold cross validation for larger data sets)
# Now lets see what our error rate was:
m11.cv$delta
# That's not too bad.
# IF we want to check the error rate of an averaged model, you need to get more creative.
# I've written some code to do this for averaged models that only have two component models.
# It shouldn't be too hard to adapt this for more models.
# function for leave one out cross validation of averaged models
Cross <- function(model1, model2, data, cost) {
library(MuMIn)
nobs <- nrow(data)
model.ave <- model.avg(model1, model2)
values <- matrix(NA, nrow=nobs, ncol=5)
values[,1] <- data$treatment
values[,2] <- predict(model.ave, type="response")
CV=0
for (i in 1:nobs) {
data2 <- data[-i,] # leave out one observasion
model12 <- glm(model1$formula, family=model1$family, data=data2)
model22 <- glm(model2$formula, family=model2$family, data=data2)
model.ave2 <- model.avg(model12, model22)
values[i,3] <- predict(model.ave2, newdata=data[i,], type="response")
values[i,4] <- round(values[i,3])
if (values[i,4]==values[i,1]) (values[i,5]=1) else values[i,5]=0
}
cv = mean(abs(values[,3]-values[,1])>0.5)
return(cv)
}
# Use the function on the component models
Cross(m11, m4, fishlakes, cost)
# That looks reasonable
# Another method to test model accurace is Area Under the Reciever Operater Curve (AUC)
# This is baisically a plot of true presences versus false presences in a
# presence-absense model.
# Load the library "pROC"
library(pROC)
# Make your reciever-operater curve
m.roc <-roc(fishlakes$treatment, predict(m.ave, backtransform=TRUE))
plot(m.roc)
# Looks like a pretty good fit. Not too bad for the small size of the data set.
# And that's all I got. Hopefully you will find it helpful. Let me know if there is anything
# else I have forgotton or done wrong. ~ Rosemary rosehartman@gmail.com
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