install.packages("randomForest")
install.packages("tidyverse")
install.packages("GGally")Introduction to Machine Learning with RandomForest
Install Packages:
Load Libraries:
library(randomForest)
library(tidyverse)
library(GGally)Boosted regression trees (BRT) represent a versatile machine learning technique applicable to both classification and regression tasks. This approach facilitates the assessment of the relative significance of numerous variables associated with a target response variable. In this workshop, our focus will be on utilizing BRT to develop a model for monthly methane fluxes originating from natural ecosystems. We’ll leverage climate and moisture conditions within these ecosystems to enhance predictive accuracy and understanding.
Read in the data:
load('data/RANDOMFOREST_DATASET.RDATA' )Our ultimate interest is in predicting monthly methane fluxes using both dynamic and static attribute of ecosystems. Before we start modeling with the data, it is a good practice to first visualize the variables. The ggpairs() function from the GGally package is a useful tool that visualizes the distribution and correlation between variables:
ggpairs(fluxnet, columns = c(3:7, 12:13))
Next we need to divide the data into testing (20%) and training (80%) sets in a reproducible way:
set.seed(111) # set the randomnumber generator
#create ID column
fluxnet$id <- 1:nrow(fluxnet)
#use 80% of dataset as training set and 30% as test set
train <- fluxnet %>% dplyr::sample_frac(0.80)
test <- dplyr::anti_join(fluxnet, train, by = 'id')We will use the randomForest() function to predict monthly natural methane efflux using several variables in the dataset. A few other key statements to use in the randomForest() function are:
- keep.forest = T: This will save the random forest output, which will be helpful in summarizing the results.
- importance = TRUE: This will assess the importance of each of the predictors, essential output in random forests.
- mtry = 1: This tells the function to randomly sample one variable at each split in the random forest. For applications in regression, the default value is the number of predictor variables divided by three (and rounded down). In the modeling, several small samples of the entire data set are taken. Any observations that are not taken are called “out-of-bag” samples.
- ntree = 500: This tells the function to grow 500 trees. Generally, a larger number of trees will produce more stable estimates. However, increasing the number of trees needs to be done with consideration of time and memory issues when dealing with large data sets.
Our response variable in the random forests model is FCH4_F_gC and predictors are P_F, TA_F, VPD_F, IGBP, NDVI, and EVI. We will only explore a few of these variables below:
FCH4_F_gC.rf <- randomForest(FCH4_F_gC ~ P_F + TA_F + VPD_F ,
data = train,
keep.forest = T,
importance = TRUE,
mtry = 1,
ntree = 500,
keep.inbag=TRUE)
FCH4_F_gC.rf
Call:
randomForest(formula = FCH4_F_gC ~ P_F + TA_F + VPD_F, data = train, keep.forest = T, importance = TRUE, mtry = 1, ntree = 500, keep.inbag = TRUE)
Type of random forest: regression
Number of trees: 500
No. of variables tried at each split: 1
Mean of squared residuals: 4.887725
% Var explained: 22.83Note the mean of squared residuals and the percent variation explained (analogous to R-squared) provided in the output.
Visualize the out-of-bag error rates of the random forests models using the plot() function. In this application, although we specified 500 trees, the out-of-bag error generally stabilizes after 100 trees:
plot(FCH4_F_gC.rf)
Some of the most helpful output in random forests is the importance of each of the predictor variables. The importance score is calculated by evaluating the regression tree with and without that variable. When evaluating the regression tree, the mean square error (MSE) will go up, down, or stay the same.
If the percent increase in MSE after removing the variable is large, it indicates an important variable. If the percent increase in MSE after removing the variable is small, it’s less important.
The importance() function prints the importance scores for each variable and the varImpPlot() function plots them:
importance(FCH4_F_gC.rf) %IncMSE IncNodePurity
P_F 11.7269452 2762.568
TA_F 29.1106456 4454.298
VPD_F -0.7084245 3396.256varImpPlot(FCH4_F_gC.rf)
Another aspect of model evaluation is comparing predictions. Although random forests models are often considered a “black box” method because their results are not easily interpreted, the predict() function provides predictions of total tree mass:
train$PRED.TPVPD <- predict(FCH4_F_gC.rf, train)
train$PRED.TPVPD 1 2 3 4 5 6
0.350966664 0.429278864 0.313910434 0.418912296 1.106883276 2.202318614
7 8 9 10 11 12
3.022301696 3.281477224 1.982611915 0.710828667 0.513731178 0.440529651
13 14 15 16 17 18
0.423833010 0.279860587 0.371487016 0.498307150 0.936792763 2.202429003
19 20 21 22 23 24
0.584097127 3.814697537 1.035535080 3.480349355 1.767388586 0.732192556
25 26 27 28 29 30
0.487254095 0.411031890 0.389717998 0.340486452 0.337745909 0.662268060
31 32 33 34 35 36
0.846607274 1.057445926 2.403118584 0.572516189 3.698548702 2.835909192
37 38 39 40 41 42
0.802947684 1.143423013 0.676826308 0.641043739 0.488707123 0.379251231
43 44 45 46 47 48
0.315522422 0.261512975 0.690590324 0.487961155 2.953092995 1.578643183
49 50 51 52 53 54
2.130515801 1.721572006 2.736948169 0.776934319 1.640462055 3.153600168
55 56 57 58 59 60
7.646926404 6.835070552 1.037728598 0.374152315 1.049627742 2.081257999
61 62 63 64 65 66
1.124287950 0.604855671 0.670482666 0.761253054 0.206999823 0.433200877
67 68 69 70 71 72
0.752380451 0.426073762 0.222362734 1.012824599 0.262397242 1.742353734
73 74 75 76 77 78
1.635003299 0.726266987 0.387179570 1.138539924 0.735700517 0.496176925
79 80 81 82 83 84
0.585429940 1.448738513 0.773433394 0.219944262 0.905490335 0.965036433
85 86 87 88 89 90
2.173433298 0.690692175 2.097052031 1.578422868 2.097958541 3.498357683
91 92 93 94 95 96
1.790640635 6.595011399 0.932766638 2.790858891 4.256334356 1.308749512
97 98 99 100 101 102
0.294418840 1.315675200 0.635219978 0.301323511 0.443618683 0.963547668
103 104 105 106 107 108
0.213003224 1.017388068 0.654954329 0.730847957 0.293852780 0.404445256
109 110 111 112 113 114
0.174803398 0.183022055 0.540337242 0.372990615 0.091798887 0.569426291
115 116 117 118 119 120
0.633679309 0.132305375 0.085387653 0.781615646 1.117640973 0.112640327
121 122 123 124 125 126
1.837179391 1.639796888 0.086019047 0.278281849 0.365172124 2.233347544
127 128 129 130 131 132
0.816182644 1.508493142 0.303020770 0.708380725 0.642802520 0.916800286
133 134 135 136 137 138
5.721636509 1.738748689 0.474685634 2.749514872 2.077956662 1.254022333
139 140 141 142 143 144
5.706288209 2.738208415 0.590629677 1.118304071 2.716054553 5.099980652
145 146 147 148 149 150
3.983072173 0.965444502 1.659923242 0.912270359 7.016639798 1.992233306
151 152 153 154 155 156
7.064628027 0.580233628 7.624291639 0.511706938 0.523403391 7.311759127
157 158 159 160 161 162
0.413081693 2.615485887 1.737803176 4.041238549 1.766462799 0.378158206
163 164 165 166 167 168
1.095346427 1.756824110 0.796378218 5.051853990 5.954580676 3.474148805
169 170 171 172 173 174
2.565140713 0.867434888 0.538638973 1.696448825 0.265605511 0.711388620
175 176 177 178 179 180
0.332579885 1.152890181 0.161130895 0.123131558 0.734373503 1.136376349
181 182 183 184 185 186
0.320969032 1.663430779 3.110695368 0.242585633 0.505072358 1.140161420
187 188 189 190 191 192
0.851390131 1.071771476 1.839179031 0.637214355 0.202589105 0.274153351
193 194 195 196 197 198
0.109863304 0.195861100 0.940964660 0.975494373 0.167648474 0.359387404
199 200 201 202 203 204
0.180352975 2.845530542 0.071864543 0.280249651 0.440519431 0.402323824
205 206 207 208 209 210
0.895949134 0.632782960 0.714863603 0.257169462 3.221095723 1.169616608
211 212 213 214 215 216
0.124731449 0.195806026 0.542832946 0.940700661 0.960319390 0.255120260
217 218 219 220 221 222
0.406463453 0.322686002 0.868392469 0.517672473 1.228435930 0.248966587
223 224 225 226 227 228
0.392391140 0.374838512 0.234492682 1.142514595 0.966696768 0.415182137
229 230 231 232 233 234
0.453868582 1.266918517 0.904053662 3.482301871 1.412714264 0.716085175
235 236 237 238 239 240
0.547671777 2.235410240 0.739637308 0.361864774 1.598877413 0.111295017
241 242 243 244 245 246
0.678749343 1.824585623 0.132786405 0.253973400 3.244061260 0.619423508
247 248 249 250 251 252
2.696579716 0.381349587 1.304924370 0.841318717 1.404538529 5.074112507
253 254 255 256 257 258
1.091185551 2.433840657 0.835469160 0.390162136 3.453057420 0.892346779
259 260 261 262 263 264
1.256747363 1.768921752 5.559813717 3.642332054 6.916058334 0.345531128
265 266 267 268 269 270
3.609315795 3.458312122 5.411483135 0.478304689 0.384067687 1.437609539
271 272 273 274 275 276
1.646644444 0.880818558 1.837048719 2.144814211 5.179255187 1.097206418
277 278 279 280 281 282
1.038038519 2.968948482 7.818837967 3.256186938 2.412005486 5.419321707
283 284 285 286 287 288
0.813317122 8.317115079 2.601755469 0.843429860 1.612596659 2.860754089
289 290 291 292 293 294
0.816462385 2.172526008 1.340129398 5.117156056 1.275575291 4.462547926
295 296 297 298 299 300
1.436489958 5.341489754 6.841656521 2.469832570 0.441526857 1.610415035
301 302 303 304 305 306
2.125540705 1.595491350 2.847664153 6.501367627 1.109501291 6.475184329
307 308 309 310 311 312
1.007149232 0.280221096 0.561981959 3.314203089 6.628252055 0.831186784
313 314 315 316 317 318
1.215601255 5.237720926 1.883128960 2.408583467 1.325263889 3.733852759
319 320 321 322 323 324
5.463872633 0.274794480 5.627900247 1.334480215 1.615528957 1.759371603
325 326 327 328 329 330
4.213020843 0.240711557 0.140864700 0.230417115 0.481527167 4.990077329
331 332 333 334 335 336
1.408444343 0.717380467 0.480762063 0.522399253 0.599568414 0.261180604
337 338 339 340 341 342
0.650229297 1.213234689 2.678496029 0.088922976 0.403422319 0.170017229
343 344 345 346 347 348
1.867639035 1.375723662 0.238104475 1.343953452 0.585615214 0.431887055
349 350 351 352 353 354
0.419542218 0.327553092 0.854287088 0.708303466 0.642098880 0.252738257
355 356 357 358 359 360
0.719312298 1.109625844 0.116976115 1.097257013 0.276706131 0.553577086
361 362 363 364 365 366
2.161842623 0.113232453 2.089783482 0.236194592 2.564091189 0.189153563
367 368 369 370 371 372
0.207067256 0.437531195 4.302379780 0.315423479 0.729131454 0.373449287
373 374 375 376 377 378
0.081579816 0.216232553 0.605548923 0.233032154 0.488667389 0.212117520
379 380 381 382 383 384
2.369578546 0.100417073 0.272551495 0.229942998 0.404410682 0.812587221
385 386 387 388 389 390
1.227797302 4.171470801 0.517796566 0.169644735 0.232706420 0.190779549
391 392 393 394 395 396
3.440407131 0.787629147 0.438585080 0.334631760 2.678008905 0.448884859
397 398 399 400 401 402
0.210995605 0.277910907 2.012415825 0.211872962 0.567612565 2.551500208
403 404 405 406 407 408
3.272335602 1.400061696 1.167298354 0.345972295 1.093672968 0.206106718
409 410 411 412 413 414
1.669648952 0.131664918 2.604217697 3.192156989 0.428175081 0.285481063
415 416 417 418 419 420
0.338054229 0.753645508 0.506670906 0.717317100 0.367000573 0.738708482
421 422 423 424 425 426
1.094189654 3.160629273 3.305837721 5.706801716 1.592265430 2.811905665
427 428 429 430 431 432
0.500651788 0.594767532 0.583573842 0.221870210 2.855619593 3.954433601
433 434 435 436 437 438
1.032011262 0.857245197 0.728714314 1.836422539 1.296894125 1.700360179
439 440 441 442 443 444
1.704780292 1.304512532 4.609975803 3.656038932 4.537352098 2.002747940
445 446 447 448 449 450
3.057017886 0.402028949 3.822736954 0.757225344 1.343776950 0.797768429
451 452 453 454 455 456
1.970830947 0.883421710 0.761662008 0.860911293 6.232388290 0.411650784
457 458 459 460 461 462
7.391289267 5.052575707 2.897728615 1.459895408 1.839558696 2.225035682
463 464 465 466 467 468
2.069839957 6.794525818 0.895532118 2.372073435 0.695066681 1.393262267
469 470 471 472 473 474
1.409907929 0.663635225 1.131757609 1.904746198 1.773330010 3.822910825
475 476 477 478 479 480
4.750213461 0.333814698 3.669693651 2.419805937 0.545465177 0.851112821
481 482 483 484 485 486
1.796899789 4.381171022 1.428787046 6.618562052 1.981808341 2.898379465
487 488 489 490 491 492
4.659597821 8.698427651 8.338040435 3.580130861 0.593177355 7.540711014
493 494 495 496 497 498
0.880808864 2.852968465 0.977674926 0.917384897 0.751613159 0.397899065
499 500 501 502 503 504
3.754276493 0.399449397 1.000565480 0.979945876 2.397566344 5.263825779
505 506 507 508 509 510
1.500887519 0.556404047 2.250189570 5.081832079 7.612294106 0.945893649
511 512 513 514 515 516
0.417440760 0.762586273 0.881976517 6.924831145 0.416076855 0.313096903
517 518 519 520 521 522
1.698788875 1.571980278 2.382211072 2.335398462 0.808777247 0.332719900
523 524 525 526 527 528
3.248697459 0.515274048 0.191094324 2.265436030 0.599119942 0.508611309
529 530 531 532 533 534
0.428075670 2.212952544 0.463761916 0.352454562 0.925609388 1.657284645
535 536 537 538 539 540
0.330225455 0.315324891 0.849592141 0.246265465 5.683251152 2.685665941
541 542 543 544 545 546
0.159464362 0.144749382 0.434161426 0.914926933 0.279924539 0.752641095
547 548 549 550 551 552
0.378937178 0.198264525 0.156441470 0.127113093 0.585831722 1.728382034
553 554 555 556 557 558
0.834243895 2.261492194 0.323016288 0.357745888 0.761505549 2.407468989
559 560 561 562 563 564
0.304576233 2.629076863 0.404900739 0.714781898 2.426439046 0.472006599
565 566 567 568 569 570
0.322854210 2.797427854 0.345026562 2.616930006 0.569869232 0.807208619
571 572 573 574 575 576
0.059898757 0.665997196 0.370959144 2.346359213 0.041038771 0.287973666
577 578 579 580 581 582
0.215228943 2.983084688 1.284400290 0.307688596 0.341851275 2.039107634
583 584 585 586 587 588
0.221027943 2.559661802 0.492738005 0.046215031 0.295389415 0.186752263
589 590 591 592 593 594
0.256309195 1.687585264 0.136925435 0.686472811 0.259220001 0.132700535
595 596 597 598 599 600
5.841913703 0.067085190 0.088354585 1.778163693 0.555626899 0.419058809
601 602 603 604 605 606
3.215060842 0.483693143 0.324181280 0.652183894 0.053432310 3.949401989
607 608 609 610 611 612
1.021956996 2.476573074 0.236075873 0.298624046 0.058419988 1.706406668
613 614 615 616 617 618
0.635436307 1.648275917 0.508729223 0.210895517 2.602523526 1.103833210
619 620 621 622 623 624
0.115804942 0.061096171 0.813879207 0.781319893 0.337162220 0.306586730
625 626 627 628 629 630
2.701530460 1.384468297 0.177347018 2.198232515 0.164880093 3.692138483
631 632 633 634 635 636
2.976804746 0.321295302 0.089944834 2.713756016 3.013610964 1.857772525
637 638 639 640 641 642
0.055991091 0.594671063 0.128753664 0.186348906 0.330821579 0.948174432
643 644 645 646 647 648
4.719617726 0.628194958 0.197045193 0.471155412 2.126221578 0.799794605
649 650 651 652 653 654
0.204289894 0.568477114 0.305549248 0.818968803 0.623515127 0.313003952
655 656 657 658 659 660
0.110224217 0.116701379 0.220427869 2.311666592 3.444459402 0.145019012
661 662 663 664 665 666
0.819459606 0.340985657 0.707879417 1.499386786 1.461651128 2.669656031
667 668 669 670 671 672
0.743745305 0.662503498 0.754180648 0.124163955 3.946030639 0.184667763
673 674 675 676 677 678
1.022760120 0.107811587 0.473573122 0.457661714 0.718359762 1.461011024
679 680 681 682 683 684
0.428822116 0.119802966 1.272056766 4.545447550 0.354497834 1.208003675
685 686 687 688 689 690
1.774268009 2.611481873 1.287356219 5.031336240 0.606969435 1.823415622
691 692 693 694 695 696
0.902348277 0.283283191 0.285222773 1.322732484 2.425216758 1.222837562
697 698 699 700 701 702
1.776902123 0.266118103 0.403286137 1.154377312 0.417933461 4.602694831
703 704 705 706 707 708
1.560900360 0.604858847 2.712437444 1.125059407 0.803152561 4.250846958
709 710 711 712 713 714
0.403265624 0.988811430 0.664166239 0.299602608 1.197125758 3.158216469
715 716 717 718 719 720
1.432480665 1.192793856 1.144408776 2.248032395 2.487198546 7.652198740
721 722 723 724 725 726
0.464151385 0.509666753 0.742193981 0.767816432 5.951472429 3.390012020
727 728 729 730 731 732
2.974523933 0.878668152 1.152185633 0.926861541 2.324451191 7.514802195
733 734 735 736 737 738
3.730998260 0.436926059 2.760120440 2.735118105 0.528855148 0.757755270
739 740 741 742 743 744
4.079776558 1.258371809 0.739512768 0.818673237 7.596992570 0.615707482
745 746 747 748 749 750
3.636913185 3.207969217 1.655289947 0.907874704 1.897222775 0.721417060
751 752 753 754 755 756
1.012286204 0.419571869 1.809822100 2.071164090 2.867316921 2.242358148
757 758 759 760 761 762
4.208542015 1.379509839 1.374822948 1.141867454 2.546489509 0.451095825
763 764 765 766 767 768
7.373174531 1.601487123 1.374967616 4.289448526 1.905399056 0.924178296
769 770 771 772 773 774
4.378347551 4.213009850 1.648930090 0.513944115 5.647742964 1.750755006
775 776 777 778 779 780
0.814208607 0.995666895 0.781674614 5.778822070 0.318409932 0.446619636
781 782 783 784 785 786
0.262218839 0.485497062 0.616579919 0.321633399 0.334520498 0.772693862
787 788 789 790 791 792
1.357150774 1.048510426 1.569515044 1.558852448 0.751644028 0.663691270
793 794 795 796 797 798
1.334417824 0.853717185 1.753199531 2.845723093 0.553138213 0.868242129
799 800 801 802 803 804
0.347470902 1.545783162 0.710729403 0.510977867 0.541766908 0.320030181
805 806 807 808 809 810
0.590462753 0.463967893 0.194959072 0.411941083 1.489427310 0.454785248
811 812 813 814 815 816
0.604422472 0.568959208 0.291028335 0.348156234 1.707557375 0.819273401
817 818 819 820 821 822
3.567708237 1.143034589 0.219133454 5.676736377 3.133410059 0.782985063
823 824 825 826 827 828
0.113882810 0.203905548 0.193514245 0.433819599 0.119823213 0.125000371
829 830 831 832 833 834
0.205912404 1.303123109 0.958428142 1.248074867 1.294003886 0.240089684
835 836 837 838 839 840
0.231631486 0.369689148 0.273089738 0.316919253 1.613587569 0.173089866
841 842 843 844 845 846
3.199714376 0.323829170 1.764372476 0.648976320 0.269645890 0.605441025
847 848 849 850 851 852
0.967479284 0.489109783 0.313524094 0.550104354 0.116240056 1.305652584
853 854 855 856 857 858
2.580152402 0.423004855 0.436733545 0.507421956 1.078786491 0.234283508
859 860 861 862 863 864
0.416518554 0.285764469 0.265671729 0.159152464 0.071872844 2.670690927
865 866 867 868 869 870
0.285756002 0.751198417 0.669690527 0.087331376 0.175380383 1.006655840
871 872 873 874 875 876
0.284143316 2.081063896 0.730563194 3.256094186 0.173376466 0.612542759
877 878 879 880 881 882
0.047587148 0.091737932 0.230952161 1.369671393 0.118977341 0.296670397
883 884 885 886 887 888
0.279592242 0.181932492 1.679712242 0.250441503 0.185840596 2.103425373
889 890 891 892 893 894
5.424374949 0.882954598 0.873264494 0.152852955 1.671242786 1.278176790
895 896 897 898 899 900
0.128583373 2.751004687 0.072031128 0.171661694 0.207548710 1.432621113
901 902 903 904 905 906
1.569638161 0.065605183 0.107437410 0.149602328 0.777808209 0.392975768
907 908 909 910 911 912
0.290803820 4.491587887 0.217536326 0.605732263 1.288175693 0.422565958
913 914 915 916 917 918
0.307129184 0.151057853 0.448038694 1.070717264 0.570563572 0.548198065
919 920 921 922 923 924
0.043556204 0.097031652 0.165588485 0.052220233 0.184542762 0.576617124
925 926 927 928 929 930
0.154931131 0.705675141 2.007663827 3.343750715 0.582197052 1.334101270
931 932 933 934 935 936
0.265039781 0.086751041 0.357755271 0.961283039 0.349622117 1.829586279
937 938 939 940 941 942
1.464298098 3.799402754 0.173548165 0.200221135 0.144116796 0.381448529
943 944 945 946 947 948
0.507333221 1.101265706 0.250244568 3.387462505 0.781077471 1.150787307
949 950 951 952 953 954
0.186607631 0.392404711 0.435921050 0.327417874 0.715047637 0.144133465
955 956 957 958 959 960
0.134530668 2.698860623 3.212113620 0.313128640 1.046849946 2.623098899
961 962 963 964 965 966
0.788862626 0.400406286 0.825739053 2.698784616 1.018036232 4.163933189
967 968 969 970 971 972
1.405223613 0.476823567 1.739980022 0.502323121 2.828521821 0.671408370
973 974 975 976 977 978
0.699352864 1.317512574 0.612277262 0.587220997 0.487713590 0.693689176
979 980 981 982 983 984
6.230916502 0.447215323 1.432911899 1.109021041 0.465843116 0.501564683
985 986 987 988 989 990
0.856522906 1.029591502 0.552110637 1.458590312 4.772931582 0.654772270
991 992 993 994 995 996
1.487897961 0.976107460 1.009957725 1.394919392 8.314150936 0.730267339
997 998 999 1000 1001 1002
1.095099587 0.561673641 0.612545434 3.486668831 0.861312277 8.782244105
1003 1004 1005 1006 1007 1008
3.031409456 0.779650856 1.410704775 1.816808202 1.332279101 0.672017680
1009 1010 1011 1012 1013 1014
0.794440745 1.190906361 2.237288492 0.542049421 2.257502773 2.044533800
1015 1016 1017 1018 1019 1020
1.483151678 1.189860905 5.816064125 2.181583802 0.914652603 1.311425659
1021 1022 1023 1024 1025 1026
1.831284943 5.579580713 4.904180763 1.389003422 1.377298775 3.351553282
1027 1028 1029 1030 1031 1032
0.979236388 6.043235219 0.756185783 2.119186052 3.554319286 0.688527366
1033 1034 1035 1036 1037 1038
2.239039165 0.289048422 1.199174882 6.329140086 1.524569026 2.638680225
1039 1040 1041 1042 1043 1044
0.533196938 2.268867073 1.526367491 6.467254622 1.297414269 0.625529333
1045 1046 1047 1048 1049 1050
3.174140516 0.512634777 7.586726259 0.826988095 0.774133469 1.333476360
1051 1052 1053 1054 1055 1056
0.223832981 1.543860499 1.932358723 15.754246414 0.313755026 0.794239576
1057 1058 1059 1060 1061 1062
1.261574842 1.004008419 0.762913307 2.346609607 0.220065986 5.114617484
1063 1064 1065 1066 1067 1068
0.232599463 1.070515200 1.764293683 0.988720510 0.909721406 0.279259033
1069 1070 1071 1072 1073 1074
2.380961287 4.592840870 1.013539311 0.377117710 0.248732016 1.532005411
1075 1076 1077 1078 1079 1080
1.411812491 0.462177716 0.570740877 1.593607073 0.301540461 1.096372292
1081 1082 1083 1084 1085 1086
3.358071526 0.817521452 0.631773775 4.761316612 0.592666462 0.160520771
1087 1088 1089 1090 1091 1092
0.195193872 1.613643158 1.586691377 3.908245377 4.333069476 0.703619654
1093 1094 1095 1096 1097 1098
0.230142010 1.392379920 0.394579157 0.133992403 0.187666509 4.772139183
1099 1100 1101 1102 1103 1104
0.216190260 0.646534414 0.930464684 0.461015120 0.431696943 3.811833363
1105 1106 1107 1108 1109 1110
0.207496434 0.175288744 0.438815330 0.852818707 0.490036132 0.899456212
1111 1112 1113 1114 1115 1116
0.618350897 0.087752763 3.393364761 0.815907965 0.195019987 2.663453707
1117 1118 1119 1120 1121 1122
0.467741689 0.279159628 0.235320113 0.928748734 0.256399050 0.188349092
1123 1124 1125 1126 1127 1128
0.222798788 1.462620750 0.416549727 1.246646493 0.827849802 0.163658883
1129 1130 1131 1132 1133 1134
0.432934576 0.507280571 0.174689418 1.174979815 1.170158968 0.242868165
1135 1136 1137 1138 1139 1140
0.327267921 0.884280371 1.264470705 0.497348596 0.648191158 0.194174328
1141 1142 1143 1144 1145 1146
0.348733941 0.241002062 0.291533547 0.247607139 2.072273565 1.278031259
1147 1148 1149 1150 1151 1152
3.794653862 0.150439232 1.192568662 0.075401104 0.683435553 0.896936673
1153 1154 1155 1156 1157 1158
0.249830309 0.104794563 1.605475199 0.340154340 0.392975859 0.948155116
1159 1160 1161 1162 1163 1164
0.689686091 0.186095426 0.133697122 0.047787195 0.084728471 0.408390163
1165 1166 1167 1168 1169 1170
0.943586488 1.134249538 0.166382464 0.074217395 0.200200800 1.224668354
1171 1172 1173 1174 1175 1176
0.242389500 0.320928307 0.583030206 0.154463331 0.081002514 0.383773613
1177 1178 1179 1180 1181 1182
0.267320595 0.323063853 1.687043962 0.197526100 0.183918867 1.003540461
1183 1184 1185 1186 1187 1188
0.742171413 4.042422073 0.222620242 1.313606642 0.662164435 0.169694483
1189 1190 1191 1192 1193 1194
0.119973872 0.227189350 0.102085560 1.278761456 0.191832959 0.203008022
1195 1196 1197 1198 1199 1200
0.162256152 0.177203767 0.802661960 0.160638952 2.139813777 0.249959076
1201 1202 1203 1204 1205 1206
0.123792700 0.138064387 0.625199731 0.128113651 0.706630633 2.762135384
1207 1208 1209 1210 1211 1212
0.088227450 0.182471141 0.133027138 2.296004141 0.939506525 0.129138702
1213 1214 1215 1216 1217 1218
0.685636646 0.766684074 0.181661544 0.349756451 0.109992993 0.235842660
1219 1220 1221 1222 1223 1224
0.388246621 0.116703214 3.168190160 4.350758286 0.137389323 0.308512679
1225 1226 1227 1228 1229 1230
0.366394588 0.439487967 0.199765189 0.394925584 1.015624487 0.275420688
1231 1232 1233 1234 1235 1236
1.033346180 0.232484823 0.226132882 1.153189166 3.431949741 0.256313590
1237 1238 1239 1240 1241 1242
0.169893156 4.023495717 0.432144485 0.281792434 0.318871842 2.517484068
1243 1244 1245 1246 1247 1248
0.926961415 0.424805179 0.725624053 2.445536063 0.815304661 3.066527521
1249 1250 1251 1252 1253 1254
5.515128424 2.359523282 1.184098336 1.047385961 0.959288726 0.194449616
1255 1256 1257 1258 1259 1260
0.451430879 6.044835263 0.472015548 6.131889235 11.938022552 5.619543253
1261 1262 1263 1264 1265 1266
1.646545195 6.228464455 0.500835961 0.565764877 0.489472006 1.682476629
1267 1268 1269 1270 1271 1272
1.664301497 1.026008909 0.582682972 4.158303889 0.597005324 0.714133102
1273 1274 1275 1276 1277 1278
2.294727994 1.512397735 4.894612820 1.266621514 2.112198074 1.577795372
1279 1280 1281 1282 1283 1284
0.554749831 1.546510494 1.172572870 0.283097923 0.440292457 1.495324965
1285 1286 1287 1288 1289 1290
1.210806640 1.152802615 1.831194064 1.505622404 14.331473307 3.236364037
1291 1292 1293 1294 1295 1296
1.504015703 0.918603703 3.387154160 1.569899183 0.977793548 2.398637038
1297 1298 1299 1300 1301 1302
0.754769309 1.511483775 2.099961005 0.605162119 0.826379241 1.523521608
1303 1304 1305 1306 1307 1308
5.939658914 1.139733970 1.287540227 5.196741061 2.267269111 0.575780334
1309 1310 1311 1312 1313 1314
2.325079749 1.620954493 2.118303537 0.851296256 2.009079514 0.640133568
1315 1316 1317 1318 1319 1320
1.066779870 7.272057662 1.100840136 0.421673487 1.881294700 2.103936147
1321 1322 1323 1324 1325 1326
7.377278311 0.838708314 0.506791133 17.067229636 1.139693806 0.662331652
1327 1328 1329 1330 1331 1332
0.919979462 2.322778831 1.640543002 0.206907100 1.115740349 2.235118904
1333 1334 1335 1336 1337 1338
1.663213253 0.905114104 0.831023683 2.172395558 1.111954535 4.489645849
1339 1340 1341 1342 1343 1344
0.995081675 2.436281508 0.657676824 1.787664921 3.351395681 1.612586595
1345 1346 1347 1348 1349 1350
1.781981748 0.468076663 7.128135968 4.624616317 6.576320299 2.731723444
1351 1352 1353 1354 1355 1356
2.538065926 1.380584816 1.674770581 0.376534104 2.033100480 1.729611536
1357 1358 1359 1360 1361 1362
0.851627858 8.120079805 0.275248780 0.251880942 1.307773199 0.730735670
1363 1364 1365 1366 1367 1368
7.738330354 1.133302791 0.683460973 0.866208542 1.577769909 1.491947512
1369 1370 1371 1372 1373 1374
5.097276250 0.720323263 0.252366333 3.005786872 0.399123524 4.347426480
1375 1376 1377 1378 1379 1380
4.430553047 1.438405365 0.687959148 0.376427596 1.502687511 2.908464852
1381 1382 1383 1384 1385 1386
11.265189637 1.365334065 0.276984774 0.179086889 1.156748410 0.383819435
1387 1388 1389 1390 1391 1392
0.763139717 5.243811630 0.663041074 1.422956999 0.232870389 1.047557638
1393 1394 1395 1396 1397 1398
0.477040840 1.512772116 0.379697787 1.799870790 0.522280834 0.218461498
1399 1400 1401 1402 1403 1404
1.707732501 8.311554310 0.375063029 0.268035727 0.486389000 0.706756009
1405 1406 1407 1408 1409 1410
0.955475964 1.458513616 4.641145469 0.234941122 0.259327713 0.467351823
1411 1412 1413 1414 1415 1416
0.411097786 0.233729696 0.400667263 1.295192088 0.254846322 0.873692073
1417 1418 1419 1420 1421 1422
2.416639995 0.097816476 2.703787917 0.242167712 0.321221721 0.289828779
1423 1424 1425 1426 1427 1428
0.312007734 1.488977993 1.371394709 4.421120503 0.465171322 0.624281618
1429 1430 1431 1432 1433 1434
0.892621099 0.205692966 1.524350944 0.160595392 0.101412623 0.440878323
1435 1436 1437 1438 1439 1440
0.538717198 0.275866285 0.370263567 0.176380010 0.269113229 0.349016571
1441 1442 1443 1444 1445 1446
0.292362327 0.144956598 3.343414655 0.274252385 0.167749102 0.220536234
1447 1448 1449 1450 1451 1452
0.065701281 1.394635173 0.929074278 0.072143483 0.097813791 0.031431060
1453 1454 1455 1456 1457 1458
0.465377608 0.354467992 0.207211490 3.893555896 0.311050228 1.182554562
1459 1460 1461 1462 1463 1464
0.160220257 1.235713728 0.306843617 0.083388981 0.589378524 0.170969924
1465 1466 1467 1468 1469 1470
0.389061818 0.234484817 1.198254990 0.345126411 0.433388664 1.136063117
1471 1472 1473 1474 1475 1476
0.277253569 0.165234349 0.413952391 0.060965920 0.463632685 0.279323440
1477 1478 1479 1480 1481 1482
0.178740904 0.608231588 1.165940405 0.092988105 0.273045170 0.476987319
1483 1484 1485 1486 1487 1488
1.898260236 0.092985623 0.063696527 0.092586481 0.249602041 0.663119663
1489 1490 1491 1492 1493 1494
0.854601781 0.429373381 1.950506883 0.124555182 0.081314926 0.806168464
1495 1496 1497 1498 1499 1500
0.522084723 0.404541549 0.338077072 0.380606239 0.100254430 0.103678365
1501 1502 1503 1504 1505 1506
0.196169727 0.341594851 0.138055426 0.139520281 0.128788003 0.228731256
1507 1508 1509 1510 1511 1512
0.622548549 1.280566588 0.133375884 0.506488276 0.392629936 0.284890502
1513 1514 1515 1516 1517 1518
0.150858068 0.943160412 0.137605688 0.961521923 1.266867075 2.494393134
1519 1520 1521 1522 1523 1524
0.626367457 1.240457825 0.169012798 0.270656177 0.805144435 1.740524474
1525 1526 1527 1528 1529 1530
0.330651798 0.479788498 1.734986338 0.180931375 0.216806189 0.191038046
1531 1532 1533 1534 1535 1536
0.390723890 0.191615937 0.317080607 2.277178277 0.347280015 0.453375887
1537 1538 1539 1540 1541 1542
0.166467575 0.377844743 0.065396434 1.153987545 0.896402842 1.690653384
1543 1544 1545 1546 1547 1548
0.172803872 1.243620709 0.375006197 0.203228390 0.597077011 0.349388733
1549 1550 1551 1552 1553 1554
0.824509915 0.376931096 0.184249925 4.159987361 2.016117677 3.318246366
1555 1556 1557 1558 1559 1560
0.227623275 0.290017600 3.429547115 0.780847631 0.559635995 0.334879102
1561 1562 1563 1564 1565 1566
0.399124720 1.047429756 4.430326209 0.359189496 0.218101436 0.225104861
1567 1568 1569 1570 1571 1572
0.836938751 0.929730205 0.495647025 2.875490262 0.852946528 1.592857536
1573 1574 1575 1576 1577 1578
1.542083210 3.190227831 1.306558945 1.473870057 1.873548734 1.395309999
1579 1580 1581 1582 1583 1584
0.651269745 2.199385103 1.553040377 1.592713047 1.787644414 0.430347880
1585 1586 1587 1588 1589 1590
2.137576647 0.713131688 0.670234059 1.307594405 1.948486692 3.545707767
1591 1592 1593 1594 1595 1596
4.245699839 2.324657432 0.889793416 1.113009799 4.230292983 3.247328614
1597 1598 1599 1600 1601 1602
5.493215269 0.498181114 2.062123741 5.687264592 6.001447547 5.937284356
1603 1604 1605 1606 1607 1608
0.367299048 5.803944486 5.390946569 0.292413931 1.807992983 2.181125838
1609 1610 1611 1612 1613 1614
2.122746429 0.705273941 2.007617288 2.090396371 2.179073542 1.142648011
1615 1616 1617 1618 1619 1620
1.052817105 7.906706842 0.415693571 1.093394817 4.345094734 1.413812595
1621 1622 1623 1624 1625 1626
1.768407610 3.504028719 4.737532619 0.501881914 4.131064775 1.983806320
1627 1628 1629 1630 1631 1632
1.223845396 1.716690299 0.667166470 5.568970966 0.675369911 0.182988105
1633 1634 1635 1636 1637 1638
1.216619466 0.417116925 2.111909368 0.312646952 1.186899636 0.924124046
1639 1640 1641 1642 1643 1644
0.450775428 1.883836740 0.262484390 0.642639966 1.539980683 0.158651847
1645 1646 1647 1648 1649 1650
0.527284254 0.530828544 0.516677312 0.922215138 0.947761878 0.218331432
1651 1652 1653 1654 1655 1656
3.380128566 0.925738719 0.355272067 2.867916401 1.368055395 0.394143029
1657 1658 1659 1660 1661 1662
0.200096258 0.373242787 0.050628163 0.139098856 0.067334994 0.313399779
1663 1664 1665 1666 1667 1668
0.400311064 1.614149600 0.129502522 1.055914053 0.714030748 1.878940211
1669 1670 1671 1672 1673 1674
0.398534123 0.251017945 0.571831849 0.508485075 1.171186065 2.199443527
1675 1676 1677 1678 1679 1680
0.228788944 0.125205235 0.533695402 -0.538659734 0.386941681 0.297161157
1681 1682 1683 1684 1685 1686
0.386370341 0.068105087 0.398942466 0.026211365 0.771262092 0.761758133
1687 1688 1689 1690 1691 1692
0.314338172 0.484648317 0.886945921 0.092256148 0.483332996 0.287617276
1693 1694 1695 1696 1697 1698
0.268855918 1.080283295 3.093544040 0.090864802 0.121080011 1.199892706
1699 1700 1701 1702 1703 1704
0.752196641 0.840429113 0.834981104 0.100838728 0.090195927 0.477742267
1705 1706 1707 1708 1709 1710
0.166577811 0.241297014 -0.340930702 0.182389627 -0.468093976 0.340814447
1711 1712 1713 1714 1715 1716
0.087036367 0.385905616 0.167032025 1.001012086 0.263162394 5.949135755
1717 1718 1719 1720 1721 1722
1.455883064 0.187841642 0.484268841 0.084720452 0.186127869 0.747963309
1723 1724 1725 1726 1727 1728
0.074357088 0.360888696 0.122486147 0.007637823 0.133595843 0.531517457
1729 1730 1731 1732 1733 1734
0.681009384 6.875788092 2.060721607 0.149519093 1.431519074 0.207191692
1735 1736 1737 1738 1739 1740
-0.290862152 0.383008875 0.139544717 0.218581870 0.451250563 0.277409419
1741 1742 1743 1744 1745 1746
0.103005514 0.104889920 0.450195593 2.743240945 0.199002451 2.057297910
1747 1748 1749 1750 1751 1752
1.793615271 0.079395626 0.654798269 0.866653301 3.135160603 0.485839133
1753 1754 1755 1756 1757 1758
0.689533625 0.184827807 1.968390020 1.412099876 0.361374279 0.260403457
1759 1760 1761 1762 1763 1764
1.065135065 0.058599934 7.490325907 0.918539923 0.102147284 1.040698894
1765 1766 1767 1768 1769 1770
2.346275328 0.903855700 5.077222682 0.352690368 3.655135185 2.098104915
1771 1772 1773 1774 1775 1776
2.427854206 0.393704425 0.330778725 0.438554213 0.857527050 0.401400512
1777 1778 1779 1780 1781 1782
0.253215849 6.278722503 1.364958528 0.549883341 0.599816802 3.677415487
1783 1784 1785 1786 1787 1788
3.665837844 4.603685518 0.604129123 1.528503123 0.798374958 2.261134317
1789 1790 1791 1792 1793 1794
1.469359006 0.186194181 1.081106551 0.388850928 2.426078891 0.739642579
1795 1796 1797 1798 1799 1800
1.932137161 0.777214764 1.235699020 5.021303265 2.082367044 4.986257259
1801 1802 1803 1804 1805 1806
0.893825211 1.727916650 3.318694957 0.953633867 1.148079350 4.434596977
1807 1808 1809 1810 1811 1812
0.577673324 5.844755789 8.007369756 0.700570310 2.978351307 1.867177738
1813 1814 1815 1816 1817 1818
1.588656177 1.321536256 6.510804233 1.401017276 1.258352938 2.644313487
1819 1820 1821 1822 1823 1824
1.610667593 0.638359831 3.071783013 1.466506465 0.198742399 1.220287378
1825 1826 1827 1828 1829 1830
3.349078135 1.724866176 1.393344950 0.863721734 1.009947584 4.546209952
1831 1832 1833 1834 1835 1836
0.626058347 4.135555269 5.885135112 1.244786888 1.198527106 0.848928610
1837 1838 1839 1840 1841 1842
0.510977263 1.291954900 0.928567898 3.624009337 1.958661383 2.977041545
1843 1844 1845 1846 1847 1848
0.669452869 0.740918706 0.419229788 3.688144941 0.725907930 0.603720371
1849 1850 1851 1852 1853 1854
7.037566955 0.777255794 0.628735497 6.341245340 3.152338403 0.630139705
1855 1856 1857 1858 1859 1860
0.546856903 0.588737572 0.198295824 4.965625566 0.186883597 1.340908642
1861 1862 1863 1864 1865 1866
1.101026594 1.860742750 1.386376309 0.674212418 0.088279356 0.659654475
1867 1868 1869 1870 1871 1872
0.618029944 0.326013740 0.182006711 0.541765795 0.149539757 0.354666284
1873 1874 1875 1876 1877 1878
1.027448839 0.166783745 0.528637024 2.039648539 5.622906874 0.433337366
1879 1880 1881 1882 1883 1884
1.307855634 0.458797609 0.350378347 1.127463212 0.260706491 0.545876849
1885 1886 1887 1888 1889 1890
0.909055830 0.965707308 0.425256288 0.438555382 0.278587981 0.116073520
1891 1892 1893 1894 1895 1896
1.522961021 0.549055202 0.379720335 0.339652057 1.047915493 0.387034066 Compare the observed (FCH4_F_gC) versus predicted (PRED.TPVPD):
ggplot() + geom_point( data = train, aes( x=FCH4_F_gC, y= PRED.TPVPD )) +
geom_smooth(method='lm')
summary(lm(data=train, PRED.TPVPD~FCH4_F_gC))
Call:
lm(formula = PRED.TPVPD ~ FCH4_F_gC, data = train)
Residuals:
Min 1Q Median 3Q Max
-2.8501 -0.3881 -0.2159 0.2347 4.1151
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.519090 0.015808 32.84 <2e-16 ***
FCH4_F_gC 0.639029 0.005478 116.65 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.6003 on 1894 degrees of freedom
Multiple R-squared: 0.8778, Adjusted R-squared: 0.8777
F-statistic: 1.361e+04 on 1 and 1894 DF, p-value: < 2.2e-16See how well the model performs on data that was not used to train the model:
test$PRED.TPVPD <- predict(FCH4_F_gC.rf, test)
ggplot() + geom_point( data = test, aes( x=FCH4_F_gC, y= PRED.TPVPD )) +
geom_smooth(method='lm')
summary(lm(data=test, PRED.TPVPD~FCH4_F_gC))
Call:
lm(formula = PRED.TPVPD ~ FCH4_F_gC, data = test)
Residuals:
Min 1Q Median 3Q Max
-2.6482 -0.8116 -0.4033 0.4567 5.9730
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.06617 0.06553 16.27 <2e-16 ***
FCH4_F_gC 0.32516 0.02412 13.48 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.235 on 464 degrees of freedom
Multiple R-squared: 0.2814, Adjusted R-squared: 0.2799
F-statistic: 181.7 on 1 and 464 DF, p-value: < 2.2e-16Final Model Development:
The current model includes only climate variables from the tower. Use either a forward or backward selection method to develop your final model using your own data sets.
The forward selection approach starts with no variables and adds each new variable incrementally, testing for statistical significance, while the backward elimination method begins with a full model and then removes the least statistically significant variables one at a time.
Save your final model and datasets in a .Rdata object for next class where we will perform sensitivity analyses on the models.
save( FCH4_F_gC.rf , file="data/products/FinalModel.RDATA")