Homework 8
Isabel R
11/8/2020
8.7
Refer to Exercises 6.3 and 7.5 which describe a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several tree-based models:
A
Which tree-based regression model gives the optimal resampling and test set performance?
library(AppliedPredictiveModeling)
data(ChemicalManufacturingProcess)
# Reproducible
set.seed(42)
knn_model <- preProcess(ChemicalManufacturingProcess, "knnImpute")
df <- predict(knn_model, ChemicalManufacturingProcess)
df <- df %>%
select_at(vars(-one_of(nearZeroVar(., names = TRUE))))
in_train <- createDataPartition(df$Yield, times = 1, p = 0.8, list = FALSE)
train_df <- df[in_train, ]
test_df <- df[-in_train, ]
pls_model <- train(
Yield ~ ., data = train_df, method = "pls",
center = TRUE,
scale = TRUE,
trControl = trainControl("cv", number = 10),
tuneLength = 25
)
pls_predictions <- predict(pls_model, test_df)
pls_in_sample <- pls_model$results[pls_model$results$ncomp == pls_model$bestTune$ncomp,]
results <- data.frame(t(postResample(pred = pls_predictions, obs = test_df$Yield))) %>%
mutate("In Sample RMSE" = pls_in_sample$RMSE,
"In Sample Rsquared" = pls_in_sample$Rsquared,
"In Sample MAE" = pls_in_sample$MAE,
"Model"= "PLS")
pls_model## Partial Least Squares
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 130, 129, 128, 129, 130, 129, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 0.8824790 0.3779221 0.6711462
## 2 1.1458456 0.4219806 0.7086431
## 3 0.7363066 0.5244517 0.5688553
## 4 0.8235294 0.5298005 0.5933120
## 5 0.9670735 0.4846010 0.6371199
## 6 0.9959036 0.4776684 0.6427478
## 7 0.9119517 0.4986338 0.6200233
## 8 0.9068621 0.5012144 0.6293371
## 9 0.8517370 0.5220166 0.6163795
## 10 0.8919356 0.5062912 0.6332243
## 11 0.9173758 0.4934557 0.6463164
## 12 0.9064125 0.4791526 0.6485663
## 13 0.9255289 0.4542181 0.6620193
## 14 1.0239913 0.4358371 0.6944056
## 15 1.0754710 0.4365214 0.7077991
## 16 1.1110579 0.4269065 0.7135684
## 17 1.1492855 0.4210485 0.7222868
## 18 1.1940639 0.4132534 0.7396357
## 19 1.2271867 0.4079005 0.7494818
## 20 1.2077102 0.4022859 0.7470327
## 21 1.2082648 0.4026711 0.7452969
## 22 1.2669285 0.3987044 0.7634170
## 23 1.3663033 0.3970188 0.7957514
## 24 1.4531634 0.3898475 0.8243034
## 25 1.5624265 0.3820102 0.8612935
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 3.Data was fit against a series of tree based models and caret was used to match the same paramaters in order to determine the preformance against the similar PLS model.
Bagged Tree
set.seed(42)
bagControl = bagControl(fit = ctreeBag$fit, predict = ctreeBag$pred, aggregate = ctreeBag$aggregate)
bag_model <- train(Yield ~ ., data = train_df, method="bag", bagControl = bagControl,
center = TRUE,
scale = TRUE,
trControl = trainControl("cv", number = 10),
tuneLength = 25)## Warning: executing %dopar% sequentially: no parallel backend registeredbag_predictions <- predict(bag_model, test_df)
bag_in_sample <- merge(bag_model$results, bag_model$bestTune)
results <- data.frame(t(postResample(pred = bag_predictions, obs = test_df$Yield))) %>%
mutate("In Sample RMSE" = bag_in_sample$RMSE,
"In Sample Rsquared" = bag_in_sample$Rsquared,
"In Sample MAE" = bag_in_sample$MAE,
"Model"= "Bagged Tree") %>%
rbind(results)
bag_model## Bagged Model
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 129, 130, 129, 130, 130, ...
## Resampling results:
##
## RMSE Rsquared MAE
## 0.7108683 0.4717657 0.5795483
##
## Tuning parameter 'vars' was held constant at a value of 56Boosted Tree
set.seed(42)
gbm_model <- train(Yield ~ ., data = train_df, method="gbm", verbose = FALSE,
trControl = trainControl("cv", number = 10),
tuneLength = 25)
gbm_predictions <- predict(gbm_model, test_df)
gbm_in_sample <- merge(gbm_model$results, gbm_model$bestTune)
results <- data.frame(t(postResample(pred = gbm_predictions, obs = test_df$Yield))) %>%
mutate("In Sample RMSE" = gbm_in_sample$RMSE,
"In Sample Rsquared" = gbm_in_sample$Rsquared,
"In Sample MAE" = gbm_in_sample$MAE,
"Model"= "Boosted Tree") %>%
rbind(results)
gbm_model## Stochastic Gradient Boosting
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 129, 130, 129, 130, 130, ...
## Resampling results across tuning parameters:
##
## interaction.depth n.trees RMSE Rsquared MAE
## 1 50 0.6529787 0.5702357 0.5102064
## 1 100 0.6259745 0.5906080 0.4846082
## 1 150 0.6099166 0.6047640 0.4860877
## 1 200 0.6008357 0.6159204 0.4746704
## 1 250 0.6007583 0.6168513 0.4745437
## 1 300 0.6032872 0.6139154 0.4803398
## 1 350 0.6054569 0.6124108 0.4810323
## 1 400 0.6042296 0.6141087 0.4831893
## 1 450 0.6044401 0.6176478 0.4809852
## 1 500 0.6054335 0.6184590 0.4809517
## 1 550 0.6061891 0.6193797 0.4796327
## 1 600 0.6056039 0.6199645 0.4771155
## 1 650 0.6083802 0.6177853 0.4796680
## 1 700 0.6112744 0.6142575 0.4820985
## 1 750 0.6150272 0.6119709 0.4849456
## 1 800 0.6132495 0.6140022 0.4824066
## 1 850 0.6129022 0.6147128 0.4805281
## 1 900 0.6125136 0.6163699 0.4799557
## 1 950 0.6146513 0.6141389 0.4791453
## 1 1000 0.6158677 0.6136756 0.4810977
## 1 1050 0.6168063 0.6135476 0.4807789
## 1 1100 0.6190710 0.6114224 0.4824817
## 1 1150 0.6178899 0.6133618 0.4805481
## 1 1200 0.6182632 0.6126484 0.4816822
## 1 1250 0.6190874 0.6120263 0.4828504
## 2 50 0.6094282 0.6099501 0.4849066
## 2 100 0.5829629 0.6335127 0.4565230
## 2 150 0.5838239 0.6333416 0.4594031
## 2 200 0.5794192 0.6416762 0.4522288
## 2 250 0.5703484 0.6522903 0.4427181
## 2 300 0.5704290 0.6539219 0.4424843
## 2 350 0.5688872 0.6558810 0.4446840
## 2 400 0.5691133 0.6553808 0.4440911
## 2 450 0.5693332 0.6558510 0.4436964
## 2 500 0.5675464 0.6582781 0.4421581
## 2 550 0.5658889 0.6603078 0.4396887
## 2 600 0.5660413 0.6600440 0.4397280
## 2 650 0.5670866 0.6590858 0.4400525
## 2 700 0.5668798 0.6595438 0.4396349
## 2 750 0.5666876 0.6596874 0.4395221
## 2 800 0.5668211 0.6596993 0.4396469
## 2 850 0.5665125 0.6601553 0.4395041
## 2 900 0.5667711 0.6598908 0.4398854
## 2 950 0.5669461 0.6596749 0.4398769
## 2 1000 0.5668896 0.6597418 0.4397258
## 2 1050 0.5668324 0.6599450 0.4398214
## 2 1100 0.5665139 0.6602574 0.4396333
## 2 1150 0.5666514 0.6601821 0.4397815
## 2 1200 0.5668290 0.6600264 0.4399304
## 2 1250 0.5668629 0.6599759 0.4400462
## 3 50 0.5964119 0.6301569 0.4620894
## 3 100 0.5881904 0.6348098 0.4617679
## 3 150 0.5784579 0.6432397 0.4539545
## 3 200 0.5756343 0.6493645 0.4495719
## 3 250 0.5753652 0.6492650 0.4496511
## 3 300 0.5739679 0.6499200 0.4490757
## 3 350 0.5744236 0.6496053 0.4496752
## 3 400 0.5731088 0.6511659 0.4488762
## 3 450 0.5743237 0.6506949 0.4493729
## 3 500 0.5740582 0.6510667 0.4491126
## 3 550 0.5737973 0.6513584 0.4490028
## 3 600 0.5736313 0.6516578 0.4486977
## 3 650 0.5734303 0.6520309 0.4486500
## 3 700 0.5734154 0.6521713 0.4487097
## 3 750 0.5734448 0.6521538 0.4486533
## 3 800 0.5733412 0.6523101 0.4485162
## 3 850 0.5734461 0.6522107 0.4486230
## 3 900 0.5733855 0.6522783 0.4486340
## 3 950 0.5734464 0.6522402 0.4487534
## 3 1000 0.5734346 0.6522662 0.4487900
## 3 1050 0.5734458 0.6522690 0.4488393
## 3 1100 0.5735230 0.6521787 0.4489117
## 3 1150 0.5734965 0.6522345 0.4488955
## 3 1200 0.5734652 0.6522657 0.4489010
## 3 1250 0.5734822 0.6522470 0.4489104
## 4 50 0.6090419 0.6106657 0.4697679
## 4 100 0.5954252 0.6226990 0.4637289
## 4 150 0.5938504 0.6285557 0.4636849
## 4 200 0.5913247 0.6319587 0.4642710
## 4 250 0.5900504 0.6333095 0.4639411
## 4 300 0.5896414 0.6341805 0.4634896
## 4 350 0.5895137 0.6345933 0.4633461
## 4 400 0.5895641 0.6348717 0.4637587
## 4 450 0.5897582 0.6347995 0.4642484
## 4 500 0.5898016 0.6348652 0.4640096
## 4 550 0.5901324 0.6345240 0.4644099
## 4 600 0.5903075 0.6345846 0.4645382
## 4 650 0.5906552 0.6344835 0.4647610
## 4 700 0.5906150 0.6345581 0.4646932
## 4 750 0.5904937 0.6347022 0.4646343
## 4 800 0.5903896 0.6348218 0.4647111
## 4 850 0.5904498 0.6348500 0.4648654
## 4 900 0.5903898 0.6348947 0.4648645
## 4 950 0.5905029 0.6348003 0.4649357
## 4 1000 0.5904679 0.6348542 0.4649824
## 4 1050 0.5905540 0.6348192 0.4650847
## 4 1100 0.5904812 0.6348914 0.4651039
## 4 1150 0.5905393 0.6348489 0.4651573
## 4 1200 0.5905692 0.6348523 0.4652096
## 4 1250 0.5905788 0.6348482 0.4652295
## 5 50 0.6019146 0.6193173 0.4631369
## 5 100 0.5718941 0.6522686 0.4417011
## 5 150 0.5652677 0.6602092 0.4392289
## 5 200 0.5615494 0.6644658 0.4390921
## 5 250 0.5617600 0.6643786 0.4400462
## 5 300 0.5596646 0.6653772 0.4374645
## 5 350 0.5600163 0.6651947 0.4374533
## 5 400 0.5594723 0.6657756 0.4364679
## 5 450 0.5583903 0.6671558 0.4358012
## 5 500 0.5582863 0.6672867 0.4358657
## 5 550 0.5585848 0.6668710 0.4361121
## 5 600 0.5586374 0.6668762 0.4362419
## 5 650 0.5588214 0.6666570 0.4364302
## 5 700 0.5590060 0.6664883 0.4365978
## 5 750 0.5589198 0.6665628 0.4366476
## 5 800 0.5589112 0.6665959 0.4367284
## 5 850 0.5588357 0.6666270 0.4366683
## 5 900 0.5588534 0.6666288 0.4366668
## 5 950 0.5588659 0.6666386 0.4366916
## 5 1000 0.5588004 0.6667090 0.4366808
## 5 1050 0.5588444 0.6666598 0.4367332
## 5 1100 0.5588288 0.6667027 0.4367230
## 5 1150 0.5587907 0.6667457 0.4366934
## 5 1200 0.5587934 0.6667445 0.4367111
## 5 1250 0.5587895 0.6667425 0.4367281
## 6 50 0.6018491 0.6113981 0.4716015
## 6 100 0.5860809 0.6279896 0.4539058
## 6 150 0.5789599 0.6340675 0.4501756
## 6 200 0.5715997 0.6426798 0.4421709
## 6 250 0.5711400 0.6437785 0.4446479
## 6 300 0.5722309 0.6432605 0.4457324
## 6 350 0.5728877 0.6433494 0.4461208
## 6 400 0.5735122 0.6430660 0.4468629
## 6 450 0.5733378 0.6435084 0.4468686
## 6 500 0.5736811 0.6432701 0.4474261
## 6 550 0.5737036 0.6433590 0.4473096
## 6 600 0.5738540 0.6432025 0.4476653
## 6 650 0.5739788 0.6431127 0.4478362
## 6 700 0.5740895 0.6430439 0.4480447
## 6 750 0.5740191 0.6431101 0.4479443
## 6 800 0.5739330 0.6432375 0.4478419
## 6 850 0.5741192 0.6430959 0.4480611
## 6 900 0.5742059 0.6429815 0.4481779
## 6 950 0.5742488 0.6429632 0.4482300
## 6 1000 0.5742852 0.6429315 0.4482727
## 6 1050 0.5742550 0.6429979 0.4482394
## 6 1100 0.5743812 0.6428550 0.4483377
## 6 1150 0.5744985 0.6427302 0.4484260
## 6 1200 0.5745169 0.6427252 0.4484495
## 6 1250 0.5745410 0.6427004 0.4484620
## 7 50 0.6199541 0.5939358 0.4951611
## 7 100 0.5904056 0.6257145 0.4697978
## 7 150 0.5788458 0.6390945 0.4585648
## 7 200 0.5810272 0.6391831 0.4611296
## 7 250 0.5799441 0.6409543 0.4606679
## 7 300 0.5800624 0.6409086 0.4596577
## 7 350 0.5806014 0.6403463 0.4610040
## 7 400 0.5805843 0.6404279 0.4609606
## 7 450 0.5808030 0.6404105 0.4609477
## 7 500 0.5806460 0.6408355 0.4606353
## 7 550 0.5801929 0.6413834 0.4605745
## 7 600 0.5803194 0.6413844 0.4606553
## 7 650 0.5805963 0.6411193 0.4608334
## 7 700 0.5807950 0.6410027 0.4609297
## 7 750 0.5807957 0.6410385 0.4609906
## 7 800 0.5808788 0.6410234 0.4610401
## 7 850 0.5808231 0.6411133 0.4609822
## 7 900 0.5808365 0.6410813 0.4609990
## 7 950 0.5808931 0.6410494 0.4610153
## 7 1000 0.5809359 0.6410051 0.4610537
## 7 1050 0.5808882 0.6410698 0.4610093
## 7 1100 0.5809232 0.6410468 0.4610294
## 7 1150 0.5809114 0.6410602 0.4610554
## 7 1200 0.5808922 0.6410764 0.4610722
## 7 1250 0.5809613 0.6410143 0.4611178
## 8 50 0.5763016 0.6411581 0.4576852
## 8 100 0.5716689 0.6461974 0.4512790
## 8 150 0.5759381 0.6437704 0.4563453
## 8 200 0.5721415 0.6496414 0.4538074
## 8 250 0.5711192 0.6516050 0.4518189
## 8 300 0.5695114 0.6546120 0.4513573
## 8 350 0.5689287 0.6555732 0.4504089
## 8 400 0.5682439 0.6561605 0.4498706
## 8 450 0.5673344 0.6572600 0.4491474
## 8 500 0.5674381 0.6572173 0.4490904
## 8 550 0.5670931 0.6576854 0.4489108
## 8 600 0.5667498 0.6580690 0.4488511
## 8 650 0.5666761 0.6581715 0.4488999
## 8 700 0.5666796 0.6582255 0.4489354
## 8 750 0.5665660 0.6583684 0.4489615
## 8 800 0.5663936 0.6586085 0.4488358
## 8 850 0.5663429 0.6586493 0.4488768
## 8 900 0.5662484 0.6587890 0.4488474
## 8 950 0.5662163 0.6588234 0.4488634
## 8 1000 0.5662062 0.6588372 0.4488826
## 8 1050 0.5661932 0.6588655 0.4488774
## 8 1100 0.5661859 0.6588721 0.4489328
## 8 1150 0.5661797 0.6589055 0.4489740
## 8 1200 0.5661731 0.6589180 0.4489745
## 8 1250 0.5661145 0.6589825 0.4489516
## 9 50 0.6167604 0.5965443 0.4845607
## 9 100 0.6055422 0.6101877 0.4735896
## 9 150 0.6027718 0.6130671 0.4745875
## 9 200 0.6064713 0.6092537 0.4803259
## 9 250 0.6025144 0.6149249 0.4778493
## 9 300 0.6044546 0.6123663 0.4795388
## 9 350 0.6048698 0.6115446 0.4806716
## 9 400 0.6055499 0.6107397 0.4814121
## 9 450 0.6053731 0.6108421 0.4821199
## 9 500 0.6056554 0.6105514 0.4825302
## 9 550 0.6062967 0.6099543 0.4830778
## 9 600 0.6062888 0.6100437 0.4831844
## 9 650 0.6063035 0.6100249 0.4832666
## 9 700 0.6063524 0.6100332 0.4834070
## 9 750 0.6065921 0.6097913 0.4836381
## 9 800 0.6065971 0.6098266 0.4837327
## 9 850 0.6067575 0.6097239 0.4838410
## 9 900 0.6068762 0.6095239 0.4839607
## 9 950 0.6069309 0.6094834 0.4839398
## 9 1000 0.6070451 0.6093556 0.4840833
## 9 1050 0.6070858 0.6093011 0.4840669
## 9 1100 0.6071045 0.6092895 0.4841145
## 9 1150 0.6071044 0.6093033 0.4841501
## 9 1200 0.6071309 0.6092787 0.4841950
## 9 1250 0.6071436 0.6092698 0.4842299
## 10 50 0.5970134 0.6171065 0.4623301
## 10 100 0.5806102 0.6398879 0.4516936
## 10 150 0.5687076 0.6525233 0.4416021
## 10 200 0.5721478 0.6492513 0.4463209
## 10 250 0.5769418 0.6459730 0.4509770
## 10 300 0.5781494 0.6456177 0.4515166
## 10 350 0.5799840 0.6438356 0.4534752
## 10 400 0.5799262 0.6437909 0.4532906
## 10 450 0.5804882 0.6433379 0.4535657
## 10 500 0.5809207 0.6427982 0.4541454
## 10 550 0.5811243 0.6425842 0.4543062
## 10 600 0.5813681 0.6424302 0.4544117
## 10 650 0.5812722 0.6425518 0.4544515
## 10 700 0.5814412 0.6423282 0.4544904
## 10 750 0.5815164 0.6422026 0.4545465
## 10 800 0.5816406 0.6419893 0.4546413
## 10 850 0.5817970 0.6417711 0.4546952
## 10 900 0.5818765 0.6416974 0.4547529
## 10 950 0.5819495 0.6416149 0.4547905
## 10 1000 0.5819670 0.6416085 0.4547866
## 10 1050 0.5820416 0.6415048 0.4548642
## 10 1100 0.5821291 0.6413995 0.4549316
## 10 1150 0.5821326 0.6413981 0.4549135
## 10 1200 0.5821708 0.6413569 0.4549586
## 10 1250 0.5821957 0.6413248 0.4549680
## 11 50 0.6007956 0.6191324 0.4784111
## 11 100 0.5796223 0.6436577 0.4611684
## 11 150 0.5734513 0.6497914 0.4595051
## 11 200 0.5760920 0.6478978 0.4603030
## 11 250 0.5764815 0.6483934 0.4592201
## 11 300 0.5770282 0.6479640 0.4592198
## 11 350 0.5763090 0.6487221 0.4583147
## 11 400 0.5758337 0.6494612 0.4581384
## 11 450 0.5758699 0.6496084 0.4581600
## 11 500 0.5754348 0.6501079 0.4575764
## 11 550 0.5753623 0.6503882 0.4575615
## 11 600 0.5751066 0.6507755 0.4575770
## 11 650 0.5750791 0.6508957 0.4575429
## 11 700 0.5751269 0.6508885 0.4574905
## 11 750 0.5750977 0.6508783 0.4575510
## 11 800 0.5751921 0.6507287 0.4576147
## 11 850 0.5752069 0.6507458 0.4576468
## 11 900 0.5752048 0.6507309 0.4576749
## 11 950 0.5751624 0.6507659 0.4575584
## 11 1000 0.5751346 0.6508012 0.4575377
## 11 1050 0.5751284 0.6508137 0.4575096
## 11 1100 0.5751163 0.6508334 0.4575075
## 11 1150 0.5751286 0.6508189 0.4575395
## 11 1200 0.5750890 0.6508693 0.4575222
## 11 1250 0.5750407 0.6509139 0.4574603
## 12 50 0.6131404 0.6008363 0.4788888
## 12 100 0.5936990 0.6206144 0.4563439
## 12 150 0.5917700 0.6239359 0.4570861
## 12 200 0.5894059 0.6276284 0.4536889
## 12 250 0.5896794 0.6286413 0.4545724
## 12 300 0.5884641 0.6307350 0.4541598
## 12 350 0.5885899 0.6311055 0.4538239
## 12 400 0.5878622 0.6319971 0.4533814
## 12 450 0.5876460 0.6325633 0.4531581
## 12 500 0.5873139 0.6327759 0.4527693
## 12 550 0.5872261 0.6329262 0.4530022
## 12 600 0.5875665 0.6325250 0.4532315
## 12 650 0.5876798 0.6324167 0.4532977
## 12 700 0.5876485 0.6325664 0.4532492
## 12 750 0.5876823 0.6325857 0.4532712
## 12 800 0.5879170 0.6323502 0.4534515
## 12 850 0.5879436 0.6323289 0.4534417
## 12 900 0.5880458 0.6322095 0.4534969
## 12 950 0.5880053 0.6322652 0.4534268
## 12 1000 0.5880199 0.6322607 0.4534472
## 12 1050 0.5880897 0.6321977 0.4535073
## 12 1100 0.5880935 0.6321941 0.4534805
## 12 1150 0.5880697 0.6322349 0.4534862
## 12 1200 0.5881165 0.6321864 0.4535333
## 12 1250 0.5881200 0.6321888 0.4535375
## 13 50 0.5973542 0.6314045 0.4668008
## 13 100 0.5777799 0.6451084 0.4518852
## 13 150 0.5764224 0.6467808 0.4476571
## 13 200 0.5730664 0.6505212 0.4451696
## 13 250 0.5743130 0.6495475 0.4462130
## 13 300 0.5760493 0.6476727 0.4459779
## 13 350 0.5766260 0.6469370 0.4465765
## 13 400 0.5770238 0.6468019 0.4468128
## 13 450 0.5776063 0.6459700 0.4475754
## 13 500 0.5779502 0.6456783 0.4478369
## 13 550 0.5779233 0.6457420 0.4477710
## 13 600 0.5781181 0.6454777 0.4481283
## 13 650 0.5782368 0.6453590 0.4482780
## 13 700 0.5783686 0.6452265 0.4484776
## 13 750 0.5784837 0.6450636 0.4487266
## 13 800 0.5785037 0.6450326 0.4487840
## 13 850 0.5786308 0.6449255 0.4489184
## 13 900 0.5786399 0.6448911 0.4490071
## 13 950 0.5786643 0.6448690 0.4490676
## 13 1000 0.5787736 0.6447447 0.4491924
## 13 1050 0.5787891 0.6447278 0.4491872
## 13 1100 0.5788049 0.6447156 0.4492184
## 13 1150 0.5788276 0.6446876 0.4492568
## 13 1200 0.5788448 0.6446723 0.4492837
## 13 1250 0.5788611 0.6446606 0.4493125
## 14 50 0.5968688 0.6288067 0.4721340
## 14 100 0.5788231 0.6442392 0.4626092
## 14 150 0.5772605 0.6493066 0.4581304
## 14 200 0.5767852 0.6504154 0.4555545
## 14 250 0.5763805 0.6510261 0.4554558
## 14 300 0.5773394 0.6501146 0.4569615
## 14 350 0.5771256 0.6504539 0.4561920
## 14 400 0.5774954 0.6500725 0.4563451
## 14 450 0.5778210 0.6498560 0.4567000
## 14 500 0.5773189 0.6507293 0.4564541
## 14 550 0.5774635 0.6506929 0.4566913
## 14 600 0.5772649 0.6509344 0.4564884
## 14 650 0.5769523 0.6513005 0.4562758
## 14 700 0.5768395 0.6514243 0.4561250
## 14 750 0.5767784 0.6515344 0.4562432
## 14 800 0.5767428 0.6516513 0.4561898
## 14 850 0.5767717 0.6516118 0.4562955
## 14 900 0.5767780 0.6516089 0.4563007
## 14 950 0.5767695 0.6515845 0.4563348
## 14 1000 0.5768071 0.6515531 0.4563581
## 14 1050 0.5767456 0.6516372 0.4563169
## 14 1100 0.5767604 0.6516236 0.4563322
## 14 1150 0.5767172 0.6516701 0.4562795
## 14 1200 0.5766858 0.6517006 0.4562711
## 14 1250 0.5766666 0.6517396 0.4562572
## 15 50 0.5984904 0.6144377 0.4802185
## 15 100 0.5843983 0.6293893 0.4687758
## 15 150 0.5763789 0.6365162 0.4607338
## 15 200 0.5742064 0.6397660 0.4613239
## 15 250 0.5734581 0.6414163 0.4627411
## 15 300 0.5732190 0.6423065 0.4629835
## 15 350 0.5725697 0.6433780 0.4630833
## 15 400 0.5718269 0.6444742 0.4627995
## 15 450 0.5718025 0.6447416 0.4631744
## 15 500 0.5718086 0.6446100 0.4633308
## 15 550 0.5719365 0.6446516 0.4634589
## 15 600 0.5718646 0.6447368 0.4634482
## 15 650 0.5715927 0.6451576 0.4633120
## 15 700 0.5714562 0.6453500 0.4633540
## 15 750 0.5714828 0.6453266 0.4634053
## 15 800 0.5716535 0.6452634 0.4636229
## 15 850 0.5716339 0.6453263 0.4636592
## 15 900 0.5715742 0.6454348 0.4636541
## 15 950 0.5715357 0.6455050 0.4637054
## 15 1000 0.5715801 0.6454600 0.4637473
## 15 1050 0.5715296 0.6455215 0.4636962
## 15 1100 0.5714731 0.6456070 0.4636752
## 15 1150 0.5714961 0.6455984 0.4637025
## 15 1200 0.5714283 0.6456968 0.4636602
## 15 1250 0.5714074 0.6457320 0.4636621
## 16 50 0.5845598 0.6367314 0.4522037
## 16 100 0.5744352 0.6415904 0.4402636
## 16 150 0.5712235 0.6450458 0.4374079
## 16 200 0.5706646 0.6461059 0.4395498
## 16 250 0.5743295 0.6426962 0.4431993
## 16 300 0.5732029 0.6443089 0.4421847
## 16 350 0.5740836 0.6434172 0.4426110
## 16 400 0.5733769 0.6441363 0.4427320
## 16 450 0.5731878 0.6440416 0.4426181
## 16 500 0.5733640 0.6440319 0.4428262
## 16 550 0.5734077 0.6440675 0.4428775
## 16 600 0.5733253 0.6442436 0.4429795
## 16 650 0.5731203 0.6444578 0.4429265
## 16 700 0.5732675 0.6444389 0.4430143
## 16 750 0.5731228 0.6445695 0.4428747
## 16 800 0.5732311 0.6445276 0.4431213
## 16 850 0.5732604 0.6445157 0.4432044
## 16 900 0.5732764 0.6444899 0.4432273
## 16 950 0.5731499 0.6446022 0.4431385
## 16 1000 0.5732311 0.6445054 0.4432125
## 16 1050 0.5732592 0.6445116 0.4432604
## 16 1100 0.5732651 0.6444995 0.4432389
## 16 1150 0.5732933 0.6444539 0.4433079
## 16 1200 0.5733533 0.6443725 0.4433261
## 16 1250 0.5733543 0.6443782 0.4433468
## 17 50 0.5895081 0.6221239 0.4584180
## 17 100 0.5598563 0.6545783 0.4403988
## 17 150 0.5588101 0.6549230 0.4345365
## 17 200 0.5585532 0.6557803 0.4346063
## 17 250 0.5560925 0.6593080 0.4346842
## 17 300 0.5583117 0.6567464 0.4355277
## 17 350 0.5589839 0.6564977 0.4365358
## 17 400 0.5585887 0.6567415 0.4358248
## 17 450 0.5579936 0.6581041 0.4363710
## 17 500 0.5576780 0.6586560 0.4363073
## 17 550 0.5580179 0.6583182 0.4369656
## 17 600 0.5576574 0.6586239 0.4365961
## 17 650 0.5573910 0.6588929 0.4364291
## 17 700 0.5572706 0.6591183 0.4364193
## 17 750 0.5572105 0.6592226 0.4363436
## 17 800 0.5572080 0.6592986 0.4364028
## 17 850 0.5571794 0.6593780 0.4364372
## 17 900 0.5572748 0.6592692 0.4364702
## 17 950 0.5572903 0.6592425 0.4365164
## 17 1000 0.5573969 0.6591232 0.4366330
## 17 1050 0.5573523 0.6592176 0.4366466
## 17 1100 0.5573181 0.6592760 0.4366223
## 17 1150 0.5572999 0.6593232 0.4366195
## 17 1200 0.5573417 0.6592814 0.4366678
## 17 1250 0.5573217 0.6593154 0.4366610
## 18 50 0.5947040 0.6238031 0.4720874
## 18 100 0.5618769 0.6575285 0.4478613
## 18 150 0.5582539 0.6634045 0.4444225
## 18 200 0.5585195 0.6646903 0.4463124
## 18 250 0.5632000 0.6587717 0.4503918
## 18 300 0.5628079 0.6600173 0.4498614
## 18 350 0.5627775 0.6601182 0.4500888
## 18 400 0.5624382 0.6605836 0.4498481
## 18 450 0.5630086 0.6602329 0.4503341
## 18 500 0.5625749 0.6607663 0.4500855
## 18 550 0.5625871 0.6610884 0.4501850
## 18 600 0.5627920 0.6609869 0.4503990
## 18 650 0.5627910 0.6610874 0.4501716
## 18 700 0.5629293 0.6609290 0.4501911
## 18 750 0.5629849 0.6608811 0.4504471
## 18 800 0.5631089 0.6607372 0.4505341
## 18 850 0.5632879 0.6605472 0.4507397
## 18 900 0.5634311 0.6604467 0.4508773
## 18 950 0.5635290 0.6603438 0.4509308
## 18 1000 0.5636527 0.6602004 0.4510463
## 18 1050 0.5637119 0.6601604 0.4510915
## 18 1100 0.5637187 0.6601415 0.4510943
## 18 1150 0.5637947 0.6600683 0.4511788
## 18 1200 0.5637589 0.6601116 0.4511481
## 18 1250 0.5638153 0.6600584 0.4511662
## 19 50 0.6044116 0.6084186 0.4816248
## 19 100 0.5884591 0.6259706 0.4666916
## 19 150 0.5827201 0.6350315 0.4611196
## 19 200 0.5796750 0.6394943 0.4593404
## 19 250 0.5791659 0.6405009 0.4592163
## 19 300 0.5789062 0.6406001 0.4594678
## 19 350 0.5792869 0.6402798 0.4606605
## 19 400 0.5798080 0.6398658 0.4610008
## 19 450 0.5798865 0.6398399 0.4611347
## 19 500 0.5796314 0.6402471 0.4607525
## 19 550 0.5799321 0.6402072 0.4611976
## 19 600 0.5798439 0.6403842 0.4609075
## 19 650 0.5798640 0.6404004 0.4609272
## 19 700 0.5799447 0.6403739 0.4610496
## 19 750 0.5801595 0.6401531 0.4611883
## 19 800 0.5800469 0.6402696 0.4610050
## 19 850 0.5801075 0.6402613 0.4611237
## 19 900 0.5801117 0.6402842 0.4610773
## 19 950 0.5800802 0.6403546 0.4611275
## 19 1000 0.5801482 0.6402883 0.4612403
## 19 1050 0.5800854 0.6403723 0.4612398
## 19 1100 0.5800651 0.6404008 0.4612760
## 19 1150 0.5800433 0.6404542 0.4612893
## 19 1200 0.5800546 0.6404666 0.4613544
## 19 1250 0.5800492 0.6404551 0.4613605
## 20 50 0.6228995 0.5928646 0.4924395
## 20 100 0.6009344 0.6133889 0.4698906
## 20 150 0.5921427 0.6222307 0.4687025
## 20 200 0.5883624 0.6284961 0.4663482
## 20 250 0.5858482 0.6313708 0.4644570
## 20 300 0.5854396 0.6320113 0.4637267
## 20 350 0.5850790 0.6320588 0.4644387
## 20 400 0.5844287 0.6334042 0.4640988
## 20 450 0.5848621 0.6327404 0.4649257
## 20 500 0.5849726 0.6328714 0.4651716
## 20 550 0.5848708 0.6330092 0.4652380
## 20 600 0.5851218 0.6326644 0.4654536
## 20 650 0.5853962 0.6324062 0.4658945
## 20 700 0.5854769 0.6323859 0.4659694
## 20 750 0.5854284 0.6324044 0.4659240
## 20 800 0.5856137 0.6322070 0.4661607
## 20 850 0.5858048 0.6320155 0.4663029
## 20 900 0.5857902 0.6321231 0.4662757
## 20 950 0.5858142 0.6320788 0.4662986
## 20 1000 0.5859219 0.6319654 0.4663609
## 20 1050 0.5859580 0.6319822 0.4663748
## 20 1100 0.5860260 0.6319045 0.4664469
## 20 1150 0.5861297 0.6317874 0.4665715
## 20 1200 0.5861911 0.6317411 0.4666073
## 20 1250 0.5861864 0.6317425 0.4666093
## 21 50 0.6164913 0.5907092 0.4901770
## 21 100 0.5954901 0.6129761 0.4706662
## 21 150 0.5863253 0.6208539 0.4555843
## 21 200 0.5880713 0.6212227 0.4594044
## 21 250 0.5878737 0.6214425 0.4575625
## 21 300 0.5863312 0.6232168 0.4574849
## 21 350 0.5874788 0.6219323 0.4588074
## 21 400 0.5879728 0.6216350 0.4597942
## 21 450 0.5875109 0.6219386 0.4597765
## 21 500 0.5874788 0.6220713 0.4599140
## 21 550 0.5875259 0.6220454 0.4600137
## 21 600 0.5878106 0.6216276 0.4602113
## 21 650 0.5880222 0.6214441 0.4604127
## 21 700 0.5881523 0.6212943 0.4605623
## 21 750 0.5882456 0.6212172 0.4608117
## 21 800 0.5883022 0.6211843 0.4609491
## 21 850 0.5883325 0.6211449 0.4610155
## 21 900 0.5884684 0.6210333 0.4611763
## 21 950 0.5884012 0.6211157 0.4612100
## 21 1000 0.5884770 0.6210339 0.4613186
## 21 1050 0.5885063 0.6210078 0.4613713
## 21 1100 0.5885325 0.6209880 0.4613699
## 21 1150 0.5885974 0.6209189 0.4614618
## 21 1200 0.5885644 0.6209809 0.4614654
## 21 1250 0.5885900 0.6209606 0.4615024
## 22 50 0.5793334 0.6434253 0.4720771
## 22 100 0.5531895 0.6722105 0.4488228
## 22 150 0.5488134 0.6781810 0.4432762
## 22 200 0.5528279 0.6739731 0.4470342
## 22 250 0.5495858 0.6780192 0.4443609
## 22 300 0.5493595 0.6789946 0.4426837
## 22 350 0.5502390 0.6779176 0.4441018
## 22 400 0.5515463 0.6764037 0.4447485
## 22 450 0.5512482 0.6765891 0.4447522
## 22 500 0.5507834 0.6775022 0.4440172
## 22 550 0.5508227 0.6774242 0.4439655
## 22 600 0.5512931 0.6770631 0.4443603
## 22 650 0.5514199 0.6769012 0.4444753
## 22 700 0.5513916 0.6769650 0.4444461
## 22 750 0.5512924 0.6771605 0.4443759
## 22 800 0.5514432 0.6769484 0.4444075
## 22 850 0.5515481 0.6768914 0.4445889
## 22 900 0.5516099 0.6768201 0.4446169
## 22 950 0.5516678 0.6767554 0.4446328
## 22 1000 0.5516392 0.6768049 0.4446332
## 22 1050 0.5516028 0.6768805 0.4446273
## 22 1100 0.5515640 0.6769180 0.4445721
## 22 1150 0.5515192 0.6769851 0.4445507
## 22 1200 0.5515205 0.6769964 0.4445526
## 22 1250 0.5515608 0.6769583 0.4445800
## 23 50 0.6177465 0.5985763 0.4831558
## 23 100 0.5937322 0.6267084 0.4623962
## 23 150 0.6002425 0.6181106 0.4665577
## 23 200 0.5959912 0.6256254 0.4651166
## 23 250 0.5976436 0.6234317 0.4671482
## 23 300 0.5983712 0.6239639 0.4676933
## 23 350 0.5969445 0.6255335 0.4662105
## 23 400 0.5972253 0.6253612 0.4668455
## 23 450 0.5973307 0.6254383 0.4672388
## 23 500 0.5972284 0.6255382 0.4674735
## 23 550 0.5969328 0.6258570 0.4674252
## 23 600 0.5968363 0.6260482 0.4676239
## 23 650 0.5971095 0.6257743 0.4679849
## 23 700 0.5971499 0.6257096 0.4681145
## 23 750 0.5972320 0.6256212 0.4682903
## 23 800 0.5973860 0.6254261 0.4684687
## 23 850 0.5974018 0.6254181 0.4685405
## 23 900 0.5974908 0.6253233 0.4686105
## 23 950 0.5975844 0.6252652 0.4687825
## 23 1000 0.5976395 0.6251821 0.4688300
## 23 1050 0.5976240 0.6251807 0.4688325
## 23 1100 0.5976592 0.6251428 0.4689031
## 23 1150 0.5976260 0.6251732 0.4689478
## 23 1200 0.5976233 0.6251752 0.4689585
## 23 1250 0.5976330 0.6251617 0.4689663
## 24 50 0.6308858 0.5776525 0.4972108
## 24 100 0.6046511 0.6104362 0.4799937
## 24 150 0.5995390 0.6177781 0.4799586
## 24 200 0.5978228 0.6194035 0.4813903
## 24 250 0.5976961 0.6207397 0.4819837
## 24 300 0.5980968 0.6207244 0.4820177
## 24 350 0.5978139 0.6210982 0.4823949
## 24 400 0.5976232 0.6215346 0.4820746
## 24 450 0.5987533 0.6205269 0.4830158
## 24 500 0.5986787 0.6208225 0.4832110
## 24 550 0.5988664 0.6206171 0.4833016
## 24 600 0.5987075 0.6208757 0.4833147
## 24 650 0.5988573 0.6207512 0.4835311
## 24 700 0.5989057 0.6207085 0.4837492
## 24 750 0.5989222 0.6207121 0.4837938
## 24 800 0.5988335 0.6208467 0.4838003
## 24 850 0.5989063 0.6208014 0.4838899
## 24 900 0.5988832 0.6208370 0.4839103
## 24 950 0.5988937 0.6208618 0.4839207
## 24 1000 0.5989267 0.6208511 0.4839856
## 24 1050 0.5989133 0.6208810 0.4839989
## 24 1100 0.5988945 0.6209149 0.4839993
## 24 1150 0.5989049 0.6209117 0.4840228
## 24 1200 0.5989236 0.6209006 0.4840094
## 24 1250 0.5988978 0.6209304 0.4840227
## 25 50 0.5967884 0.6181418 0.4722004
## 25 100 0.5761255 0.6368342 0.4559817
## 25 150 0.5671111 0.6485046 0.4470742
## 25 200 0.5646577 0.6522515 0.4440080
## 25 250 0.5639557 0.6540791 0.4446264
## 25 300 0.5643908 0.6541095 0.4458751
## 25 350 0.5645825 0.6548046 0.4472483
## 25 400 0.5646346 0.6549075 0.4471908
## 25 450 0.5657594 0.6538895 0.4484154
## 25 500 0.5667385 0.6529176 0.4492661
## 25 550 0.5667006 0.6530126 0.4490882
## 25 600 0.5669719 0.6528129 0.4495295
## 25 650 0.5668937 0.6530017 0.4495543
## 25 700 0.5670696 0.6529264 0.4496043
## 25 750 0.5671854 0.6528701 0.4498735
## 25 800 0.5671214 0.6529534 0.4498998
## 25 850 0.5671270 0.6529565 0.4498827
## 25 900 0.5671469 0.6529419 0.4498852
## 25 950 0.5671453 0.6529481 0.4499353
## 25 1000 0.5671302 0.6530179 0.4499500
## 25 1050 0.5671623 0.6529877 0.4499665
## 25 1100 0.5671858 0.6529748 0.4499741
## 25 1150 0.5672006 0.6529891 0.4499975
## 25 1200 0.5672042 0.6530004 0.4500351
## 25 1250 0.5672439 0.6529631 0.4500798
##
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
##
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 150, interaction.depth =
## 22, shrinkage = 0.1 and n.minobsinnode = 10.Random Forest
set.seed(42)
rf_model <- train(Yield ~ ., data = train_df, method = "ranger",
scale = TRUE,
trControl = trainControl("cv", number = 10),
tuneLength = 25)
rf_predictions <- predict(rf_model, test_df)
rf_in_sample <- merge(rf_model$results, rf_model$bestTune)
results <- data.frame(t(postResample(pred = rf_predictions, obs = test_df$Yield))) %>%
mutate("In Sample RMSE" = rf_in_sample$RMSE,
"In Sample Rsquared" = rf_in_sample$Rsquared,
"In Sample MAE" = rf_in_sample$MAE,
"Model"= "Random Forest") %>%
rbind(results)
rf_model## Random Forest
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 129, 130, 129, 130, 130, ...
## Resampling results across tuning parameters:
##
## mtry splitrule RMSE Rsquared MAE
## 2 variance 0.6497858 0.6438354 0.5345934
## 2 extratrees 0.7107005 0.5913499 0.5896222
## 4 variance 0.6171845 0.6644030 0.5076339
## 4 extratrees 0.6635219 0.6303318 0.5515317
## 6 variance 0.6040398 0.6653486 0.4934050
## 6 extratrees 0.6438055 0.6420607 0.5349385
## 8 variance 0.5955708 0.6700645 0.4806501
## 8 extratrees 0.6262944 0.6656202 0.5207843
## 11 variance 0.5898819 0.6693959 0.4744251
## 11 extratrees 0.6146979 0.6750476 0.5068688
## 13 variance 0.5903434 0.6629506 0.4755268
## 13 extratrees 0.6078146 0.6769346 0.5042883
## 15 variance 0.5875867 0.6652769 0.4701072
## 15 extratrees 0.6046625 0.6756825 0.4957882
## 17 variance 0.5840520 0.6641550 0.4649468
## 17 extratrees 0.6063868 0.6668625 0.4976930
## 20 variance 0.5890784 0.6532341 0.4674457
## 20 extratrees 0.5946979 0.6841960 0.4852246
## 22 variance 0.5879453 0.6542423 0.4622086
## 22 extratrees 0.5963783 0.6790233 0.4886738
## 24 variance 0.5858153 0.6551814 0.4636970
## 24 extratrees 0.5971505 0.6726166 0.4875783
## 26 variance 0.5880400 0.6496644 0.4626234
## 26 extratrees 0.5981009 0.6718938 0.4871614
## 29 variance 0.5895010 0.6475055 0.4643408
## 29 extratrees 0.5967249 0.6668901 0.4851825
## 31 variance 0.5951690 0.6376674 0.4677508
## 31 extratrees 0.5976439 0.6635536 0.4847677
## 33 variance 0.5928874 0.6411724 0.4669791
## 33 extratrees 0.5924849 0.6768113 0.4838468
## 35 variance 0.5867051 0.6489605 0.4611046
## 35 extratrees 0.5929398 0.6699430 0.4837254
## 38 variance 0.6004208 0.6315682 0.4740340
## 38 extratrees 0.5968329 0.6645022 0.4862917
## 40 variance 0.5964688 0.6348283 0.4651849
## 40 extratrees 0.5939651 0.6651959 0.4825585
## 42 variance 0.5923281 0.6392379 0.4630702
## 42 extratrees 0.5927962 0.6625781 0.4817914
## 44 variance 0.5956628 0.6331507 0.4641829
## 44 extratrees 0.5925441 0.6628893 0.4776745
## 47 variance 0.6043288 0.6220066 0.4688005
## 47 extratrees 0.5964637 0.6564644 0.4838434
## 49 variance 0.6009236 0.6281433 0.4683679
## 49 extratrees 0.5942796 0.6633846 0.4830116
## 51 variance 0.6009500 0.6258047 0.4727813
## 51 extratrees 0.5895383 0.6664917 0.4784356
## 53 variance 0.6023795 0.6254545 0.4713244
## 53 extratrees 0.5917877 0.6623634 0.4786651
## 56 variance 0.6031440 0.6269611 0.4686278
## 56 extratrees 0.5920145 0.6621812 0.4794944
##
## Tuning parameter 'min.node.size' was held constant at a value of 5
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were mtry = 17, splitrule = variance
## and min.node.size = 5.Conditional Inference Random Forest
set.seed(42)
crf_model <- train(Yield ~ ., data = train_df, method = "cforest",
trControl = trainControl("cv", number = 10),
tuneLength = 25)
crf_predictions <- predict(crf_model, test_df)
crf_in_sample <- merge(crf_model$results, crf_model$bestTune)
results <- data.frame(t(postResample(pred = crf_predictions, obs = test_df$Yield))) %>%
mutate("In Sample RMSE" = crf_in_sample$RMSE,
"In Sample Rsquared" = crf_in_sample$Rsquared,
"In Sample MAE" = crf_in_sample$MAE,
"Model"= "Conditional Random Forest") %>%
rbind(results)
crf_model## Conditional Inference Random Forest
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 129, 130, 129, 130, 130, ...
## Resampling results across tuning parameters:
##
## mtry RMSE Rsquared MAE
## 2 0.7898970 0.5184391 0.6525080
## 4 0.7046135 0.5646303 0.5780069
## 6 0.6725218 0.5887280 0.5500396
## 8 0.6602660 0.5914750 0.5383059
## 11 0.6542383 0.5867416 0.5291135
## 13 0.6475067 0.5904548 0.5256915
## 15 0.6498053 0.5834067 0.5264809
## 17 0.6515475 0.5761058 0.5269520
## 20 0.6511948 0.5722409 0.5237739
## 22 0.6461205 0.5776471 0.5218458
## 24 0.6476044 0.5719672 0.5225875
## 26 0.6514498 0.5667591 0.5257020
## 29 0.6503738 0.5666119 0.5229556
## 31 0.6513746 0.5628461 0.5228537
## 33 0.6531447 0.5604409 0.5239990
## 35 0.6532619 0.5584804 0.5256739
## 38 0.6564974 0.5523390 0.5270321
## 40 0.6590074 0.5488009 0.5304481
## 42 0.6557320 0.5530412 0.5254378
## 44 0.6584156 0.5500981 0.5268187
## 47 0.6578192 0.5469014 0.5257655
## 49 0.6625088 0.5418367 0.5306678
## 51 0.6614085 0.5431193 0.5296342
## 53 0.6631957 0.5386486 0.5286492
## 56 0.6677752 0.5318607 0.5336618
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 22.Results
| RMSE | Rsquared | MAE | In Sample RMSE | In Sample Rsquared | In Sample MAE | Model |
|---|---|---|---|---|---|---|
| 0.6192577 | 0.6771122 | 0.5059984 | 0.7363066 | 0.5244517 | 0.5688553 | PLS |
| 0.6319866 | 0.7554852 | 0.4616119 | 0.5840520 | 0.6641550 | 0.4649468 | Random Forest |
| 0.6569218 | 0.6667230 | 0.4849000 | 0.5488134 | 0.6781810 | 0.4432762 | Boosted Tree |
| 0.6934245 | 0.6790718 | 0.5093532 | 0.6461205 | 0.5776471 | 0.5218458 | Conditional Random Forest |
| 0.7166524 | 0.6160449 | 0.5447146 | 0.7108683 | 0.4717657 | 0.5795483 | Bagged Tree |
All tree model’s fit the in sample data better than the PLS model but may overfit the data as the RMSE on the test set is higher for the random forest and boosted tree. The boosted tree model is the only on that out preformed the PLS on the test set.
B
Which predictors are most important in the optimal tree-based regression model? Do either the biological or process variables dominate the list? How do the top 10 important predictors compare to the top 10 predictors for the optimal linear and nonlinear models?
The top ten predictors are as follows
## loess r-squared variable importance
##
## only 20 most important variables shown (out of 56)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess13 93.82
## ManufacturingProcess09 89.93
## ManufacturingProcess17 88.20
## BiologicalMaterial06 82.61
## BiologicalMaterial03 79.44
## ManufacturingProcess36 73.85
## BiologicalMaterial12 72.36
## ManufacturingProcess06 69.00
## ManufacturingProcess11 62.34
## ManufacturingProcess31 56.39
## BiologicalMaterial02 50.34
## BiologicalMaterial11 48.53
## BiologicalMaterial09 44.76
## ManufacturingProcess30 41.87
## BiologicalMaterial08 40.24
## ManufacturingProcess29 38.54
## ManufacturingProcess33 38.16
## BiologicalMaterial04 36.92
## ManufacturingProcess25 36.83The manufacturing process variables are dominant as the same variables are found in both lists but in different orders of importance.
## pls variable importance
##
## only 20 most important variables shown (out of 56)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess09 88.04
## ManufacturingProcess36 82.20
## ManufacturingProcess13 82.11
## ManufacturingProcess17 80.25
## ManufacturingProcess06 59.06
## ManufacturingProcess11 55.93
## BiologicalMaterial02 55.46
## BiologicalMaterial06 54.64
## BiologicalMaterial03 54.50
## ManufacturingProcess33 53.91
## ManufacturingProcess12 52.04
## BiologicalMaterial08 49.76
## BiologicalMaterial12 47.40
## ManufacturingProcess34 45.47
## BiologicalMaterial11 45.05
## BiologicalMaterial01 44.18
## BiologicalMaterial04 42.95
## ManufacturingProcess04 39.94
## ManufacturingProcess28 36.61C
Plot the optimal single tree with the distribution of yield in the terminal nodes. Does this view of the data provide additional knowledge about the biological or process predictors and their relationship with yield?
set.seed(1)
cart_model <- train(Yield ~ ., data = train_df, method = "rpart",
trControl = trainControl("cv", number = 10),
tuneLength = 25)## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
This function indicates if you want to maximize yield, then the manufacturing process 32 must be greater than or equal to 0.19, process 13 < -0.85 and the Biological material 3 >= 0.49 which will produce the greatest yield.