18  Results

Objectives

This chapter presents the results obtained with the classifier trained in Chapter 17.

library(tidyverse)
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.1     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(caret)
Loading required package: lattice

Attaching package: 'caret'

The following object is masked from 'package:purrr':

    lift

First, we load the estimated models from Chapter 17.

load("../data/out/estim/v3/grid_search_rf_sah.rda")
load("../data/out/estim/v3/grid_search_xgb_sah.rda")
load("../data/out/estim/v3/svm_model_sah.rda")
load("../data/out/estim/v3/glmnet_model_sah.rda")

18.1 Grid Search Results

18.1.1 Summary

The summary of the grid search process can be displayed. The chosen hyperparameters are given at the end of each summary.

grid_search_rf
Random Forest 

4305 samples
  91 predictor
   2 classes: 'Not_D_and_inf_Q1', 'Not_D_and_sup_Q1' 

No pre-processing
Resampling: Cross-Validated (5 fold, repeated 10 times) 
Summary of sample sizes: 3445, 3444, 3444, 3444, 3443, 3444, ... 
Resampling results across tuning parameters:

  mtry  min.node.size  ROC        Sens          Spec     
  3      50            0.6730495  0.0092635479  0.9983834
  3      75            0.6736373  0.0048655242  0.9993072
  3     100            0.6731015  0.0020404508  0.9998680
  3     150            0.6726082  0.0001568627  0.9999340
  4      50            0.6739269  0.0212743554  0.9966017
  4      75            0.6742251  0.0120901652  0.9981853
  4     100            0.6736399  0.0071428130  0.9987793
  4     150            0.6732947  0.0024322989  0.9998350
  5      50            0.6748114  0.0306157172  0.9941277
  5      75            0.6743623  0.0199404045  0.9965360
  5     100            0.6736946  0.0135022387  0.9980535
  5     150            0.6732621  0.0053382739  0.9992411
  6      50            0.6746108  0.0409013432  0.9910923
  6      75            0.6741555  0.0284180948  0.9944907
  6     100            0.6734979  0.0204894241  0.9967337
  6     150            0.6737092  0.0089482785  0.9987463
  7      50            0.6736712  0.0492209356  0.9893106
  7      75            0.6743368  0.0350125058  0.9928407
  7     100            0.6742522  0.0265354331  0.9948864
  7     150            0.6731619  0.0132657094  0.9980204
  8      50            0.6736567  0.0580114250  0.9865721
  8      75            0.6739156  0.0427818434  0.9907951
  8     100            0.6735730  0.0328124132  0.9936326
  8     150            0.6739220  0.0178974834  0.9969319
  9      50            0.6742330  0.0629559981  0.9851537
  9      75            0.6738231  0.0487494210  0.9895413
  9     100            0.6738584  0.0376038289  0.9919172
  9     150            0.6732811  0.0216668211  0.9957438

Tuning parameter 'splitrule' was held constant at a value of gini
Sens was used to select the optimal model using the largest value.
The final values used for the model were mtry = 9, splitrule = gini
 and min.node.size = 50.
grid_search_xgb
eXtreme Gradient Boosting 

4305 samples
  91 predictor
   2 classes: 'Not_D_and_inf_Q1', 'Not_D_and_sup_Q1' 

No pre-processing
Resampling: Cross-Validated (5 fold, repeated 10 times) 
Summary of sample sizes: 3444, 3444, 3444, 3445, 3443, 3444, ... 
Resampling results across tuning parameters:

  max_depth  gamma  colsample_bytree  min_child_weight  subsample  ROC      
  3           0     0.1                50               0.7        0.6785363
  3           0     0.1                50               0.8        0.6799875
  3           0     0.1                50               0.9        0.6804500
  3           0     0.1                50               1.0        0.6823648
  3           0     0.1               100               0.7        0.6740347
  3           0     0.1               100               0.8        0.6750796
  3           0     0.1               100               0.9        0.6767909
  3           0     0.1               100               1.0        0.6769700
  3           0     0.1               150               0.7        0.6574394
  3           0     0.1               150               0.8        0.6664940
  3           0     0.1               150               0.9        0.6716528
  3           0     0.1               150               1.0        0.6742771
  3           0     0.2                50               0.7        0.6823229
  3           0     0.2                50               0.8        0.6826816
  3           0     0.2                50               0.9        0.6830717
  3           0     0.2                50               1.0        0.6841141
  3           0     0.2               100               0.7        0.6787506
  3           0     0.2               100               0.8        0.6799038
  3           0     0.2               100               0.9        0.6796900
  3           0     0.2               100               1.0        0.6796796
  3           0     0.2               150               0.7        0.6628077
  3           0     0.2               150               0.8        0.6714751
  3           0     0.2               150               0.9        0.6759224
  3           0     0.2               150               1.0        0.6772249
  3           0     0.3                50               0.7        0.6829134
  3           0     0.3                50               0.8        0.6832605
  3           0     0.3                50               0.9        0.6838021
  3           0     0.3                50               1.0        0.6850128
  3           0     0.3               100               0.7        0.6799040
  3           0     0.3               100               0.8        0.6805631
  3           0     0.3               100               0.9        0.6807553
  3           0     0.3               100               1.0        0.6812284
  3           0     0.3               150               0.7        0.6653150
  3           0     0.3               150               0.8        0.6731625
  3           0     0.3               150               0.9        0.6769188
  3           0     0.3               150               1.0        0.6789956
  3           0     0.4                50               0.7        0.6835646
  3           0     0.4                50               0.8        0.6843785
  3           0     0.4                50               0.9        0.6837642
  3           0     0.4                50               1.0        0.6849679
  3           0     0.4               100               0.7        0.6805164
  3           0     0.4               100               0.8        0.6807898
  3           0     0.4               100               0.9        0.6809159
  3           0     0.4               100               1.0        0.6812688
  3           0     0.4               150               0.7        0.6660034
  3           0     0.4               150               0.8        0.6739234
  3           0     0.4               150               0.9        0.6775012
  3           0     0.4               150               1.0        0.6793173
  3           0     0.5                50               0.7        0.6838229
  3           0     0.5                50               0.8        0.6840511
  3           0     0.5                50               0.9        0.6837561
  3           0     0.5                50               1.0        0.6845494
  3           0     0.5               100               0.7        0.6808015
  3           0     0.5               100               0.8        0.6814586
  3           0     0.5               100               0.9        0.6813246
  3           0     0.5               100               1.0        0.6810916
  3           0     0.5               150               0.7        0.6666182
  3           0     0.5               150               0.8        0.6745138
  3           0     0.5               150               0.9        0.6779811
  3           0     0.5               150               1.0        0.6793098
  3           0     0.6                50               0.7        0.6835108
  3           0     0.6                50               0.8        0.6840414
  3           0     0.6                50               0.9        0.6838978
  3           0     0.6                50               1.0        0.6842257
  3           0     0.6               100               0.7        0.6808373
  3           0     0.6               100               0.8        0.6812973
  3           0     0.6               100               0.9        0.6807972
  3           0     0.6               100               1.0        0.6809873
  3           0     0.6               150               0.7        0.6670491
  3           0     0.6               150               0.8        0.6745420
  3           0     0.6               150               0.9        0.6778977
  3           0     0.6               150               1.0        0.6794917
  3           0     0.7                50               0.7        0.6836444
  3           0     0.7                50               0.8        0.6839783
  3           0     0.7                50               0.9        0.6838917
  3           0     0.7                50               1.0        0.6841779
  3           0     0.7               100               0.7        0.6810108
  3           0     0.7               100               0.8        0.6817369
  3           0     0.7               100               0.9        0.6811319
  3           0     0.7               100               1.0        0.6806386
  3           0     0.7               150               0.7        0.6672749
  3           0     0.7               150               0.8        0.6745525
  3           0     0.7               150               0.9        0.6778563
  3           0     0.7               150               1.0        0.6790577
  3           0     0.8                50               0.7        0.6837489
  3           0     0.8                50               0.8        0.6843278
  3           0     0.8                50               0.9        0.6839312
  3           0     0.8                50               1.0        0.6840723
  3           0     0.8               100               0.7        0.6812223
  3           0     0.8               100               0.8        0.6817090
  3           0     0.8               100               0.9        0.6813720
  3           0     0.8               100               1.0        0.6804816
  3           0     0.8               150               0.7        0.6673856
  3           0     0.8               150               0.8        0.6749276
  3           0     0.8               150               0.9        0.6783571
  3           0     0.8               150               1.0        0.6789135
  3           0     0.9                50               0.7        0.6833488
  3           0     0.9                50               0.8        0.6840435
  3           0     0.9                50               0.9        0.6838433
  3           0     0.9                50               1.0        0.6838195
  3           0     0.9               100               0.7        0.6812963
  3           0     0.9               100               0.8        0.6819089
  3           0     0.9               100               0.9        0.6811500
  3           0     0.9               100               1.0        0.6803536
  3           0     0.9               150               0.7        0.6674431
  3           0     0.9               150               0.8        0.6748335
  3           0     0.9               150               0.9        0.6785783
  3           0     0.9               150               1.0        0.6784079
  3           0     1.0                50               0.7        0.6836496
  3           0     1.0                50               0.8        0.6844347
  3           0     1.0                50               0.9        0.6837424
  3           0     1.0                50               1.0        0.6833267
  3           0     1.0               100               0.7        0.6815057
  3           0     1.0               100               0.8        0.6815743
  3           0     1.0               100               0.9        0.6813530
  3           0     1.0               100               1.0        0.6802621
  3           0     1.0               150               0.7        0.6674454
  3           0     1.0               150               0.8        0.6751188
  3           0     1.0               150               0.9        0.6783930
  3           0     1.0               150               1.0        0.6782824
  3           5     0.1                50               0.7        0.6784367
  3           5     0.1                50               0.8        0.6801792
  3           5     0.1                50               0.9        0.6809131
  3           5     0.1                50               1.0        0.6827148
  3           5     0.1               100               0.7        0.6728828
  3           5     0.1               100               0.8        0.6744917
  3           5     0.1               100               0.9        0.6762808
  3           5     0.1               100               1.0        0.6763473
  3           5     0.1               150               0.7        0.6570285
  3           5     0.1               150               0.8        0.6656909
  3           5     0.1               150               0.9        0.6705388
  3           5     0.1               150               1.0        0.6735731
  3           5     0.2                50               0.7        0.6823980
  3           5     0.2                50               0.8        0.6828969
  3           5     0.2                50               0.9        0.6828840
  3           5     0.2                50               1.0        0.6843282
  3           5     0.2               100               0.7        0.6785868
  3           5     0.2               100               0.8        0.6791173
  3           5     0.2               100               0.9        0.6796671
  3           5     0.2               100               1.0        0.6795147
  3           5     0.2               150               0.7        0.6626534
  3           5     0.2               150               0.8        0.6712973
  3           5     0.2               150               0.9        0.6754683
  3           5     0.2               150               1.0        0.6769809
  3           5     0.3                50               0.7        0.6831722
  3           5     0.3                50               0.8        0.6841054
  3           5     0.3                50               0.9        0.6842646
  3           5     0.3                50               1.0        0.6848902
  3           5     0.3               100               0.7        0.6794977
  3           5     0.3               100               0.8        0.6806805
  3           5     0.3               100               0.9        0.6807250
  3           5     0.3               100               1.0        0.6811460
  3           5     0.3               150               0.7        0.6649378
  3           5     0.3               150               0.8        0.6730824
  3           5     0.3               150               0.9        0.6766321
  3           5     0.3               150               1.0        0.6783281
  3           5     0.4                50               0.7        0.6835420
  3           5     0.4                50               0.8        0.6841345
  3           5     0.4                50               0.9        0.6839566
  3           5     0.4                50               1.0        0.6846661
  3           5     0.4               100               0.7        0.6806217
  3           5     0.4               100               0.8        0.6811754
  3           5     0.4               100               0.9        0.6809684
  3           5     0.4               100               1.0        0.6811957
  3           5     0.4               150               0.7        0.6657427
  3           5     0.4               150               0.8        0.6739782
  3           5     0.4               150               0.9        0.6774749
  3           5     0.4               150               1.0        0.6794038
  3           5     0.5                50               0.7        0.6834947
  3           5     0.5                50               0.8        0.6842232
  3           5     0.5                50               0.9        0.6838899
  3           5     0.5                50               1.0        0.6844803
  3           5     0.5               100               0.7        0.6808606
  3           5     0.5               100               0.8        0.6809895
  3           5     0.5               100               0.9        0.6811073
  3           5     0.5               100               1.0        0.6812405
  3           5     0.5               150               0.7        0.6664351
  3           5     0.5               150               0.8        0.6743021
  3           5     0.5               150               0.9        0.6782797
  3           5     0.5               150               1.0        0.6793346
  3           5     0.6                50               0.7        0.6839208
  3           5     0.6                50               0.8        0.6844647
  3           5     0.6                50               0.9        0.6842903
  3           5     0.6                50               1.0        0.6845620
  3           5     0.6               100               0.7        0.6810347
  3           5     0.6               100               0.8        0.6812369
  3           5     0.6               100               0.9        0.6814214
  3           5     0.6               100               1.0        0.6809212
  3           5     0.6               150               0.7        0.6666044
  3           5     0.6               150               0.8        0.6743755
  3           5     0.6               150               0.9        0.6782092
  3           5     0.6               150               1.0        0.6793694
  3           5     0.7                50               0.7        0.6836577
  3           5     0.7                50               0.8        0.6845236
  3           5     0.7                50               0.9        0.6841699
  3           5     0.7                50               1.0        0.6841241
  3           5     0.7               100               0.7        0.6806693
  3           5     0.7               100               0.8        0.6816725
  3           5     0.7               100               0.9        0.6812272
  3           5     0.7               100               1.0        0.6807908
  3           5     0.7               150               0.7        0.6669845
  3           5     0.7               150               0.8        0.6745803
  3           5     0.7               150               0.9        0.6781941
  3           5     0.7               150               1.0        0.6790916
  3           5     0.8                50               0.7        0.6839334
  3           5     0.8                50               0.8        0.6843188
  3           5     0.8                50               0.9        0.6839173
  3           5     0.8                50               1.0        0.6837272
  3           5     0.8               100               0.7        0.6814689
  3           5     0.8               100               0.8        0.6816174
  3           5     0.8               100               0.9        0.6817295
  3           5     0.8               100               1.0        0.6807373
  3           5     0.8               150               0.7        0.6673576
  3           5     0.8               150               0.8        0.6747715
  3           5     0.8               150               0.9        0.6781211
  3           5     0.8               150               1.0        0.6788837
  3           5     0.9                50               0.7        0.6834884
  3           5     0.9                50               0.8        0.6842008
  3           5     0.9                50               0.9        0.6839661
  3           5     0.9                50               1.0        0.6838640
  3           5     0.9               100               0.7        0.6808610
  3           5     0.9               100               0.8        0.6814620
  3           5     0.9               100               0.9        0.6815448
  3           5     0.9               100               1.0        0.6805508
  3           5     0.9               150               0.7        0.6675919
  3           5     0.9               150               0.8        0.6745821
  3           5     0.9               150               0.9        0.6783292
  3           5     0.9               150               1.0        0.6786147
  3           5     1.0                50               0.7        0.6836123
  3           5     1.0                50               0.8        0.6845634
  3           5     1.0                50               0.9        0.6837803
  3           5     1.0                50               1.0        0.6833642
  3           5     1.0               100               0.7        0.6816649
  3           5     1.0               100               0.8        0.6816864
  3           5     1.0               100               0.9        0.6816138
  3           5     1.0               100               1.0        0.6804587
  3           5     1.0               150               0.7        0.6672914
  3           5     1.0               150               0.8        0.6752591
  3           5     1.0               150               0.9        0.6782267
  3           5     1.0               150               1.0        0.6783631
  3          10     0.1                50               0.7        0.6769570
  3          10     0.1                50               0.8        0.6780180
  3          10     0.1                50               0.9        0.6796155
  3          10     0.1                50               1.0        0.6807513
  3          10     0.1               100               0.7        0.6700527
  3          10     0.1               100               0.8        0.6719129
  3          10     0.1               100               0.9        0.6742686
  3          10     0.1               100               1.0        0.6748560
  3          10     0.1               150               0.7        0.6527969
  3          10     0.1               150               0.8        0.6625560
  3          10     0.1               150               0.9        0.6679017
  3          10     0.1               150               1.0        0.6713966
  3          10     0.2                50               0.7        0.6809766
  3          10     0.2                50               0.8        0.6821112
  3          10     0.2                50               0.9        0.6823345
  3          10     0.2                50               1.0        0.6837345
  3          10     0.2               100               0.7        0.6755791
  3          10     0.2               100               0.8        0.6775316
  3          10     0.2               100               0.9        0.6776636
  3          10     0.2               100               1.0        0.6776296
  3          10     0.2               150               0.7        0.6596128
  3          10     0.2               150               0.8        0.6686204
  3          10     0.2               150               0.9        0.6727705
  3          10     0.2               150               1.0        0.6748224
  3          10     0.3                50               0.7        0.6822670
  3          10     0.3                50               0.8        0.6831851
  3          10     0.3                50               0.9        0.6831822
  3          10     0.3                50               1.0        0.6843161
  3          10     0.3               100               0.7        0.6775455
  3          10     0.3               100               0.8        0.6786321
  3          10     0.3               100               0.9        0.6791556
  3          10     0.3               100               1.0        0.6789010
  3          10     0.3               150               0.7        0.6621308
  3          10     0.3               150               0.8        0.6706682
  3          10     0.3               150               0.9        0.6745561
  3          10     0.3               150               1.0        0.6758722
  3          10     0.4                50               0.7        0.6833161
  3          10     0.4                50               0.8        0.6836598
  3          10     0.4                50               0.9        0.6836312
  3          10     0.4                50               1.0        0.6845025
  3          10     0.4               100               0.7        0.6789957
  3          10     0.4               100               0.8        0.6795424
  3          10     0.4               100               0.9        0.6798404
  3          10     0.4               100               1.0        0.6790884
  3          10     0.4               150               0.7        0.6635092
  3          10     0.4               150               0.8        0.6716255
  3          10     0.4               150               0.9        0.6755761
  3          10     0.4               150               1.0        0.6766906
  3          10     0.5                50               0.7        0.6834997
  3          10     0.5                50               0.8        0.6838629
  3          10     0.5                50               0.9        0.6835847
  3          10     0.5                50               1.0        0.6841762
  3          10     0.5               100               0.7        0.6793281
  3          10     0.5               100               0.8        0.6798023
  3          10     0.5               100               0.9        0.6803992
  3          10     0.5               100               1.0        0.6793602
  3          10     0.5               150               0.7        0.6642946
  3          10     0.5               150               0.8        0.6725202
  3          10     0.5               150               0.9        0.6762016
  3          10     0.5               150               1.0        0.6770255
  3          10     0.6                50               0.7        0.6836984
  3          10     0.6                50               0.8        0.6844185
  3          10     0.6                50               0.9        0.6838703
  3          10     0.6                50               1.0        0.6839984
  3          10     0.6               100               0.7        0.6796540
  3          10     0.6               100               0.8        0.6801761
  3          10     0.6               100               0.9        0.6806752
  3          10     0.6               100               1.0        0.6791478
  3          10     0.6               150               0.7        0.6649074
  3          10     0.6               150               0.8        0.6730252
  3          10     0.6               150               0.9        0.6767059
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  3          10     0.7                50               0.7        0.6837089
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  3          10     0.7               100               0.7        0.6801369
  3          10     0.7               100               0.8        0.6807163
  3          10     0.7               100               0.9        0.6806090
  3          10     0.7               100               1.0        0.6782027
  3          10     0.7               150               0.7        0.6653787
  3          10     0.7               150               0.8        0.6733405
  3          10     0.7               150               0.9        0.6769530
  3          10     0.7               150               1.0        0.6768070
  3          10     0.8                50               0.7        0.6839297
  3          10     0.8                50               0.8        0.6845420
  3          10     0.8                50               0.9        0.6840121
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  3          10     0.8               100               0.7        0.6802750
  3          10     0.8               100               0.8        0.6808074
  3          10     0.8               100               0.9        0.6808027
  3          10     0.8               100               1.0        0.6779320
  3          10     0.8               150               0.7        0.6658129
  3          10     0.8               150               0.8        0.6733939
  3          10     0.8               150               0.9        0.6773002
  3          10     0.8               150               1.0        0.6759357
  3          10     0.9                50               0.7        0.6842033
  3          10     0.9                50               0.8        0.6844227
  3          10     0.9                50               0.9        0.6846245
  3          10     0.9                50               1.0        0.6829669
  3          10     0.9               100               0.7        0.6804863
  3          10     0.9               100               0.8        0.6805764
  3          10     0.9               100               0.9        0.6808074
  3          10     0.9               100               1.0        0.6774826
  3          10     0.9               150               0.7        0.6660555
  3          10     0.9               150               0.8        0.6737338
  3          10     0.9               150               0.9        0.6774274
  3          10     0.9               150               1.0        0.6750149
  3          10     1.0                50               0.7        0.6842948
  3          10     1.0                50               0.8        0.6844909
  3          10     1.0                50               0.9        0.6839677
  3          10     1.0                50               1.0        0.6817418
  3          10     1.0               100               0.7        0.6809214
  3          10     1.0               100               0.8        0.6810347
  3          10     1.0               100               0.9        0.6812914
  3          10     1.0               100               1.0        0.6747461
  3          10     1.0               150               0.7        0.6665210
  3          10     1.0               150               0.8        0.6738406
  3          10     1.0               150               0.9        0.6773406
  3          10     1.0               150               1.0        0.6726771
  4           0     0.1                50               0.7        0.6785887
  4           0     0.1                50               0.8        0.6804697
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  4           0     0.1               100               0.7        0.6747017
  4           0     0.1               100               0.8        0.6759857
  4           0     0.1               100               0.9        0.6777560
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  4           0     0.1               150               0.7        0.6569400
  4           0     0.1               150               0.8        0.6666460
  4           0     0.1               150               0.9        0.6717537
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  4           0     0.2                50               0.7        0.6833539
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  4           0     0.2               100               0.8        0.6810590
  4           0     0.2               100               0.9        0.6819928
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  4           0     0.2               150               0.7        0.6632031
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  4           0     0.2               150               0.9        0.6769270
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  4           0     0.3                50               0.7        0.6839596
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  4           0     0.3                50               0.9        0.6852112
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  4           0     0.3               100               0.9        0.6829039
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  4           0     0.3               150               0.7        0.6651174
  4           0     0.3               150               0.8        0.6740691
  4           0     0.3               150               0.9        0.6786712
  4           0     0.3               150               1.0        0.6805926
  4           0     0.4                50               0.7        0.6846938
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  4           0     0.4                50               0.9        0.6855421
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  4           0     0.4               100               0.7        0.6823251
  4           0     0.4               100               0.8        0.6830910
  4           0     0.4               100               0.9        0.6829714
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  4           0     0.4               150               0.7        0.6661499
  4           0     0.4               150               0.8        0.6745502
  4           0     0.4               150               0.9        0.6794759
  4           0     0.4               150               1.0        0.6815686
  4           0     0.5                50               0.7        0.6837851
  4           0     0.5                50               0.8        0.6845903
  4           0     0.5                50               0.9        0.6849844
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  4           0     0.5               100               0.7        0.6823526
  4           0     0.5               100               0.8        0.6834240
  4           0     0.5               100               0.9        0.6835065
  4           0     0.5               100               1.0        0.6837519
  4           0     0.5               150               0.7        0.6662796
  4           0     0.5               150               0.8        0.6753265
  4           0     0.5               150               0.9        0.6796613
  4           0     0.5               150               1.0        0.6815626
  4           0     0.6                50               0.7        0.6838439
  4           0     0.6                50               0.8        0.6846989
  4           0     0.6                50               0.9        0.6847631
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  4           0     0.6               100               0.7        0.6825915
  4           0     0.6               100               0.8        0.6832943
  4           0     0.6               100               0.9        0.6834876
  4           0     0.6               100               1.0        0.6832892
  4           0     0.6               150               0.7        0.6667859
  4           0     0.6               150               0.8        0.6751991
  4           0     0.6               150               0.9        0.6799837
  4           0     0.6               150               1.0        0.6817407
  4           0     0.7                50               0.7        0.6843881
  4           0     0.7                50               0.8        0.6848167
  4           0     0.7                50               0.9        0.6841751
  4           0     0.7                50               1.0        0.6857201
  4           0     0.7               100               0.7        0.6826066
  4           0     0.7               100               0.8        0.6836009
  4           0     0.7               100               0.9        0.6834746
  4           0     0.7               100               1.0        0.6828719
  4           0     0.7               150               0.7        0.6669883
  4           0     0.7               150               0.8        0.6757563
  4           0     0.7               150               0.9        0.6801773
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  4           0     0.8                50               0.7        0.6838366
  4           0     0.8                50               0.8        0.6842557
  4           0     0.8                50               0.9        0.6844975
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  4           0     0.8               100               0.7        0.6828616
  4           0     0.8               100               0.8        0.6834171
  4           0     0.8               100               0.9        0.6832383
  4           0     0.8               100               1.0        0.6824551
  4           0     0.8               150               0.7        0.6673020
  4           0     0.8               150               0.8        0.6756287
  4           0     0.8               150               0.9        0.6801321
  4           0     0.8               150               1.0        0.6810231
  4           0     0.9                50               0.7        0.6838687
  4           0     0.9                50               0.8        0.6845633
  4           0     0.9                50               0.9        0.6843064
  4           0     0.9                50               1.0        0.6848396
  4           0     0.9               100               0.7        0.6828125
  4           0     0.9               100               0.8        0.6830402
  4           0     0.9               100               0.9        0.6830213
  4           0     0.9               100               1.0        0.6822768
  4           0     0.9               150               0.7        0.6676349
  4           0     0.9               150               0.8        0.6756713
  4           0     0.9               150               0.9        0.6800897
  4           0     0.9               150               1.0        0.6808588
  4           0     1.0                50               0.7        0.6838496
  4           0     1.0                50               0.8        0.6837487
  4           0     1.0                50               0.9        0.6841289
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  4           0     1.0               100               0.7        0.6828933
  4           0     1.0               100               0.8        0.6831734
  4           0     1.0               100               0.9        0.6829842
  4           0     1.0               100               1.0        0.6819633
  4           0     1.0               150               0.7        0.6672810
  4           0     1.0               150               0.8        0.6758417
  4           0     1.0               150               0.9        0.6803102
  4           0     1.0               150               1.0        0.6804185
  4           5     0.1                50               0.7        0.6795265
  4           5     0.1                50               0.8        0.6812279
  4           5     0.1                50               0.9        0.6821469
  4           5     0.1                50               1.0        0.6830941
  4           5     0.1               100               0.7        0.6737614
  4           5     0.1               100               0.8        0.6751482
  4           5     0.1               100               0.9        0.6769885
  4           5     0.1               100               1.0        0.6776616
  4           5     0.1               150               0.7        0.6565280
  4           5     0.1               150               0.8        0.6652969
  4           5     0.1               150               0.9        0.6705104
  4           5     0.1               150               1.0        0.6740213
  4           5     0.2                50               0.7        0.6833892
  4           5     0.2                50               0.8        0.6841534
  4           5     0.2                50               0.9        0.6848291
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  4           5     0.2               100               0.7        0.6793860
  4           5     0.2               100               0.8        0.6810354
  4           5     0.2               100               0.9        0.6814726
  4           5     0.2               100               1.0        0.6817671
  4           5     0.2               150               0.7        0.6629588
  4           5     0.2               150               0.8        0.6719335
  4           5     0.2               150               0.9        0.6762828
  4           5     0.2               150               1.0        0.6781018
  4           5     0.3                50               0.7        0.6845054
  4           5     0.3                50               0.8        0.6854853
  4           5     0.3                50               0.9        0.6853394
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  4           5     0.3               100               0.7        0.6816656
  4           5     0.3               100               0.8        0.6822376
  4           5     0.3               100               0.9        0.6828767
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  4           5     0.3               150               0.7        0.6648764
  4           5     0.3               150               0.8        0.6739606
  4           5     0.3               150               0.9        0.6778354
  4           5     0.3               150               1.0        0.6802764
  4           5     0.4                50               0.7        0.6845579
  4           5     0.4                50               0.8        0.6851879
  4           5     0.4                50               0.9        0.6853033
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  4           5     0.4               100               0.7        0.6817553
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  4           5     0.4               100               0.9        0.6834016
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  4           5     0.4               150               0.7        0.6659514
  4           5     0.4               150               0.8        0.6744439
  4           5     0.4               150               0.9        0.6789579
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  4           5     0.5                50               0.7        0.6845190
  4           5     0.5                50               0.8        0.6849921
  4           5     0.5                50               0.9        0.6850417
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  4           5     0.5               100               0.7        0.6821906
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  4           5     0.5               100               0.9        0.6832763
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  4           5     0.5               150               0.7        0.6662950
  4           5     0.5               150               0.8        0.6753060
  4           5     0.5               150               0.9        0.6798350
  4           5     0.5               150               1.0        0.6815837
  4           5     0.6                50               0.7        0.6845954
  4           5     0.6                50               0.8        0.6853719
  4           5     0.6                50               0.9        0.6851227
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  4           5     0.6               100               0.7        0.6817970
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  4           5     0.6               100               0.9        0.6836658
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  4           5     0.6               150               0.7        0.6669770
  4           5     0.6               150               0.8        0.6755822
  4           5     0.6               150               0.9        0.6797993
  4           5     0.6               150               1.0        0.6815879
  4           5     0.7                50               0.7        0.6844380
  4           5     0.7                50               0.8        0.6848396
  4           5     0.7                50               0.9        0.6846173
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  4           5     0.7               100               0.7        0.6827032
  4           5     0.7               100               0.8        0.6830325
  4           5     0.7               100               0.9        0.6834612
  4           5     0.7               100               1.0        0.6831935
  4           5     0.7               150               0.7        0.6673289
  4           5     0.7               150               0.8        0.6753270
  4           5     0.7               150               0.9        0.6801373
  4           5     0.7               150               1.0        0.6816244
  4           5     0.8                50               0.7        0.6842031
  4           5     0.8                50               0.8        0.6841562
  4           5     0.8                50               0.9        0.6847958
  4           5     0.8                50               1.0        0.6855225
  4           5     0.8               100               0.7        0.6825718
  4           5     0.8               100               0.8        0.6833189
  4           5     0.8               100               0.9        0.6833561
  4           5     0.8               100               1.0        0.6827082
  4           5     0.8               150               0.7        0.6671520
  4           5     0.8               150               0.8        0.6756187
  4           5     0.8               150               0.9        0.6801268
  4           5     0.8               150               1.0        0.6811754
  4           5     0.9                50               0.7        0.6839809
  4           5     0.9                50               0.8        0.6844102
  4           5     0.9                50               0.9        0.6845324
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  4           5     0.9               100               0.7        0.6828692
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  4           5     0.9               100               0.9        0.6832706
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  4           5     0.9               150               0.7        0.6673917
  4           5     0.9               150               0.8        0.6757522
  4           5     0.9               150               0.9        0.6801905
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  4           5     1.0                50               0.7        0.6837129
  4           5     1.0                50               0.8        0.6845494
  4           5     1.0                50               0.9        0.6843867
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  4           5     1.0               100               0.7        0.6826822
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  4           5     1.0               100               0.9        0.6833112
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  4           5     1.0               150               0.7        0.6676002
  4           5     1.0               150               0.8        0.6758239
  4           5     1.0               150               0.9        0.6802764
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  4          10     0.1                50               0.7        0.6780565
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  4          10     0.1               150               0.7        0.6532465
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  4          10     0.2                50               0.7        0.6828825
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  4          10     0.3                50               0.7        0.6842649
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  4          10     0.3               100               0.7        0.6791046
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  4          10     0.3               150               0.7        0.6624594
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  4          10     0.4                50               0.7        0.6849503
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  4          10     0.4               150               0.7        0.6638417
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  4          10     0.5                50               0.7        0.6850038
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  4          10     0.5               100               0.7        0.6806546
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  4          10     0.5               150               0.7        0.6645207
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  4          10     0.5               150               0.9        0.6776891
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  4          10     0.6                50               0.7        0.6845946
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  4          10     0.6               100               0.7        0.6812755
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  4          10     0.6               150               0.7        0.6649350
  4          10     0.6               150               0.8        0.6737816
  4          10     0.6               150               0.9        0.6782110
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  4          10     0.7                50               0.7        0.6851083
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  5           0     0.6                50               0.7        0.6837460
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  5           0     0.7                50               0.7        0.6836088
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  5           0     0.7               150               0.7        0.6672615
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  5           0     0.8                50               0.7        0.6833102
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  5           0     0.8               150               0.7        0.6674582
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  5           0     0.9                50               0.7        0.6830865
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  5           0     0.9               150               0.7        0.6675621
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  5           5     0.1               150               0.7        0.6567276
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  5           5     0.2                50               0.7        0.6838925
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  5           5     0.3                50               0.7        0.6847005
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  5           5     0.3               150               0.7        0.6648564
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  5           5     0.4                50               0.7        0.6846228
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  5           5     0.5                50               0.7        0.6841655
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  5           5     0.6                50               0.7        0.6841938
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  5           5     0.6               150               0.7        0.6669997
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  5           5     0.7                50               0.7        0.6841909
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  5           5     0.7               150               0.7        0.6672557
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  5           5     0.8                50               0.7        0.6840764
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  5           5     0.8               150               0.7        0.6675664
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  5           5     0.9                50               0.7        0.6836793
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  5           5     0.9               150               0.7        0.6673175
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  5          10     0.7                50               0.7        0.6852050
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  5          10     0.7               150               0.7        0.6652582
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  6          10     0.8               150               0.7        0.6662588
  6          10     0.8               150               0.8        0.6742240
  6          10     0.8               150               0.9        0.6790967
  6          10     0.8               150               1.0        0.6791401
  6          10     0.9                50               0.7        0.6844932
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  0.6061285  0.6621892
  0.6048711  0.6649286
  0.6059710  0.6659845
  0.6045570  0.6656223
  0.5934908  0.6403159
  0.6007920  0.6511379
  0.6084076  0.6535794
  0.6093441  0.6569441
  0.5866608  0.6837012
  0.5853247  0.6864394
  0.5834451  0.6883520
  0.5867426  0.6897380
  0.6060457  0.6622230
  0.6080889  0.6637737
  0.6068325  0.6650280
  0.6062838  0.6650609
  0.5968665  0.6410089
  0.6043999  0.6514018
  0.6080948  0.6535461
  0.6104453  0.6570431
  0.5850140  0.6834373
  0.5846200  0.6867686
  0.5825821  0.6880886
  0.5869826  0.6873302
  0.6061260  0.6632453
  0.6073827  0.6643343
  0.6069128  0.6650942
  0.6053407  0.6634773
  0.5976501  0.6425592
  0.6041674  0.6521280
  0.6108411  0.6535466
  0.6121692  0.6550299
  0.5852472  0.6839983
  0.5822665  0.6869011
  0.5828986  0.6897377
  0.5849412  0.6881203
  0.6047148  0.6644008
  0.6077727  0.6634443
  0.6065209  0.6632790
  0.6047914  0.6641380
  0.5970993  0.6432855
  0.6056579  0.6502143
  0.6128028  0.6533817
  0.6138996  0.6555585
  0.5854853  0.6835696
  0.5865058  0.6877587
  0.5818762  0.6896059
  0.5858027  0.6883199
  0.6090286  0.6628504
  0.6062819  0.6630484
  0.6056576  0.6645330
  0.6049474  0.6633788
  0.5998462  0.6404147
  0.6051854  0.6518313
  0.6128788  0.6532826
  0.6125654  0.6553937
  0.5858799  0.6850207
  0.5837576  0.6866700
  0.5821143  0.6872964
  0.5840769  0.6872638
  0.6072271  0.6623886
  0.6069927  0.6640057
  0.6058123  0.6649954
  0.6053361  0.6628842
  0.5967871  0.6401515
  0.6062853  0.6509399
  0.6111499  0.6542394
  0.6138191  0.6548326
  0.5847006  0.6842625
  0.5837573  0.6863066
  0.5841504  0.6878239
  0.5840806  0.6855806
  0.6076174  0.6627847
  0.6089517  0.6649296
  0.6073821  0.6642693
  0.6051820  0.6633462
  0.5976477  0.6406783
  0.6080895  0.6501814
  0.6120151  0.6542391
  0.6127216  0.6555261
  0.5923147  0.6711294
  0.5887852  0.6716576
  0.5880790  0.6735372
  0.5874479  0.6762437
  0.5939636  0.6563813
  0.5971823  0.6561512
  0.5988309  0.6588565
  0.5987482  0.6601427
  0.5836857  0.6348042
  0.5879991  0.6458587
  0.5920046  0.6503128
  0.5966302  0.6525890
  0.5910588  0.6769371
  0.5905861  0.6794444
  0.5894853  0.6819183
  0.5873664  0.6826436
  0.6021291  0.6593518
  0.6020469  0.6625856
  0.6034584  0.6647966
  0.6026784  0.6651266
  0.5873710  0.6385344
  0.5978895  0.6509060
  0.6025188  0.6555919
  0.6033043  0.6570444
  0.5926247  0.6798078
  0.5891706  0.6828095
  0.5876051  0.6837334
  0.5889369  0.6849206
  0.6047930  0.6616951
  0.6054195  0.6646638
  0.6057360  0.6650611
  0.6062866  0.6655557
  0.5930230  0.6407437
  0.6001618  0.6515986
  0.6063668  0.6537452
  0.6070709  0.6570099
  0.5919981  0.6813575
  0.5881547  0.6829086
  0.5865055  0.6842622
  0.5909044  0.6849203
  0.6058916  0.6614315
  0.6064431  0.6631797
  0.6077780  0.6648633
  0.6076983  0.6640050
  0.5949807  0.6412724
  0.6016588  0.6523256
  0.6086429  0.6548987
  0.6090347  0.6576692
  0.5901948  0.6831732
  0.5905073  0.6840633
  0.5871326  0.6843931
  0.5884712  0.6862730
  0.6083221  0.6605408
  0.6069887  0.6638396
  0.6074615  0.6630481
  0.6069897  0.6640062
  0.5956887  0.6409424
  0.6047957  0.6501809
  0.6089572  0.6528212
  0.6112293  0.6569105
  0.5898771  0.6821838
  0.5869748  0.6846575
  0.5867436  0.6856463
  0.5883971  0.6857458
  0.6069106  0.6639388
  0.6080862  0.6627507
  0.6066732  0.6649294
  0.6075390  0.6644015
  0.5986719  0.6408432
  0.6042442  0.6515668
  0.6096634  0.6546025
  0.6120936  0.6554927
  0.5880747  0.6813586
  0.5857999  0.6849210
  0.5856443  0.6859110
  0.5880815  0.6859111
  0.6059694  0.6635106
  0.6084799  0.6638729
  0.6076974  0.6636425
  0.6071474  0.6643351
  0.5985953  0.6412057
  0.6073834  0.6512362
  0.6109174  0.6538770
  0.6113874  0.6549639
  0.5885478  0.6842955
  0.5847763  0.6856794
  0.5850156  0.6857126
  0.5871388  0.6858114
  0.6087151  0.6618934
  0.6073812  0.6638072
  0.6075396  0.6632140
  0.6063616  0.6636427
  0.5974173  0.6412070
  0.6047948  0.6512703
  0.6125651  0.6548009
  0.6122483  0.6545684
  0.5861143  0.6831741
  0.5844635  0.6847564
  0.5835242  0.6868679
  0.5862767  0.6854821
  0.6084832  0.6626195
  0.6072259  0.6635433
  0.6059691  0.6638408
  0.6068291  0.6629500
  0.5978082  0.6420320
  0.6054982  0.6510385
  0.6113883  0.6534469
  0.6125642  0.6547336
  0.5861927  0.6819195
  0.5832104  0.6859112
  0.5837591  0.6866037
  0.5862761  0.6837336
  0.6075390  0.6632454
  0.6066765  0.6631809
  0.6072256  0.6639059
  0.6065181  0.6626205
  0.5990638  0.6402498
  0.6074618  0.6516660
  0.6129569  0.6538771
  0.6120939  0.6558888
  0.5921621  0.6650261
  0.5948285  0.6708655
  0.5957675  0.6697775
  0.5972583  0.6723508
  0.5933392  0.6547007
  0.5953806  0.6550628
  0.5973377  0.6575052
  0.5956156  0.6594177
  0.5818839  0.6330904
  0.5880040  0.6443083
  0.5891027  0.6507746
  0.5944360  0.6541075
  0.5975739  0.6712950
  0.5980479  0.6741326
  0.5972568  0.6739341
  0.5978092  0.6746939
  0.6012632  0.6594192
  0.6012614  0.6595172
  0.6028322  0.6610022
  0.6010298  0.6623558
  0.5883931  0.6361249
  0.5950641  0.6483668
  0.5993055  0.6552290
  0.5989915  0.6557568
  0.6000040  0.6721865
  0.6014973  0.6743964
  0.5981247  0.6762780
  0.5985941  0.6755850
  0.6042470  0.6600445
  0.6025932  0.6615640
  0.6044780  0.6624543
  0.6067578  0.6615308
  0.5911434  0.6380065
  0.5982813  0.6493241
  0.6027612  0.6535807
  0.6033843  0.6546350
  0.5977289  0.6751232
  0.5988272  0.6767394
  0.5992231  0.6759787
  0.5997706  0.6767060
  0.6057351  0.6585611
  0.6050289  0.6607381
  0.6077792  0.6616619
  0.6054266  0.6607719
  0.5924703  0.6407443
  0.5993049  0.6494224
  0.6049579  0.6528215
  0.6073864  0.6540742
  0.5985916  0.6755182
  0.5987466  0.6754519
  0.5978095  0.6768384
  0.5982791  0.6772005
  0.6062078  0.6593854
  0.6050279  0.6606719
  0.6076196  0.6615298
  0.6108390  0.6616953
  0.5972608  0.6396895
  0.6004020  0.6489943
  0.6065252  0.6515673
  0.6090341  0.6543713
  0.5987500  0.6748918
  0.5989860  0.6759473
  0.5965543  0.6776956
  0.5978873  0.6781906
  0.6077758  0.6594525
  0.6068353  0.6604744
  0.6090320  0.6616292
  0.6085635  0.6601453
  0.5974124  0.6390624
  0.6020482  0.6483664
  0.6097446  0.6513692
  0.6104480  0.6526222
  0.5978058  0.6756183
  0.5956897  0.6780584
  0.5961603  0.6794113
  0.5984382  0.6764424
  0.6060519  0.6591875
  0.6075387  0.6593865
  0.6098157  0.6608051
  0.6095807  0.6586599
  0.5973355  0.6397213
  0.6036974  0.6489272
  0.6096637  0.6515014
  0.6109955  0.6520938
  0.5971805  0.6756845
  0.5969474  0.6775305
  0.5961612  0.6779259
  0.5981235  0.6761788
  0.6081708  0.6622232
  0.6081667  0.6604748
  0.6102081  0.6621907
  0.6098169  0.6581646
  0.5981189  0.6400849
  0.6036168  0.6482668
  0.6092719  0.6521945
  0.6119386  0.6504777
  0.5971789  0.6746946
  0.5964761  0.6786854
  0.5954553  0.6808965
  0.5951410  0.6751547
  0.6068343  0.6595507
  0.6074606  0.6607389
  0.6107584  0.6609365
  0.6095025  0.6567465
  0.5980408  0.6401845
  0.6062069  0.6483996
  0.6102912  0.6520958
  0.6123313  0.6489270
  0.5949798  0.6770033
  0.5952981  0.6781587
  0.5943570  0.6795115
  0.5938861  0.6719222
  0.6084811  0.6613649
  0.6081701  0.6599144
  0.6075411  0.6617618
  0.6088776  0.6510712
  0.5995325  0.6399199
  0.6072274  0.6472123
  0.6115455  0.6528216
  0.6105289  0.6445067

Tuning parameter 'nrounds' was held constant at a value of 500
Tuning
 parameter 'eta' was held constant at a value of 0.01
Sens was used to select the optimal model using the largest value.
The final values used for the model were nrounds = 500, max_depth = 6, eta
 = 0.01, gamma = 0, colsample_bytree = 0.7, min_child_weight = 150
 and subsample = 1.
svm_model
Support Vector Machines with Radial Basis Function Kernel 

4305 samples
  91 predictor
   2 classes: 'Not_D_and_inf_Q1', 'Not_D_and_sup_Q1' 

Pre-processing: centered (188), scaled (188) 
Resampling: Cross-Validated (5 fold, repeated 10 times) 
Summary of sample sizes: 3444, 3444, 3444, 3445, 3443, 3444, ... 
Resampling results across tuning parameters:

  C             ROC        Sens        Spec     
  2.500000e-01  0.6845732  0.18500726  0.9394922
  5.000000e-01  0.6845750  0.18242057  0.9410422
  1.000000e+00  0.6840859  0.17991323  0.9422641
  2.000000e+00  0.6798961  0.16397684  0.9493251
  4.000000e+00  0.6703732  0.14812722  0.9539767
  8.000000e+00  0.6566924  0.12104184  0.9613335
  1.600000e+01  0.6407620  0.09100085  0.9716467
  3.200000e+01  0.6284837  0.06805521  0.9777494
  6.400000e+01  0.6192433  0.06259466  0.9794860
  1.280000e+02  0.6191579  0.06475330  0.9776136
  2.560000e+02  0.6194775  0.06690340  0.9770227
  5.120000e+02  0.6217497  0.06459543  0.9777956
  1.024000e+03  0.6177933  0.06038327  0.9787580
  2.048000e+03  0.6197161  0.05951205  0.9813836
  4.096000e+03  0.6191493  0.06151835  0.9799168
  8.192000e+03  0.6175882  0.06550064  0.9769857
  1.638400e+04  0.6181877  0.06298648  0.9787567
  3.276800e+04  0.6189728  0.06439820  0.9785556
  6.553600e+04  0.6195841  0.06335973  0.9792230
  1.310720e+05  0.6194290  0.06180079  0.9789008
  2.621440e+05  0.6198103  0.05897868  0.9798427
  5.242880e+05  0.6189223  0.06078682  0.9802061
  1.048576e+06  0.6206165  0.05781581  0.9808264
  2.097152e+06  0.6201163  0.05771642  0.9814124
  4.194304e+06  0.6181878  0.06176838  0.9784390
  8.388608e+06  0.6194077  0.06167317  0.9779674
  1.677722e+07  0.6198161  0.06217771  0.9791928
  3.355443e+07  0.6196947  0.06185587  0.9788317
  6.710886e+07  0.6202174  0.06380287  0.9792079
  1.342177e+08  0.6188412  0.06242749  0.9793425
  2.684355e+08  0.6176711  0.05789675  0.9808018
  5.368709e+08  0.6196809  0.05965965  0.9802059
  1.073742e+09  0.6201879  0.06638327  0.9778590
  2.147484e+09  0.6199448  0.06334543  0.9796292
  4.294967e+09  0.6190879  0.05958005  0.9802028
  8.589935e+09  0.6188724  0.06061197  0.9798608
  1.717987e+10  0.6185836  0.06317593  0.9782026
  3.435974e+10  0.6195006  0.05896523  0.9804261
  6.871948e+10  0.6205110  0.06532187  0.9793169
  1.374390e+11  0.6190431  0.06202322  0.9794408
  2.748779e+11  0.6185959  0.06370787  0.9791893
  5.497558e+11  0.6196803  0.06260614  0.9790483
  1.099512e+12  0.6189025  0.06194678  0.9798426
  2.199023e+12  0.6180484  0.05994673  0.9797927
  4.398047e+12  0.6201210  0.05840562  0.9803555
  8.796093e+12  0.6211872  0.06125993  0.9797466
  1.759219e+13  0.6184832  0.06168053  0.9803620
  3.518437e+13  0.6186460  0.06325937  0.9790679
  7.036874e+13  0.6193463  0.06602495  0.9777952
  1.407375e+14  0.6189965  0.05886874  0.9806771
  2.814750e+14  0.6204431  0.06429123  0.9779287
  5.629500e+14  0.6191002  0.06043461  0.9795445
  1.125900e+15  0.6196932  0.06164665  0.9792811
  2.251800e+15  0.6212284  0.06310931  0.9794839
  4.503600e+15  0.6194147  0.06195108  0.9796156
  9.007199e+15  0.6189499  0.06304764  0.9789768
  1.801440e+16  0.6190483  0.06269724  0.9789688
  3.602880e+16  0.6195203  0.05914738  0.9795222
  7.205759e+16  0.6181346  0.06159151  0.9791887
  1.441152e+17  0.6199934  0.05990134  0.9793019
  2.882304e+17  0.6211486  0.05887301  0.9810091
  5.764608e+17  0.6200023  0.06106486  0.9781537
  1.152922e+18  0.6219580  0.06558044  0.9781814
  2.305843e+18  0.6202328  0.06252719  0.9786332
  4.611686e+18  0.6184795  0.06339078  0.9791044
  9.223372e+18  0.6194937  0.05795243  0.9802058
  1.844674e+19  0.6202671  0.06154891  0.9788177
  3.689349e+19  0.6196105  0.06490157  0.9783643
  7.378698e+19  0.6204483  0.06040686  0.9794684
  1.475740e+20  0.6193828  0.06061105  0.9787396
  2.951479e+20  0.6204511  0.06179469  0.9800144
  5.902958e+20  0.6183741  0.06116540  0.9787963
  1.180592e+21  0.6209400  0.06411523  0.9785145
  2.361183e+21  0.6193779  0.06466960  0.9778560
  4.722366e+21  0.6182601  0.06461721  0.9777089
  9.444733e+21  0.6193490  0.06315944  0.9796675
  1.888947e+22  0.6190460  0.06270551  0.9792769
  3.777893e+22  0.6200651  0.06220965  0.9794672
  7.555786e+22  0.6216710  0.06198494  0.9789899
  1.511157e+23  0.6203920  0.05768892  0.9811646
  3.022315e+23  0.6190263  0.06025668  0.9797500
  6.044629e+23  0.6203105  0.06212828  0.9793594
  1.208926e+24  0.6187173  0.06250836  0.9786330
  2.417852e+24  0.6196223  0.05982369  0.9796821
  4.835703e+24  0.6187729  0.05975876  0.9795862
  9.671407e+24  0.6203110  0.06023354  0.9801699
  1.934281e+25  0.6195157  0.06502927  0.9784628
  3.868563e+25  0.6186238  0.06126218  0.9789168
  7.737125e+25  0.6184958  0.06045091  0.9782006
  1.547425e+26  0.6190884  0.06342162  0.9789310
  3.094850e+26  0.6181873  0.06142845  0.9784399
  6.189700e+26  0.6189298  0.06062272  0.9786674
  1.237940e+27  0.6187053  0.06531791  0.9788524
  2.475880e+27  0.6203114  0.06206026  0.9789872
  4.951760e+27  0.6192489  0.06124180  0.9790311
  9.903520e+27  0.6174195  0.06008044  0.9802894
  1.980704e+28  0.6193041  0.06138461  0.9798124
  3.961408e+28  0.6196082  0.06496835  0.9781007
  7.922816e+28  0.6190864  0.06123360  0.9788435
  1.584563e+29  0.6188447  0.06135820  0.9797634

Tuning parameter 'sigma' was held constant at a value of 0.00345505
ROC was used to select the optimal model using the largest value.
The final values used for the model were sigma = 0.00345505 and C = 0.5.
glmnet_model
glmnet 

4305 samples
  91 predictor
   2 classes: 'Not_D_and_inf_Q1', 'Not_D_and_sup_Q1' 

Pre-processing: centered (188), scaled (188) 
Resampling: Cross-Validated (5 fold, repeated 10 times) 
Summary of sample sizes: 3445, 3444, 3444, 3443, 3444, 3444, ... 
Resampling results across tuning parameters:

  alpha      lambda        ROC        Sens          Spec     
  0.1000000  0.0001622919  0.6820664  2.865147e-01  0.9014490
  0.1000000  0.0001777873  0.6820948  2.865935e-01  0.9014490
  0.1000000  0.0001947622  0.6821287  2.865935e-01  0.9015151
  0.1000000  0.0002133579  0.6821721  2.866719e-01  0.9015810
  0.1000000  0.0002337290  0.6822207  2.865935e-01  0.9015480
  0.1000000  0.0002560452  0.6822747  2.863582e-01  0.9016140
  0.1000000  0.0002804921  0.6823467  2.863582e-01  0.9017129
  0.1000000  0.0003072731  0.6824176  2.861229e-01  0.9016800
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  0.9909091  0.0039485299  0.6942059  2.278737e-01  0.9342118
  0.9909091  0.0043255306  0.6945165  2.242615e-01  0.9362244
  0.9909091  0.0047385269  0.6947325  2.201010e-01  0.9385337
  0.9909091  0.0051909556  0.6948708  2.159413e-01  0.9406122
  0.9909091  0.0056865816  0.6948883  2.109174e-01  0.9425587
  0.9909091  0.0062295293  0.6947355  2.040111e-01  0.9453962
  0.9909091  0.0068243170  0.6943206  1.978885e-01  0.9487617
  0.9909091  0.0074758943  0.6937617  1.894887e-01  0.9517310
  0.9909091  0.0081896834  0.6929703  1.809335e-01  0.9547661
  0.9909091  0.0089716242  0.6919371  1.723767e-01  0.9575705
  0.9909091  0.0098282238  0.6906016  1.610721e-01  0.9603418
  0.9909091  0.0107666104  0.6888418  1.488251e-01  0.9636738
  0.9909091  0.0117945929  0.6867086  1.356366e-01  0.9668409
  0.9909091  0.0129207260  0.6841686  1.226833e-01  0.9702393
  0.9909091  0.0141543809  0.6811292  1.093377e-01  0.9737036
  0.9909091  0.0155058236  0.6777788  9.591447e-02  0.9764422
  0.9909091  0.0169863003  0.6743517  8.241593e-02  0.9797084
  0.9909091  0.0186081312  0.6710091  6.695507e-02  0.9834698
  0.9909091  0.0203848124  0.6672957  5.533889e-02  0.9871981
  0.9909091  0.0223311290  0.6632861  4.372333e-02  0.9897716
  0.9909091  0.0244632774  0.6593301  3.029767e-02  0.9926749
  0.9909091  0.0267990007  0.6555860  2.134877e-02  0.9947867
  0.9909091  0.0293577360  0.6518693  1.357789e-02  0.9962714
  0.9909091  0.0321607762  0.6477874  8.475838e-03  0.9974923
  0.9909091  0.0352314471  0.6433683  4.866759e-03  0.9984822
  0.9909091  0.0385953019  0.6382367  2.747877e-03  0.9990761
  0.9909091  0.0422803333  0.6319173  1.804848e-03  0.9991750
  0.9909091  0.0463172070  0.6240009  1.176779e-03  0.9992740
  0.9909091  0.0507395164  0.6153215  5.493284e-04  0.9995050
  0.9909091  0.0555840623  0.6063874  1.571715e-04  0.9997690
  0.9909091  0.0608911595  0.5946502  0.000000e+00  0.9999670
  0.9909091  0.0667049717  0.5747619  0.000000e+00  1.0000000
  0.9909091  0.0730738795  0.5123101  0.000000e+00  1.0000000
  0.9909091  0.0800508827  0.5000000  0.000000e+00  1.0000000
  0.9909091  0.0876940415  0.5000000  0.000000e+00  1.0000000
  0.9909091  0.0960669596  0.5000000  0.000000e+00  1.0000000
  0.9909091  0.1052393135  0.5000000  0.000000e+00  1.0000000
  0.9909091  0.1152874324  0.5000000  0.000000e+00  1.0000000
  0.9909091  0.1262949331  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.0001622919  0.6830781  2.840809e-01  0.9033624
  1.0000000  0.0001777873  0.6832334  2.836097e-01  0.9035603
  1.0000000  0.0001947622  0.6834030  2.832957e-01  0.9038573
  1.0000000  0.0002133579  0.6836207  2.831391e-01  0.9041542
  1.0000000  0.0002337290  0.6838510  2.824323e-01  0.9045829
  1.0000000  0.0002560452  0.6841087  2.815677e-01  0.9048799
  1.0000000  0.0002804921  0.6843732  2.814896e-01  0.9056387
  1.0000000  0.0003072731  0.6846554  2.808612e-01  0.9057377
  1.0000000  0.0003366112  0.6849512  2.805478e-01  0.9063975
  1.0000000  0.0003687504  0.6852519  2.796072e-01  0.9067934
  1.0000000  0.0004039582  0.6855544  2.790579e-01  0.9072883
  1.0000000  0.0004425276  0.6858632  2.782730e-01  0.9079814
  1.0000000  0.0004847796  0.6861781  2.772521e-01  0.9082454
  1.0000000  0.0005310658  0.6865217  2.763881e-01  0.9089712
  1.0000000  0.0005817713  0.6868479  2.755251e-01  0.9097631
  1.0000000  0.0006373181  0.6871274  2.744267e-01  0.9102580
  1.0000000  0.0006981684  0.6873956  2.724638e-01  0.9108519
  1.0000000  0.0007648286  0.6876738  2.716782e-01  0.9114127
  1.0000000  0.0008378535  0.6879504  2.697925e-01  0.9126994
  1.0000000  0.0009178507  0.6882110  2.685370e-01  0.9133592
  1.0000000  0.0010054860  0.6885102  2.668096e-01  0.9141843
  1.0000000  0.0011014885  0.6888182  2.646908e-01  0.9148443
  1.0000000  0.0012066573  0.6891647  2.635912e-01  0.9162630
  1.0000000  0.0013218674  0.6895317  2.616285e-01  0.9174839
  1.0000000  0.0014480777  0.6899192  2.595096e-01  0.9181436
  1.0000000  0.0015863384  0.6903202  2.565249e-01  0.9191663
  1.0000000  0.0017378000  0.6907394  2.539348e-01  0.9205192
  1.0000000  0.0019037230  0.6911691  2.526024e-01  0.9215754
  1.0000000  0.0020854881  0.6915814  2.491471e-01  0.9231260
  1.0000000  0.0022846079  0.6919774  2.464792e-01  0.9242805
  1.0000000  0.0025027394  0.6923823  2.442828e-01  0.9253364
  1.0000000  0.0027416978  0.6927792  2.410638e-01  0.9270519
  1.0000000  0.0030034717  0.6931858  2.377672e-01  0.9288339
  1.0000000  0.0032902395  0.6935413  2.340775e-01  0.9302526
  1.0000000  0.0036043875  0.6938982  2.311718e-01  0.9324962
  1.0000000  0.0039485299  0.6942508  2.276381e-01  0.9343108
  1.0000000  0.0043255306  0.6945388  2.242618e-01  0.9363894
  1.0000000  0.0047385269  0.6947438  2.197869e-01  0.9385667
  1.0000000  0.0051909556  0.6948815  2.150774e-01  0.9408431
  1.0000000  0.0056865816  0.6948705  2.103681e-01  0.9428226
  1.0000000  0.0062295293  0.6947191  2.037758e-01  0.9457593
  1.0000000  0.0068243170  0.6942727  1.974961e-01  0.9490586
  1.0000000  0.0074758943  0.6937060  1.887828e-01  0.9520939
  1.0000000  0.0081896834  0.6928746  1.803838e-01  0.9548981
  1.0000000  0.0089716242  0.6918253  1.719058e-01  0.9578345
  1.0000000  0.0098282238  0.6904607  1.598163e-01  0.9607705
  1.0000000  0.0107666104  0.6886599  1.479620e-01  0.9639046
  1.0000000  0.0117945929  0.6864535  1.346948e-01  0.9669399
  1.0000000  0.0129207260  0.6838824  1.208776e-01  0.9706682
  1.0000000  0.0141543809  0.6808200  1.082390e-01  0.9739014
  1.0000000  0.0155058236  0.6774205  9.403026e-02  0.9766401
  1.0000000  0.0169863003  0.6740227  8.084607e-02  0.9799394
  1.0000000  0.0186081312  0.6706336  6.569955e-02  0.9837997
  1.0000000  0.0203848124  0.6668977  5.455396e-02  0.9873301
  1.0000000  0.0223311290  0.6628692  4.231002e-02  0.9901674
  1.0000000  0.0244632774  0.6589362  2.935557e-02  0.9928399
  1.0000000  0.0267990007  0.6552137  2.079914e-02  0.9949515
  1.0000000  0.0293577360  0.6514816  1.318512e-02  0.9963374
  1.0000000  0.0321607762  0.6473570  8.005249e-03  0.9975254
  1.0000000  0.0352314471  0.6429164  4.631465e-03  0.9986142
  1.0000000  0.0385953019  0.6376575  2.747877e-03  0.9990761
  1.0000000  0.0422803333  0.6312157  1.647985e-03  0.9991750
  1.0000000  0.0463172070  0.6230157  1.098348e-03  0.9992740
  1.0000000  0.0507395164  0.6146817  4.708970e-04  0.9995380
  1.0000000  0.0555840623  0.6057076  1.571715e-04  0.9998020
  1.0000000  0.0608911595  0.5936464  0.000000e+00  0.9999670
  1.0000000  0.0667049717  0.5721188  0.000000e+00  1.0000000
  1.0000000  0.0730738795  0.5082284  0.000000e+00  1.0000000
  1.0000000  0.0800508827  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.0876940415  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.0960669596  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.1052393135  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.1152874324  0.5000000  0.000000e+00  1.0000000
  1.0000000  0.1262949331  0.5000000  0.000000e+00  1.0000000

ROC was used to select the optimal model using the largest value.
The final values used for the model were alpha = 0.9545455 and lambda
 = 0.005686582.

18.1.2 Visualization of Results

Let us apply the resamples() function from {caret} to the list of models, to get metrics computed on the final model produced by the train() function from {caret}, i.e., the model which provided the best performances with respect to sensitivity on the validation sets (computed over the repeated 5-fold cross validation, see Chapter 17). Since we performed 10 repetitions of 5-fold cross validation, the metrics are computed on 10*5=50 validation samples.

list_models <- list(
  rf = grid_search_rf,
  xgb = grid_search_xgb,
  svm = svm_model,
  glmnet = glmnet_model
)
results <- resamples(list_models)

We can have a look at a summary of the results. The summary function we used was twoClassSummary(). This function returns three metrics: ROC-AUC, sensitivity, and specificity. For each repetition and each fold, we thus have a value for these three metrics computed on the validation sample.

summary(results)

Call:
summary.resamples(object = results)

Models: rf, xgb, svm, glmnet 
Number of resamples: 50 

ROC 
            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
rf     0.6347256 0.6645601 0.6767909 0.6742330 0.6869602 0.7125607    0
xgb    0.6464376 0.6722643 0.6839772 0.6822150 0.6923111 0.7161975    0
svm    0.6284400 0.6761443 0.6871079 0.6845750 0.6959975 0.7184689    0
glmnet 0.6553744 0.6784063 0.6950676 0.6949193 0.7065919 0.7552310    0

Sens 
             Min.    1st Qu.     Median      Mean    3rd Qu.       Max. NA's
rf     0.03921569 0.05490196 0.06090011 0.0629560 0.07086614 0.09019608    0
xgb    0.52941176 0.58921569 0.61176471 0.6138996 0.63823529 0.67058824    0
svm    0.12941176 0.16470588 0.18110236 0.1824206 0.20313803 0.24409449    0
glmnet 0.16862745 0.19607843 0.20784314 0.2127219 0.22745098 0.25882353    0

Spec 
            Min.   1st Qu.    Median      Mean   3rd Qu.      Max. NA's
rf     0.9752475 0.9818482 0.9851730 0.9851537 0.9884488 0.9983498    0
xgb    0.6056106 0.6456271 0.6584158 0.6555585 0.6662541 0.7095710    0
svm    0.8844884 0.9311335 0.9405941 0.9410422 0.9517531 0.9752475    0
glmnet 0.9075908 0.9356436 0.9438944 0.9416679 0.9484541 0.9636964    0

For each of the models, we can look at the performance metrics computed on the validation samples for the best set of hyperparameters.

bwplot(results)
Figure 18.1: Performance metrics computed on the validation samples over the repeated 5-fold cross validation process, for the final models.

Let us load the train and test samples (defined in Chapter 5):

load("../data/out/df_train_sah.rda")
load("../data/out/df_test_sah.rda")
ind_remove <- which(
  colnames(df_train) %in% c("status", "id", "PERSONNE_statut")
)

For each model, let us compute some additional metrics on the train and on the test set. We need to load the packages required to make predictions using the fitted models.

library(randomForest)
Warning: package 'randomForest' was built under R version 4.4.1
randomForest 4.7-1.2
Type rfNews() to see new features/changes/bug fixes.

Attaching package: 'randomForest'
The following object is masked from 'package:dplyr':

    combine
The following object is masked from 'package:ggplot2':

    margin
library(ranger)

Attaching package: 'ranger'
The following object is masked from 'package:randomForest':

    importance
library(xgboost)

Attaching package: 'xgboost'
The following object is masked from 'package:dplyr':

    slice
library(e1071)
library(glmnet)
Loading required package: Matrix

Attaching package: 'Matrix'
The following objects are masked from 'package:tidyr':

    expand, pack, unpack
Loaded glmnet 4.1-8

Then, we can loop over the models and compute the predictions on both the train set and the test set. For each set, we focus on the accuracy, the sensitivity, and on the specificity.

res_train <- NULL
res_test <- NULL
roc_curves <- NULL
for (mod in list_models) {
  # Predictions
  pred_train <- predict(mod, newdata = df_train[,-ind_remove])
  pred_test <- predict(mod, newdata = df_test[-ind_remove])
  # Predicted scores
  pred_train_scores <- predict(
    mod, newdata = df_train[,-ind_remove], type = "prob"
  )
  pred_test_scores <- predict(
    mod, newdata = df_test[,-ind_remove], type = "prob"
  )
  # Confusion matrices
  cm_train <- confusionMatrix(pred_train, df_train$status)
  cm_test <- confusionMatrix(pred_test, df_test$status)
  # ROC Curves
  roc_train <- MLeval::evalm(
    data.frame(pred_train_scores, df_train$status), 
    showplots = FALSE
  )
  ind_roc_train <- which(row.names(roc_train$stdres$Group1) == "AUC-ROC")
  roc_val_train <- roc_train$stdres$Group1$Score[ind_roc_train]
  roc_test <- MLeval::evalm(
    data.frame(pred_test_scores, df_test$status), 
    showplots = FALSE
  )
  ind_roc_test <- which(row.names(roc_test$stdres$Group1) == "AUC-ROC")
  roc_val_test <- roc_test$stdres$Group1$Score[ind_roc_test]
  
  # Binding the results
  res_train <- bind_rows(
    res_train, 
    tibble(
      method = mod$method, 
      accuracy = cm_train$overall["Accuracy"],
      sensitivity = cm_train$byClass[c("Sensitivity")],
      specificity = cm_train$byClass[c("Specificity")],
      auc = roc_val_train
    )
  )
  res_test <- bind_rows(
    res_test, 
    tibble(
      method = mod$method,
      accuracy = cm_test$overall["Accuracy"],
      sensitivity = cm_test$byClass[c("Sensitivity")],
      specificity = cm_test$byClass[c("Specificity")],
      auc = roc_val_test
    )
  )
  # And for the roc curves
  roc_curves <- bind_rows(
    roc_curves,
    roc_train$roc$data |> mutate(model = mod$method, sample = "train") |> 
    bind_rows(
      roc_test$roc$data |> mutate(model = mod$method, sample = "test")
    )
  )
}

The performances metrics are shown in Table 18.1.

Code
library(kableExtra)
res_train |> mutate(sample = "Train") |> 
  bind_rows(
    res_test |> mutate(sample = "Test")
  ) |> 
  mutate(sample = factor(sample, levels = c("Train", "Test"))) |> 
  pivot_wider(
    names_from = "sample", 
    values_from = c("accuracy", "sensitivity", "specificity", "auc")
  ) |> 
  kable(
    align=c('l', rep('c', 7)), digits = 3, 
    col.names = c("Method", rep(c("Train", "Test"), 4))
  ) |> 
  kable_styling("striped") %>%
  add_header_above(
    c(" " = 1, "Accuracy" = 2, "Sensitivity" = 2, "Specificity" = 2, "AUC" = 2)
  )
Table 18.1: Performance metrics on the train and on the validation set.
Accuracy
Sensitivity
Specificity
AUC
Method Train Test Train Test Train Test Train Test
ranger 0.805 0.713 0.341 0.072 1.000 0.983 0.96 0.69
xgbTree 0.686 0.644 0.676 0.610 0.690 0.658 0.75 0.68
svmRadial 0.809 0.720 0.396 0.198 0.983 0.939 0.88 0.69
glmnet 0.738 0.736 0.225 0.201 0.954 0.960 0.73 0.71

The ROC curves:

Code
source("../Codes/utils.R")
plot_roc_curves <- ggplot(
  data = roc_curves |> 
    mutate(
      model = factor(
        model, 
        levels = c("ranger", "xgbTree", "svmRadial", "glmnet"),
        labels = c(
          "Random Forest", "XGBoost", "SVM", "Penalized Logistic Regression"
        )
      ),
      sample = factor(
        sample, 
        levels = c("train", "test"), 
        labels = c("Train", "Test")
      )
    ), 
  mapping = aes(x = FPR, y = SENS, colour = model, linetype = model)) +
  geom_line() +
  scale_colour_manual(NULL, values = c(
    "Random Forest" = "#009E73", 
    "XGBoost" = "#D55E00", 
    "SVM" = "#56B4E9", 
    "Penalized Logistic Regression" = "#CC79A7"
  )) +
  scale_linetype_discrete(NULL) +
  theme_paper() +
  labs(x = "False positive rate", y = "True positive rate") +
  facet_wrap(~sample)
plot_roc_curves
Figure 18.2: ROC Curves