Chapter 5 Logistic Regression
CHUNJIE NAN
2023-01-10
5.1 Prerequisites
# Helper packages
library(dplyr) # for data wrangling## Warning: 패키지 'dplyr'는 R 버전 4.2.2에서 작성되었습니다##
## 다음의 패키지를 부착합니다: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2) # for awesome plotting## Warning: 패키지 'ggplot2'는 R 버전 4.2.2에서 작성되었습니다library(rsample) # for data splitting## Warning: 패키지 'rsample'는 R 버전 4.2.2에서 작성되었습니다library(caret) # for logistic modeling## Warning: 패키지 'caret'는 R 버전 4.2.2에서 작성되었습니다## 필요한 패키지를 로딩중입니다: latticelibrary(vip) # for variable importance## Warning: 패키지 'vip'는 R 버전 4.2.2에서 작성되었습니다##
## 다음의 패키지를 부착합니다: 'vip'## The following object is masked from 'package:utils':
##
## vilibrary(tidyr)## Warning: 패키지 'tidyr'는 R 버전 4.2.2에서 작성되었습니다library(tidyverse)## Warning: 패키지 'tidyverse'는 R 버전 4.2.2에서 작성되었습니다## ── Attaching packages
## ───────────────────────────────────────
## tidyverse 1.3.2 ──## ✔ tibble 3.1.8 ✔ stringr 1.4.1
## ✔ readr 2.1.3 ✔ forcats 0.5.2
## ✔ purrr 0.3.5## Warning: 패키지 'tibble'는 R 버전 4.2.2에서 작성되었습니다## Warning: 패키지 'readr'는 R 버전 4.2.2에서 작성되었습니다## Warning: 패키지 'purrr'는 R 버전 4.2.2에서 작성되었습니다## Warning: 패키지 'stringr'는 R 버전 4.2.2에서 작성되었습니다## Warning: 패키지 'forcats'는 R 버전 4.2.2에서 작성되었습니다## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ purrr::lift() masks caret::lift()attrition <- modeldata::attrition
df <-attrition %>%
mutate_if(is.ordered, factor, ordered = FALSE)
# Create training 70%, 30% test set.
set.seed(123)
churn_split<-initial_split(df, prop = 0.7, strata = 'Attrition')
churn_train <- training(churn_split)
churn_test<-testing(churn_split)5.3 Simple logistic regression
The first predicts the probability of attrition based on their monthly income and the second is based on whether or not the employee works overtime.
model1<-glm(Attrition ~ MonthlyIncome, family = 'binomial', data = churn_train)
model2<-glm(Attrition ~ OverTime, family = 'binomial', data = churn_train)The estimates β0 and β1 are chosen to maximize this likelihood function. What results is the predicted probability of attrition. The table below shows the coefficient estimates and related information that result from fitting a logistic regression model in order to predict the probability of Attrition = Yes for our two models
tidy(model1)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -0.886 0.157 -5.64 0.0000000174
## 2 MonthlyIncome -0.000139 0.0000272 -5.10 0.000000344tidy(model2)## # A tibble: 2 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -2.13 0.119 -17.9 1.46e-71
## 2 OverTimeYes 1.29 0.176 7.35 2.01e-13It is easier to interpret the coefficients using an exp() transformation
exp(coef(model1))## (Intercept) MonthlyIncome
## 0.4122647 0.9998614Interpretation: the odds of an employee atriting in model1 increase multiplicatively by 0.9999 for every one dollar increase in MonthlyIncome.
exp(coef(model2))## (Intercept) OverTimeYes
## 0.1189759 3.6323389Whereas the odds of attriting in model2 increase multiplcatively by 3.6323 for employees that work OverTime compared to those that do not.
# confidence interval
confint(model1)## 프로파일링이 완료되길 기다리는 중입니다...## 2.5 % 97.5 %
## (Intercept) -1.1932606571 -5.761048e-01
## MonthlyIncome -0.0001948723 -8.803311e-05confint(model2)## 프로파일링이 완료되길 기다리는 중입니다...## 2.5 % 97.5 %
## (Intercept) -2.3695727 -1.902409
## OverTimeYes 0.9463761 1.635373# confidence interval for odds
exp(confint(model1))## 프로파일링이 완료되길 기다리는 중입니다...## 2.5 % 97.5 %
## (Intercept) 0.3032309 0.5620835
## MonthlyIncome 0.9998051 0.9999120exp(confint(model2))## 프로파일링이 완료되길 기다리는 중입니다...## 2.5 % 97.5 %
## (Intercept) 0.09352068 0.1492087
## OverTimeYes 2.57635618 5.13137075.4 Multiple logistic regression
let’s go ahead and fit a model that predicts the probability of Attrition based on the MonthlyIncome and OverTime.
model3<-glm(
Attrition ~ MonthlyIncome + OverTime,
family = 'binomial',
data = churn_train
)
tidy(model3)## # A tibble: 3 × 5
## term estimate std.error statistic p.value
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -1.33 0.177 -7.54 4.74e-14
## 2 MonthlyIncome -0.000147 0.0000280 -5.27 1.38e- 7
## 3 OverTimeYes 1.35 0.180 7.50 6.59e-145.4 Assessing model accuracy
As in the last chapter, we’ll use caret::train() and fit three 10-fold cross validated logistic regression models. Extracting the accuracy measures (in this case, classification accuracy)
# Attrition ~ MonthlyIncome
set.seed(123)
cv_model1<-train(
Attrition ~ MonthlyIncome,
data = churn_train,
method = 'glm',
family = 'binomial',
trControl = trainControl(method = 'cv', number = 10)
)
# Attrition ~ MonthlyIncome + OverTime
set.seed(123)
cv_model2<-train(
Attrition ~ MonthlyIncome + OverTime,
data = churn_train,
method = 'glm',
family = 'binomial',
trControl = trainControl(method = 'cv', number = 10)
)
# Attrition ~.,
set.seed(123)
cv_model3<-train(
Attrition ~.,
data = churn_train,
method = 'glm',
family = 'binomial',
trControl = trainControl(method = 'cv', number = 10)
)Extract out of sample performance measures
summary(
resamples(
list(model1 = cv_model1,
model2 = cv_model2,
model3 = cv_model3)
)
)$statistic$Accuracy## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## model1 0.8349515 0.8349515 0.8398379 0.8395076 0.8431373 0.8446602 0
## model2 0.8349515 0.8349515 0.8398379 0.8395076 0.8431373 0.8446602 0
## model3 0.8058252 0.8529412 0.8786765 0.8715662 0.8907767 0.9320388 0We can get a better understanding of our model’s performance by assessing the confusion matrix (see Section 2.6). We can use caret::confusionMatrix() to compute a confusion matrix
# predict class
pred_class <-predict(cv_model3, churn_train)
# create confusion matrix
confusionMatrix(data = relevel(pred_class, ref = 'Yes'),
reference = relevel(churn_train$Attrition, ref = 'Yes'))## Confusion Matrix and Statistics
##
## Reference
## Prediction Yes No
## Yes 83 20
## No 82 843
##
## Accuracy : 0.9008
## 95% CI : (0.8809, 0.9184)
## No Information Rate : 0.8395
## P-Value [Acc > NIR] : 8.982e-09
##
## Kappa : 0.5658
##
## Mcnemar's Test P-Value : 1.542e-09
##
## Sensitivity : 0.50303
## Specificity : 0.97683
## Pos Pred Value : 0.80583
## Neg Pred Value : 0.91135
## Prevalence : 0.16051
## Detection Rate : 0.08074
## Detection Prevalence : 0.10019
## Balanced Accuracy : 0.73993
##
## 'Positive' Class : Yes
## Compare model1 and model3 with ROC plot
library(ROCR)## Warning: 패키지 'ROCR'는 R 버전 4.2.2에서 작성되었습니다# compute predicted probabilities
m1_prob<-predict(cv_model1, churn_train, type = 'prob')$Yes
m1_prob## [1] 0.21596299 0.22162566 0.22107613 0.16630174 0.22751553 0.18734674
## [7] 0.21591605 0.09367513 0.04632442 0.19265877 0.19121824 0.07251014
## [13] 0.25790703 0.09056822 0.02895546 0.14401949 0.22222408 0.23770921
## [19] 0.20423253 0.16364735 0.22959309 0.10951257 0.19121824 0.17956054
## [25] 0.21332242 0.15627202 0.23136329 0.16217282 0.09481110 0.18810772
## [31] 0.10496105 0.19115394 0.15367606 0.14927539 0.22800317 0.09231878
## [37] 0.09673181 0.23321737 0.22083751 0.22569344 0.21295044 0.06167747
## [43] 0.16844609 0.21713892 0.09067104 0.18457676 0.13095904 0.23618033
## [49] 0.18821360 0.05963978 0.16241783 0.16684059 0.08583124 0.17071054
## [55] 0.05928315 0.18675651 0.05683479 0.21486183 0.17469141 0.16772887
## [61] 0.03213398 0.21643281 0.12746537 0.03597891 0.21914860 0.18085073
## [67] 0.07596799 0.09656237 0.21770501 0.14955727 0.22893172 0.22516092
## [73] 0.14228514 0.17609486 0.21518941 0.17206893 0.14604780 0.18474373
## [79] 0.17752740 0.20911909 0.22043227 0.03669243 0.25130390 0.13040784
## [85] 0.23045241 0.22942149 0.10588928 0.18470198 0.23230140 0.23003474
## [91] 0.22059907 0.10023925 0.22412268 0.22690702 0.10048958 0.11005449
## [97] 0.21295044 0.23585539 0.17078906 0.08825463 0.23089523 0.19298240
## [103] 0.19819483 0.21957589 0.09889701 0.05786899 0.02512497 0.23111686
## [109] 0.23583040 0.03864682 0.20098517 0.18249946 0.16576428 0.14252215
## [115] 0.14754094 0.18514076 0.13832255 0.22991200 0.17335639 0.10077815
## [121] 0.11296603 0.09366336 0.15322586 0.15369409 0.22277565 0.08652994
## [127] 0.18415984 0.23363906 0.21869822 0.10866380 0.20893574 0.02786504
## [133] 0.23141260 0.02848754 0.19293923 0.23227668 0.21216156 0.20649472
## [139] 0.02797792 0.05831652 0.21591605 0.15292035 0.19317678 0.14455007
## [145] 0.08299233 0.22961761 0.02710913 0.22036082 0.21867453 0.16607123
## [151] 0.23366388 0.03823690 0.15977633 0.19145418 0.05969422 0.20898156
## [157] 0.23630540 0.05886706 0.15934876 0.14518547 0.02819740 0.03476810
## [163] 0.17274142 0.17984662 0.16290874 0.17605464 0.23518149 0.15676615
## [169] 0.20669923 0.18126182 0.21879298 0.22996109 0.11942774 0.19823889
## [175] 0.25875695 0.15831160 0.13627014 0.15807162 0.16160856 0.15833007
## [181] 0.17445171 0.14496196 0.16682132 0.22102839 0.07359905 0.03725015
## [187] 0.05615500 0.22625111 0.16647479 0.02771523 0.17724421 0.03158668
## [193] 0.16591770 0.14601323 0.17349549 0.12788223 0.15005163 0.14604780
## [199] 0.07715385 0.13281599 0.11585932 0.21608038 0.04298461 0.17791230
## [205] 0.22100452 0.22888278 0.06789683 0.15261533 0.17615521 0.16517087
## [211] 0.14083640 0.13913415 0.23274669 0.22306381 0.20349006 0.16589852
## [217] 0.22193669 0.23304388 0.14274253 0.19543375 0.08270792 0.17216769
## [223] 0.22467759 0.03933768 0.18593679 0.12574857 0.15731668 0.22388171
## [229] 0.18726233 0.05348352 0.20357995 0.14277646 0.18497351 0.18050187
## [235] 0.18122068 0.18200362 0.23262294 0.02799677 0.06194275 0.14211604
## [241] 0.11411010 0.22200851 0.03988613 0.17980573 0.15052961 0.17467143
## [247] 0.03270361 0.23563060 0.07306211 0.16953627 0.03350222 0.18656709
## [253] 0.08610356 0.21423110 0.12520096 0.23573049 0.09367513 0.19036216
## [259] 0.03842597 0.14808225 0.17653777 0.06174168 0.19676681 0.14203156
## [265] 0.12867279 0.17477137 0.18589482 0.07669122 0.08305565 0.13820693
## [271] 0.16438865 0.12735749 0.08743267 0.10806107 0.15986940 0.22814961
## [277] 0.09552733 0.14432737 0.02686887 0.22031319 0.14734926 0.23488240
## [283] 0.03201348 0.19839317 0.23339094 0.09821963 0.21768140 0.18955159
## [289] 0.03950566 0.15797940 0.04647776 0.15241823 0.22380946 0.02682903
## [295] 0.21917232 0.13343991 0.23598033 0.11426434 0.22112387 0.22188882
## [301] 0.12379575 0.23693139 0.25660912 0.21808299 0.17385359 0.19085405
## [307] 0.11797757 0.17795286 0.17728464 0.11094012 0.17986707 0.16326824
## [313] 0.12530728 0.12857957 0.08069037 0.17169403 0.08800953 0.05022666
## [319] 0.02820880 0.10861010 0.02802697 0.19415091 0.07517388 0.12176522
## [325] 0.19779860 0.05759751 0.22229597 0.13832255 0.14962781 0.22571767
## [331] 0.08126810 0.22956857 0.13820693 0.23067374 0.16908784 0.16492253
## [337] 0.21250933 0.16854320 0.03831855 0.14895879 0.14118902 0.20230182
## [343] 0.14731443 0.12588579 0.18597875 0.18376444 0.20738199 0.18422233
## [349] 0.21895889 0.15250780 0.22397807 0.19506346 0.18627274 0.03451314
## [355] 0.07538618 0.16647479 0.22557234 0.23448403 0.14927539 0.16906837
## [361] 0.18231339 0.14707081 0.22443621 0.09087698 0.17529181 0.19716148
## [367] 0.24553238 0.20411991 0.19066145 0.22429146 0.14859012 0.18295490
## [373] 0.08303454 0.08487888 0.16749678 0.05717758 0.14627270 0.17216769
## [379] 0.17537199 0.21810663 0.22535446 0.22956857 0.18732563 0.08570081
## [385] 0.18602073 0.20062921 0.14301415 0.21619781 0.22922549 0.07399701
## [391] 0.08336232 0.05391322 0.16014888 0.12504921 0.03322059 0.16693696
## [397] 0.23116613 0.22429146 0.17272161 0.17557255 0.14196400 0.22871156
## [403] 0.23015753 0.23785996 0.08715655 0.22988746 0.13622119 0.05902855
## [409] 0.22981384 0.09696219 0.18522442 0.17645718 0.22525768 0.15476095
## [415] 0.19980788 0.13963301 0.13594414 0.18204490 0.17888760 0.03709634
## [421] 0.15821927 0.12232967 0.12148384 0.16959483 0.03542531 0.20349006
## [427] 0.23133864 0.03563909 0.02717136 0.21827216 0.18798072 0.05608891
## [433] 0.08397877 0.18829833 0.08511607 0.16183407 0.18635681 0.08235104
## [439] 0.17084796 0.06583836 0.19324161 0.22863821 0.05792949 0.14539205
## [445] 0.02521341 0.13738345 0.06107850 0.22956857 0.03446236 0.19091828
## [451] 0.07335368 0.23363906 0.23257345 0.21803572 0.02784627 0.18916857
## [457] 0.11405405 0.23788509 0.02641949 0.21518941 0.10774082 0.03883266
## [463] 0.08448133 0.17860271 0.19242170 0.20520301 0.08972684 0.08259231
## [469] 0.19885654 0.14015008 0.03439324 0.18505712 0.21432446 0.03817068
## [475] 0.15957172 0.08834390 0.10932346 0.22537866 0.02642306 0.13868645
## [481] 0.12298605 0.21874560 0.20918788 0.06268795 0.19074703 0.20713145
## [487] 0.18568512 0.16980969 0.21749260 0.22083751 0.15702287 0.22477420
## [493] 0.15733506 0.05967088 0.16788374 0.23163457 0.20025153 0.18260289
## [499] 0.09027180 0.16427443 0.22873601 0.21789394 0.22446034 0.18142646
## [505] 0.14386576 0.21306663 0.23386252 0.18453503 0.03352467 0.20930257
## [511] 0.02843771 0.10631000 0.18015354 0.20261519 0.14734926 0.09052256
## [517] 0.21898259 0.13753137 0.17189126 0.20065145 0.06211212 0.08770958
## [523] 0.23778458 0.19665729 0.03387225 0.13819042 0.19815077 0.22429146
## [529] 0.03173543 0.04223813 0.22366500 0.03195769 0.21397452 0.25814588
## [535] 0.18017402 0.02564628 0.08759872 0.18210683 0.20227945 0.09076252
## [541] 0.16300329 0.17698156 0.23605532 0.23565557 0.14844988 0.03261601
## [547] 0.03697768 0.22883385 0.17835880 0.13360029 0.20414243 0.14048452
## [553] 0.03819613 0.07324069 0.18025594 0.09519249 0.14946914 0.03350222
## [559] 0.20143077 0.17766913 0.13685859 0.19865785 0.17811515 0.24798012
## [565] 0.16951676 0.06042986 0.14552990 0.16264426 0.22306381 0.17639675
## [571] 0.15001628 0.08667249 0.21392789 0.09346350 0.18978596 0.08318242
## [577] 0.14804728 0.15632686 0.03861079 0.21500218 0.10120608 0.20854650
## [583] 0.03597891 0.02615691 0.17529181 0.21392789 0.23558067 0.15557872
## [589] 0.15857038 0.20421000 0.18800188 0.19199123 0.08453495 0.08391480
## [595] 0.23533113 0.10097932 0.16157099 0.05769541 0.11311891 0.21008365
## [601] 0.20421000 0.18357738 0.17569298 0.16507532 0.19856959 0.25679427
## [607] 0.17288013 0.08810972 0.03755460 0.22805198 0.23723227 0.11095379
## [613] 0.23645553 0.17909131 0.17509150 0.20966987 0.14258993 0.14534038
## [619] 0.07982061 0.04275708 0.04110880 0.11433450 0.11114538 0.23128934
## [625] 0.05295964 0.23040325 0.18541279 0.18468110 0.09199404 0.16181527
## [631] 0.16687913 0.04051729 0.22741809 0.14446439 0.22690702 0.14527152
## [637] 0.15077794 0.22693134 0.22895619 0.02656607 0.16160856 0.09433629
## [643] 0.18724123 0.10780747 0.02749568 0.23623035 0.02646945 0.17811515
## [649] 0.17335639 0.22114775 0.03484727 0.21820121 0.07981043 0.02856053
## [655] 0.23453380 0.15632686 0.18332819 0.17762863 0.17639675 0.19004188
## [661] 0.17333652 0.21112073 0.21223108 0.08845561 0.17008346 0.15630858
## [667] 0.12333037 0.12052545 0.15680281 0.04772203 0.19665729 0.20203351
## [673] 0.22378538 0.16689840 0.04064683 0.06148520 0.21893518 0.16256875
## [679] 0.23773433 0.05614030 0.13769588 0.03551068 0.03467982 0.16187168
## [685] 0.16175887 0.22717462 0.04309880 0.04661927 0.22024176 0.16379919
## [691] 0.16419832 0.20932551 0.20679017 0.13503485 0.22402627 0.20158691
## [697] 0.19175479 0.08357442 0.23735772 0.09916912 0.21549391 0.12149864
## [703] 0.17228627 0.12197292 0.10274210 0.21444119 0.08501897 0.03910262
## [709] 0.20292893 0.14315013 0.16014888 0.13702242 0.20704040 0.14389991
## [715] 0.09812144 0.09634491 0.11475630 0.20364739 0.14696650 0.13286389
## [721] 0.21542362 0.16803872 0.18080966 0.22649388 0.22047992 0.21933843
## [727] 0.02860286 0.21255573 0.23087061 0.19143272 0.20154229 0.15163193
## [733] 0.19793061 0.16190930 0.06272054 0.18743117 0.18993522 0.21052108
## [739] 0.23695645 0.05994370 0.11985116 0.20518040 0.16059687 0.22349655
## [745] 0.22722330 0.13723566 0.09742442 0.14320114 0.13840518 0.22078980
## [751] 0.08960237 0.18202426 0.20038477 0.16309787 0.17720378 0.04416894
## [757] 0.25049621 0.16790310 0.13573260 0.15805317 0.22866266 0.19552095
## [763] 0.17793258 0.23543092 0.11152942 0.22076595 0.14540927 0.19214181
## [769] 0.06183812 0.20151998 0.21843778 0.02727047 0.02628433 0.17539203
## [775] 0.19356599 0.22181703 0.21720962 0.15809007 0.18726233 0.18543372
## [781] 0.17511152 0.19391245 0.03848748 0.14342240 0.16117702 0.18316221
## [787] 0.14201467 0.11822302 0.19192673 0.22465345 0.16321144 0.16155222
## [793] 0.13782761 0.15693115 0.23242503 0.15672951 0.16357147 0.23473296
## [799] 0.03343944 0.17545219 0.02813290 0.16016753 0.23445915 0.21232380
## [805] 0.21829581 0.09476352 0.11084444 0.16370428 0.14060173 0.17084796
## [811] 0.21716249 0.16693696 0.18921110 0.21624479 0.15272293 0.12706505
## [817] 0.21404447 0.26064921 0.18443075 0.18218943 0.17856204 0.14646323
## [823] 0.15801628 0.23339094 0.19692022 0.19194823 0.11077615 0.21227743
## [829] 0.16469355 0.16300329 0.07285584 0.20522562 0.16899048 0.17331666
## [835] 0.21765779 0.23136329 0.06199109 0.08860103 0.05779346 0.17274142
## [841] 0.22727199 0.22863821 0.02712742 0.16834903 0.14675808 0.02921775
## [847] 0.05912101 0.13984965 0.10802100 0.16427443 0.14085318 0.17387350
## [853] 0.21831947 0.23803592 0.21437114 0.19091828 0.19611035 0.07216595
## [859] 0.09419426 0.22400217 0.14962781 0.16338190 0.18293418 0.23580542
## [865] 0.23735772 0.22131493 0.23077216 0.02671345 0.20373733 0.20493183
## [871] 0.09801109 0.23623035 0.21556423 0.15083120 0.14909943 0.24632932
## [877] 0.17974441 0.08608175 0.18719905 0.22998564 0.26137115 0.21059020
## [883] 0.15365803 0.14050126 0.12509471 0.08884761 0.22193669 0.14011667
## [889] 0.23660573 0.22841825 0.22727199 0.22074211 0.19731513 0.09287788
## [895] 0.20288408 0.07387362 0.21010666 0.22880939 0.15525119 0.25295065
## [901] 0.16628252 0.23371353 0.21732750 0.10129438 0.14547819 0.22052757
## [907] 0.16501801 0.23096909 0.20916495 0.22934798 0.22417089 0.20448047
## [913] 0.09552733 0.09402880 0.19373916 0.21993243 0.24114231 0.23723227
## [919] 0.18650399 0.21288075 0.18539185 0.26386769 0.20583678 0.22124327
## [925] 0.14518547 0.02560474 0.16459822 0.24823873 0.23013297 0.16463635
## [931] 0.18339046 0.12486731 0.16778693 0.23750831 0.21853246 0.21865085
## [937] 0.22863821 0.22107613 0.18781150 0.22783242 0.23503191 0.08969288
## [943] 0.08652994 0.23008385 0.22805198 0.22761300 0.21988486 0.17419232
## [949] 0.23700659 0.23003474 0.25305545 0.22666393 0.10956666 0.08793168
## [955] 0.18078913 0.19817280 0.22871156 0.22340033 0.17631621 0.07089546
## [961] 0.11648560 0.22306381 0.05768787 0.22535446 0.16421734 0.21532991
## [967] 0.24162462 0.26094317 0.12004139 0.17321737 0.19352271 0.10463592
## [973] 0.11335555 0.23055076 0.22907857 0.09334611 0.21888777 0.22829611
## [979] 0.18543372 0.12640534 0.25455191 0.25713836 0.09231878 0.19916590
## [985] 0.12805239 0.19749083 0.21990864 0.17892833 0.20985370 0.22424323
## [991] 0.22907857 0.23760875 0.09685300 0.23620534 0.09147429 0.17377396
## [997] 0.24906748 0.25365858 0.24943064 0.06420352 0.14976898 0.13946656
## [1003] 0.23356461 0.11172187 0.11738742 0.22724764 0.22141051 0.22956857
## [1009] 0.15552409 0.16421734 0.18692500 0.23435964 0.21486183 0.22974024
## [1015] 0.22719896 0.13010945 0.26193355 0.22639675 0.23042783 0.26166564
## [1021] 0.09516862 0.21704468 0.22895619 0.15912605 0.17513155 0.22964213
## [1027] 0.13958306 0.08388284m3_prob<-predict(cv_model3, churn_train, type = 'prob')$Yes
m3_prob## [1] 7.257356e-02 2.505939e-01 1.164753e-01 4.503031e-02 2.456631e-02
## [6] 1.747988e-01 2.777555e-01 2.181766e-02 5.276481e-10 1.882841e-01
## [11] 2.914211e-03 2.548704e-03 4.526047e-02 1.319327e-03 2.699134e-08
## [16] 1.492621e-02 1.101428e-03 5.097941e-02 4.225771e-01 3.400936e-02
## [21] 2.211430e-02 8.519163e-02 2.109313e-02 9.964890e-02 8.728331e-02
## [26] 4.097427e-01 6.144702e-03 2.758746e-01 7.436586e-02 6.171502e-01
## [31] 6.859352e-02 5.929403e-01 5.864936e-03 9.818032e-02 2.737477e-01
## [36] 1.108052e-02 9.353811e-03 1.834998e-01 3.464646e-03 5.631772e-02
## [41] 1.002369e-02 2.990505e-02 1.831384e-01 4.825230e-02 5.641893e-03
## [46] 3.880383e-02 1.173170e-02 6.429091e-03 7.899625e-03 8.139578e-02
## [51] 5.529465e-01 4.151979e-02 2.060819e-01 1.335733e-01 2.556201e-02
## [56] 5.665005e-03 1.626673e-02 9.527190e-02 6.212639e-03 8.841978e-04
## [61] 3.686529e-02 1.080107e-02 1.573950e-01 3.249365e-09 7.963070e-02
## [66] 9.689171e-03 1.000954e-02 8.928868e-03 8.804276e-02 1.452376e-02
## [71] 2.139179e-02 9.041093e-02 1.299838e-02 4.262562e-02 2.569549e-02
## [76] 2.557687e-02 3.125502e-01 1.205004e-01 1.078704e-02 4.331529e-02
## [81] 3.897020e-02 1.356869e-01 9.317722e-02 1.090077e-02 2.869300e-01
## [86] 1.549296e-02 5.221192e-02 2.204429e-03 1.379089e-01 1.931406e-02
## [91] 6.941897e-02 5.114327e-02 6.245134e-02 3.110321e-02 8.794593e-03
## [96] 6.645823e-02 6.387980e-02 3.177851e-01 2.483103e-01 3.882137e-02
## [101] 7.174599e-02 1.062956e-01 6.240709e-02 1.127932e-03 1.092516e-02
## [106] 1.192402e-03 2.915701e-03 1.505438e-02 4.016921e-04 1.306447e-02
## [111] 2.289738e-01 1.415083e-01 1.096834e-03 2.325994e-02 1.002587e-01
## [116] 4.461469e-01 1.277558e-02 1.768466e-01 2.738160e-03 5.307641e-03
## [121] 6.291094e-03 7.424902e-02 4.471347e-03 4.260031e-02 8.643018e-03
## [126] 1.369727e-02 3.957599e-03 7.836891e-03 1.289152e-01 1.602495e-01
## [131] 1.763142e-01 1.799698e-03 9.790796e-02 2.793056e-07 3.658656e-02
## [136] 3.812821e-02 8.955679e-02 6.643194e-02 2.769744e-03 3.527106e-02
## [141] 1.089660e-02 1.956199e-02 2.797705e-02 5.142252e-02 1.475717e-01
## [146] 6.478455e-02 6.769437e-04 3.296109e-02 1.408829e-01 1.466494e-03
## [151] 2.432478e-01 5.128512e-08 3.701943e-02 1.100922e-03 2.472703e-02
## [156] 2.801390e-03 6.782990e-03 2.515804e-03 3.442601e-01 4.268081e-02
## [161] 2.428666e-03 4.049734e-03 3.766377e-03 6.917905e-02 6.940887e-02
## [166] 6.954352e-01 1.602278e-03 1.594306e-02 6.555670e-03 3.141119e-01
## [171] 1.717655e-01 2.942055e-01 4.792100e-02 8.086554e-02 4.885087e-01
## [176] 1.982910e-02 5.289370e-02 3.694322e-03 1.963333e-02 5.342964e-03
## [181] 9.525573e-02 5.873366e-01 4.720066e-01 1.682153e-01 3.655478e-02
## [186] 1.972930e-01 1.173997e-01 4.296781e-01 1.493960e-01 1.649348e-01
## [191] 1.776453e-01 7.261714e-04 7.563432e-02 3.637678e-02 2.218188e-02
## [196] 2.084258e-01 7.458887e-03 1.496847e-02 2.091669e-03 7.585118e-02
## [201] 9.612465e-02 4.562379e-02 1.095801e-02 1.323714e-02 2.986440e-01
## [206] 1.232168e-02 3.463536e-08 1.282602e-01 4.711187e-01 2.362426e-02
## [211] 1.986246e-03 1.770189e-03 1.239013e-02 1.840070e-01 2.891031e-02
## [216] 3.322034e-03 2.642303e-01 8.853938e-02 6.323299e-02 2.086599e-02
## [221] 2.152708e-02 2.081448e-03 9.361547e-03 1.121625e-02 1.992902e-01
## [226] 6.385538e-02 7.200604e-03 3.069298e-02 2.973596e-01 1.792065e-03
## [231] 1.537244e-02 3.057700e-02 6.988269e-03 2.636162e-02 2.150203e-01
## [236] 4.226717e-02 1.161596e-01 5.505954e-02 1.974663e-02 1.550256e-01
## [241] 7.714481e-03 2.108388e-02 5.928850e-04 4.387634e-02 2.158333e-02
## [246] 1.647786e-03 5.783722e-11 1.186843e-02 1.924887e-03 4.319377e-03
## [251] 9.392302e-03 4.907424e-01 1.580757e-03 3.136778e-01 7.124153e-02
## [256] 8.692423e-02 5.482352e-02 5.654733e-03 1.487968e-09 4.622367e-03
## [261] 4.124805e-02 4.163390e-02 5.624857e-02 2.267516e-01 1.579637e-01
## [266] 4.945434e-03 8.056030e-02 8.175651e-09 4.675188e-02 3.720104e-02
## [271] 1.329688e-02 3.091725e-02 2.038218e-02 8.548665e-03 7.262696e-02
## [276] 1.822148e-01 2.648399e-03 3.801419e-02 2.058060e-03 4.483040e-02
## [281] 2.095752e-01 9.443034e-02 6.807317e-08 3.646026e-01 2.238099e-02
## [286] 3.770341e-01 1.025886e-01 2.179163e-03 1.096674e-02 2.040869e-01
## [291] 3.593242e-02 3.746174e-01 3.122125e-01 3.209163e-02 3.505024e-02
## [296] 4.960160e-02 3.203892e-02 5.458334e-02 3.099334e-03 1.320974e-01
## [301] 9.310787e-03 1.121405e-01 1.592190e-02 1.267567e-01 5.512302e-03
## [306] 1.554492e-02 5.287026e-03 1.001289e-02 3.706043e-02 2.354088e-02
## [311] 6.349680e-02 2.900385e-02 7.928084e-04 4.130405e-03 7.539634e-04
## [316] 2.460557e-02 7.076553e-02 1.149759e-04 6.965601e-08 3.959462e-02
## [321] 2.121721e-09 1.205295e-01 1.785312e-03 3.088917e-01 2.517734e-01
## [326] 6.213733e-01 3.276077e-01 3.244945e-02 4.194417e-02 1.166187e-01
## [331] 2.498031e-03 7.971664e-02 1.817445e-01 1.011477e-01 2.521318e-03
## [336] 1.686243e-01 3.961941e-01 2.151795e-02 6.193361e-09 4.470210e-02
## [341] 5.864024e-01 5.898425e-02 9.554218e-03 5.812473e-02 1.674304e-03
## [346] 5.057630e-01 3.811314e-03 6.127990e-02 1.927283e-01 4.509189e-01
## [351] 1.474088e-01 5.693610e-02 6.257066e-04 2.001450e-04 7.810783e-04
## [356] 3.284735e-03 1.140099e-02 1.368105e-01 2.947104e-03 6.809814e-01
## [361] 4.813339e-02 2.137947e-01 7.717203e-02 4.263993e-02 2.770965e-01
## [366] 1.376122e-01 2.085646e-03 3.097481e-01 8.303362e-03 1.782366e-01
## [371] 1.280718e-02 2.976815e-02 2.609954e-02 2.056193e-01 8.030616e-03
## [376] 2.314906e-03 6.150019e-02 1.272053e-02 1.102748e-01 1.750190e-01
## [381] 3.267933e-01 1.715789e-01 1.862711e-01 8.127713e-03 3.558905e-01
## [386] 2.841696e-02 3.430407e-02 9.351896e-02 4.114277e-02 2.565507e-02
## [391] 7.875915e-02 3.561730e-04 9.270941e-03 3.240109e-01 5.018418e-02
## [396] 8.533353e-03 2.535299e-01 3.440529e-01 1.537254e-01 7.722016e-02
## [401] 3.931630e-02 2.137909e-02 5.750619e-02 1.165978e-01 1.379509e-02
## [406] 1.274732e-01 5.151088e-03 7.491887e-04 1.057601e-02 3.052541e-01
## [411] 1.735142e-01 6.127089e-02 1.501300e-02 7.029602e-02 3.058409e-01
## [416] 4.621838e-02 2.507300e-02 1.719051e-03 4.293533e-02 1.341682e-03
## [421] 1.803934e-01 2.477813e-03 8.724840e-03 3.176832e-02 8.794513e-09
## [426] 3.276291e-02 2.927145e-03 2.230036e-04 1.297346e-03 3.540612e-01
## [431] 1.047364e-01 2.452010e-02 3.535172e-03 4.628921e-02 9.655017e-03
## [436] 1.050236e-03 5.639349e-02 6.628395e-03 2.474075e-02 6.043509e-03
## [441] 9.381201e-02 5.972512e-02 5.689106e-02 5.693681e-02 4.781170e-05
## [446] 3.428900e-01 1.365694e-02 2.991124e-02 5.730569e-10 1.310391e-01
## [451] 3.428105e-08 2.784715e-01 2.985080e-01 7.537726e-02 1.495908e-02
## [456] 2.969947e-02 4.389949e-01 2.655130e-02 5.133881e-04 7.794150e-03
## [461] 2.200135e-02 1.184305e-02 2.223637e-02 3.118352e-02 4.058843e-01
## [466] 1.449639e-03 6.277504e-02 3.618033e-03 1.533777e-02 3.963323e-02
## [471] 3.049972e-02 1.608976e-02 1.823498e-03 1.242412e-03 4.787214e-04
## [476] 2.021979e-02 1.631330e-01 1.219727e-02 3.293542e-02 1.371136e-01
## [481] 1.139762e-02 1.430481e-01 1.276530e-01 1.564363e-02 1.512267e-01
## [486] 1.794606e-02 4.854870e-01 8.611158e-02 6.836052e-02 3.201065e-01
## [491] 1.298719e-02 4.047397e-02 3.324112e-02 1.376043e-02 3.065394e-01
## [496] 5.869750e-02 3.979967e-01 6.332899e-03 2.070749e-02 2.390593e-02
## [501] 1.140838e-01 1.866523e-02 1.632098e-01 2.864038e-01 1.937403e-03
## [506] 8.732923e-01 2.211887e-01 7.210637e-02 2.218561e-03 1.683210e-01
## [511] 1.596508e-03 1.461768e-01 1.779720e-01 1.231209e-01 1.206676e-02
## [516] 3.218812e-01 3.040380e-03 2.441711e-01 5.590603e-02 3.535783e-02
## [521] 7.655261e-02 1.007947e-02 1.396615e-03 1.959115e-02 2.680952e-05
## [526] 3.167919e-02 2.093275e-02 1.577695e-01 2.861450e-03 5.624509e-04
## [531] 2.581351e-02 1.975873e-09 2.474676e-01 1.058229e-02 5.244411e-01
## [536] 1.575118e-07 1.042778e-02 6.627863e-02 8.529353e-02 5.668124e-02
## [541] 4.733671e-02 5.907039e-02 4.483855e-01 3.469775e-02 1.495487e-03
## [546] 5.635670e-02 3.608181e-01 6.329788e-02 2.021288e-01 1.165574e-02
## [551] 1.331971e-01 5.971479e-03 1.849430e-02 1.290530e-01 8.405274e-02
## [556] 4.532338e-02 2.087574e-01 4.440317e-03 2.596398e-02 1.543630e-02
## [561] 3.645546e-03 3.874638e-02 1.083344e-01 1.565239e-02 1.836053e-01
## [566] 1.570472e-01 1.680100e-03 4.113730e-01 8.323591e-03 2.360056e-01
## [571] 4.583989e-01 5.624769e-02 9.830090e-02 1.718179e-01 4.485649e-01
## [576] 2.419742e-03 1.543675e-01 1.766597e-01 1.272789e-09 1.294297e-01
## [581] 1.851512e-01 3.969118e-01 3.114632e-03 4.157727e-04 6.110854e-02
## [586] 4.350379e-02 2.227191e-01 2.266374e-01 2.992407e-01 5.352400e-02
## [591] 3.361591e-02 4.036195e-03 6.081889e-02 5.205836e-02 3.229009e-02
## [596] 4.480067e-01 1.147322e-01 4.056278e-05 6.893146e-02 2.328253e-02
## [601] 1.015604e-01 1.443284e-01 4.724579e-02 2.393778e-01 9.919229e-02
## [606] 4.230497e-02 1.858945e-03 2.723798e-04 4.581908e-02 1.307181e-01
## [611] 1.501516e-02 2.512168e-02 7.837610e-02 1.129943e-01 5.666188e-02
## [616] 2.542810e-02 1.214904e-01 1.080286e-01 3.499075e-02 9.387505e-04
## [621] 3.640062e-02 4.756157e-02 3.348441e-02 5.805088e-01 4.311033e-01
## [626] 1.817095e-01 2.223932e-02 1.057995e-01 2.048794e-01 2.355441e-01
## [631] 1.944359e-01 3.624974e-08 1.854276e-01 1.994232e-02 1.016720e-01
## [636] 2.521330e-01 3.147042e-01 3.076336e-01 1.523740e-01 1.326329e-09
## [641] 3.534927e-02 2.108873e-02 9.590254e-02 4.097028e-02 2.794706e-08
## [646] 1.949665e-02 1.583708e-02 2.618929e-02 1.165747e-01 4.148972e-02
## [651] 9.636339e-09 1.593462e-01 1.537156e-01 1.023528e-03 3.821220e-02
## [656] 6.299048e-01 2.089645e-01 3.410865e-01 2.899529e-02 8.985492e-02
## [661] 1.545969e-01 3.924685e-02 3.587044e-03 2.909144e-02 4.091049e-01
## [666] 1.177441e-03 1.816249e-02 3.556893e-01 4.094878e-01 3.376788e-03
## [671] 6.832208e-01 3.039717e-02 1.759836e-01 1.168282e-03 2.129771e-03
## [676] 1.788870e-04 2.790538e-01 2.651341e-03 1.516904e-01 1.028939e-03
## [681] 3.835537e-03 2.593394e-04 2.382475e-03 3.590339e-03 7.696147e-02
## [686] 1.353815e-01 1.457390e-10 2.040975e-02 5.273993e-01 1.011412e-02
## [691] 2.035361e-01 1.680138e-01 2.642535e-02 2.112047e-03 5.202566e-03
## [696] 2.408241e-01 4.634950e-03 4.148365e-03 1.046094e-03 1.076582e-01
## [701] 7.623495e-03 4.691582e-03 6.607078e-01 6.168975e-02 1.133774e-01
## [706] 4.220360e-02 2.035984e-03 4.427930e-02 5.200579e-02 9.542015e-02
## [711] 3.869964e-03 4.406770e-03 2.318422e-01 8.962883e-03 2.806112e-01
## [716] 1.607395e-01 1.792986e-01 2.803084e-02 2.270945e-01 1.054498e-01
## [721] 3.487904e-02 1.116278e-02 6.138143e-02 7.925164e-02 4.543461e-03
## [726] 6.566410e-02 2.061990e-03 2.568695e-03 6.939527e-02 1.805673e-03
## [731] 1.280427e-02 1.243189e-01 1.058685e-02 1.606428e-01 2.360584e-02
## [736] 9.691748e-02 5.634224e-02 1.645243e-02 5.026052e-03 1.529827e-02
## [741] 1.456583e-01 3.867465e-02 3.127102e-02 1.008113e-02 1.077060e-01
## [746] 7.128404e-02 2.106175e-01 6.843445e-04 6.393325e-03 2.242852e-01
## [751] 9.744411e-02 1.188264e-02 1.463497e-02 2.707583e-01 1.171018e-01
## [756] 5.686155e-02 5.797389e-02 2.162429e-03 2.063984e-02 3.505411e-02
## [761] 3.973655e-01 2.879635e-02 5.786595e-01 1.672304e-01 2.464274e-03
## [766] 7.110929e-03 7.175722e-02 1.360496e-01 1.240968e-03 1.690392e-02
## [771] 4.839937e-02 7.271154e-03 1.852470e-03 1.596173e-01 2.519115e-02
## [776] 1.486712e-02 3.786770e-02 1.276036e-01 9.247477e-02 6.814218e-02
## [781] 6.027703e-02 3.332109e-01 1.077728e-01 1.586175e-02 1.676523e-01
## [786] 8.469627e-03 4.865249e-02 6.440078e-02 2.838910e-01 3.513029e-02
## [791] 3.355141e-02 1.680138e-01 7.273946e-02 6.762884e-02 5.139550e-02
## [796] 1.055951e-01 3.933564e-02 7.655910e-03 7.616947e-09 8.871112e-03
## [801] 3.777232e-04 1.457732e-01 3.435730e-02 5.952158e-02 6.522936e-03
## [806] 3.286434e-01 2.141206e-02 1.264789e-01 6.771807e-04 6.185581e-02
## [811] 7.809246e-01 7.514364e-03 2.470169e-02 1.862307e-02 3.974707e-03
## [816] 6.083529e-03 3.857508e-01 1.086984e-01 4.557218e-03 3.609857e-01
## [821] 1.035101e-01 4.698144e-01 3.943316e-03 9.514906e-02 4.939706e-03
## [826] 3.461562e-01 4.667453e-02 1.609271e-01 2.928370e-01 3.915817e-01
## [831] 1.544943e-04 5.586688e-02 8.230670e-03 5.066192e-02 4.574195e-01
## [836] 7.313286e-02 3.735927e-04 2.988765e-03 1.599765e-03 2.811706e-01
## [841] 2.157826e-01 7.067706e-01 7.978493e-03 9.662982e-03 2.661035e-04
## [846] 1.065390e-01 1.296246e-02 1.793534e-02 6.166607e-01 7.985747e-03
## [851] 1.320011e-01 1.101311e-01 4.418192e-02 1.641849e-03 4.498437e-03
## [856] 3.866690e-01 3.004301e-01 1.325201e-01 2.366365e-02 1.644280e-02
## [861] 1.030719e-01 5.856938e-03 7.720315e-02 6.675397e-01 8.846244e-01
## [866] 6.960222e-01 9.520904e-01 6.227570e-03 9.248620e-01 5.540595e-01
## [871] 1.670144e-02 5.081259e-01 6.744091e-01 8.608976e-01 5.353840e-01
## [876] 9.454922e-01 6.064292e-01 1.539989e-01 7.130667e-01 9.365319e-01
## [881] 3.298706e-01 6.550396e-01 6.376794e-01 3.481452e-01 2.315270e-02
## [886] 4.427075e-02 4.569349e-01 8.015683e-01 1.809688e-01 4.507023e-01
## [891] 4.444344e-01 1.399167e-01 7.867712e-01 1.417236e-01 6.802145e-01
## [896] 2.780804e-01 7.003051e-01 5.621512e-01 5.954496e-01 3.448923e-01
## [901] 1.597032e-01 9.653879e-01 7.683935e-01 4.177431e-01 5.552874e-01
## [906] 1.895475e-01 5.829552e-01 8.479406e-01 7.784314e-01 2.568953e-01
## [911] 7.550528e-01 3.551660e-01 3.803431e-01 9.466721e-01 7.556579e-01
## [916] 6.007698e-01 9.448367e-01 7.091897e-01 1.976330e-01 1.165001e-01
## [921] 3.471689e-01 2.645203e-01 9.538561e-01 1.223583e-01 4.969233e-01
## [926] 4.502068e-02 7.425092e-01 4.290403e-01 4.919865e-01 6.343159e-01
## [931] 1.665381e-01 2.672014e-02 4.707555e-02 6.370582e-01 2.829396e-01
## [936] 9.723424e-01 5.084803e-01 1.214238e-01 1.520940e-01 7.868569e-01
## [941] 9.405665e-01 5.301739e-02 7.633429e-01 4.482084e-01 5.739606e-01
## [946] 3.056679e-01 7.587964e-02 5.589355e-01 8.616713e-01 7.502069e-01
## [951] 7.103112e-01 4.351978e-01 1.730426e-01 1.341058e-01 2.028222e-01
## [956] 2.344368e-01 5.765799e-01 5.834816e-01 4.536861e-01 1.013450e-01
## [961] 9.159197e-01 3.287383e-01 9.499945e-01 2.028246e-01 8.181902e-01
## [966] 2.258068e-01 4.539275e-01 9.593790e-01 2.865119e-03 5.771715e-02
## [971] 3.766018e-01 7.476829e-01 7.454055e-01 9.051341e-01 2.577613e-01
## [976] 4.515130e-02 5.783866e-01 4.095341e-01 8.566012e-01 4.030639e-01
## [981] 6.004449e-01 2.602552e-01 6.112579e-02 6.426137e-01 2.621466e-02
## [986] 8.171285e-01 3.297024e-01 7.267769e-01 9.834519e-01 8.570775e-01
## [991] 6.527478e-01 3.669521e-01 3.739430e-02 6.546793e-01 1.030158e-03
## [996] 4.339341e-02 8.413326e-01 2.924887e-01 4.929293e-01 8.599415e-01
## [1001] 4.784887e-01 5.237783e-01 4.615033e-01 9.296372e-01 4.282482e-01
## [1006] 7.855412e-01 5.217853e-01 2.465884e-01 5.172352e-01 2.841584e-01
## [1011] 1.321417e-01 2.004484e-01 9.680460e-02 9.571956e-01 8.513700e-01
## [1016] 3.113893e-03 3.659451e-01 5.394854e-01 4.928046e-01 8.502186e-01
## [1021] 7.574911e-01 8.779361e-01 5.216730e-01 4.219104e-01 5.063619e-01
## [1026] 1.447476e-01 4.219170e-02 5.702003e-01# compute AUC metrics for cv_model1 and cv_model3
perf1<-prediction(m1_prob, churn_train$Attrition) %>%
performance(measure = 'tpr', x.measure = 'fpr')
perf2<-prediction(m3_prob, churn_train$Attrition) %>%
performance(measure = 'tpr', x.measure = 'fpr')
# plot ROC curves for cv_model1 and cv_model3
plot(perf1, col = 'black', lty = 2)
plot(perf2, add = TRUE, col = 'blue')
legend(0.8, 0.2, legend = c('cv_model1', 'cv_model3'),
col = c('black', 'blue'), lty = 2:1, cex = 0.6)
we can perform a PLS logistic regression to assess if reducing the
dimension of our numeric predictors helps to improve accuracy.
# 10 fold cv on PLS model tuning the number of PC
set.seed(123)
cv_model_pls<-train(
Attrition ~.,
data = churn_train,
method = 'pls',
family = 'binomial',
trContrl = trainControl(method = 'cv', number = 10),
preProcess = c('zv', 'center', 'scale'),
tunLength = 16
)
# Model with lowest RMSE
cv_model_pls$bestTune## ncomp
## 3 3# results for model with lowest loss
cv_model_pls$results %>%
filter(ncomp == pull(cv_model_pls$bestTune))## ncomp Accuracy Kappa AccuracySD KappaSD
## 1 3 0.8671796 0.2910272 0.0158012 0.08045977# plot cv RMSE
ggplot(cv_model_pls)
Feature interpretation
variable importance for logistic regression models can be computed using the absolute value of the z-statistic for each coefficient
vip(cv_model3, num_features = 20)
Similar to linear regression, logistic regression assumes a monotonic linear relationship. However, the linear relationship occurs on the logit scale; on the probability scale, the relationship will be nonlinear