#STATISTICAL MODELLING OF BANK CHURNERS
#ABSTRACT
# A bank manager is concerned with the number of clients leaving or being attrited.
#it seem that more clients are leaving and our concern is why are these clients leaving our
#bank. The manager wants to classify the clients that are most prawn to leave based on the
# data at hand, as to try and know which clients to target and what factors might influence their choice
#to leave our bank.
#The data contains info on 10127 clients ,both who are still with the bank,
# and those who are no longer with the bank.
#PROBLEM STUDY
#More and more clients are attriting/leaving our bank.
#AIM AND OBJECTIVES
#Classify the attrited clients and find out why they are leaving
# or which factors influence their decision to leave.
#Model the data and Do Machine learning as well as Predictive Analytics
#train the model
#chose the model with the best Accuracy,Precision,kappa and
#Inferential rules
#Kappa "rule of thumb" for interpretation
# 0.81-1.00 ALMOST PERFECT
# 0.61-0.80 SUBSTATIAL
# 0.41-0.60 MODERATE
# 0.21-0.40 FAIR
# 0.00-0.20 SLIGHT
# <0.00 POOR
#Accuracy- the proportion of all properly classified cases is measured by accuracy
#sensitivity-the number of cases in which the positive class was actually predicted divided by the total number of cases
#whose observed data fall into the positive class -the prediction accuracy for those who quit
#specificity-the proportion of people we said would stay relative to the overall number of people that stayed
#prevalence-base probability of those who quit
#we can say that based on the prevalence it's likely that _% of people are going to quit
#balanced accuracy= (sensitivity+specificity)/2
##This will be our measures of perfomance for our models##
#MODELING
#Step-WISE LOGISTIC REGRESSION
#LOGISTIC REGRESSION- k-fold cross-validation
#LASSO REGRESSION ANALYSIS-- k-fold cross validation+Variable importance analysis
#Random Forest Modeling
#Decision Trees--RPART
#Ridge Regression-- k-fold cross-validation +variable importance
# we are going to deploy 5 models and pick the best
##First we set
#Setting the working directory
setwd("C:\\Users\\Xholi\\Downloads")
#Loading the packages that will prove to useful
pacman::p_load(pacman,dplyr,GGally,ggvis,rio,
shiny,stringr,tidyr,rmarkdown,
httr,ggplot2,ggthemes,plotly,dummies,caret,
psych,rpart,rpart.plot,DT,pROC,randomForest,ROCR,
lubridate)
library(readr)
#load the data
df<-read.csv("BankChurners.csv")
#clean the data
df1<-df[,-1]
Churners<-df1[,-c(21,22)]
#change Attrited to Quit and existing to Stay
#changing Attrition and Existing customer
Churners$Attrition_Flag[Churners$Attrition_Flag=="Existing Customer"]<-"Stay"
Churners$Attrition_Flag[Churners$Attrition_Flag=="Attrited Customer"]<-"Quit"
head(Churners)
## Attrition_Flag Customer_Age Gender Dependent_count Education_Level
## 1 Stay 45 M 3 High School
## 2 Stay 49 F 5 Graduate
## 3 Stay 51 M 3 Graduate
## 4 Stay 40 F 4 High School
## 5 Stay 40 M 3 Uneducated
## 6 Stay 44 M 2 Graduate
## Marital_Status Income_Category Card_Category Months_on_book
## 1 Married $60K - $80K Blue 39
## 2 Single Less than $40K Blue 44
## 3 Married $80K - $120K Blue 36
## 4 Unknown Less than $40K Blue 34
## 5 Married $60K - $80K Blue 21
## 6 Married $40K - $60K Blue 36
## Total_Relationship_Count Months_Inactive_12_mon Contacts_Count_12_mon
## 1 5 1 3
## 2 6 1 2
## 3 4 1 0
## 4 3 4 1
## 5 5 1 0
## 6 3 1 2
## Credit_Limit Total_Revolving_Bal Avg_Open_To_Buy Total_Amt_Chng_Q4_Q1
## 1 12691 777 11914 1.335
## 2 8256 864 7392 1.541
## 3 3418 0 3418 2.594
## 4 3313 2517 796 1.405
## 5 4716 0 4716 2.175
## 6 4010 1247 2763 1.376
## Total_Trans_Amt Total_Trans_Ct Total_Ct_Chng_Q4_Q1 Avg_Utilization_Ratio
## 1 1144 42 1.625 0.061
## 2 1291 33 3.714 0.105
## 3 1887 20 2.333 0.000
## 4 1171 20 2.333 0.760
## 5 816 28 2.500 0.000
## 6 1088 24 0.846 0.311
#set random seed so that your results can be reproducable
set.seed(1992)
#create training and testing data
#we created our partioning by 70/30
intrain<-createDataPartition(Churners$Attrition_Flag,p=0.7,
list = F,
times = 1)
#creating both testing and training data sets
training <-Churners[intrain,]
testing <-Churners[-intrain,]
#Re-label values as factors
#re label
testing$Attrition_Flag<-as.factor(testing$Attrition_Flag)
training$Attrition_Flag<-as.factor(training$Attrition_Flag)
##MODELING
#MODEL 1
#STEP-WISE LOGISTIC REGRESSION-10,000 STEPS
#STEP-WISE REGRESSION
Model1 <-glm(as.factor(Attrition_Flag)~.,data=training,
family=binomial(logit))
Model1_step <-step(Model1,
direction = "both",
steps = 10000,
trace = F)
predictions_step <-predict(Model1_step,testing,
type = "response")
#to decide the cut-off point
pred_step <-prediction(predictions_step,testing$Attrition_Flag)
plot(performance(pred_step,"tpr","fpr"),colorize=T)
auc_step<-performance(pred_step,"auc")
auc_step
## A performance instance
## 'Area under the ROC curve'
roc_step<-roc(response=testing$Attrition_Flag,predictor=predictions_step)
## Setting levels: control = Quit, case = Stay
## Setting direction: controls < cases
d<-coords(roc_step,"best","threshold",transpose=T)
d
## threshold specificity sensitivity
## 0.8067485 0.8299180 0.8690196
# threshold specificity sensitivity
# 0.8067485 0.8299180 0.8690196
#Forming confusion matrix from the decided cut-off point
Attrition_step <-ifelse(predictions_step>=d[[1]],"Stay","Quit")
testing$Attrition_Flag<-as.factor(testing$Attrition_Flag)
Attrition_step<-as.factor(Attrition_step)
#confusion matrix
cm_1 <-confusionMatrix(testing$Attrition_Flag,Attrition_step)
cm_1
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 405 83
## Stay 334 2216
##
## Accuracy : 0.8627
## 95% CI : (0.85, 0.8748)
## No Information Rate : 0.7567
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5786
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.5480
## Specificity : 0.9639
## Pos Pred Value : 0.8299
## Neg Pred Value : 0.8690
## Prevalence : 0.2433
## Detection Rate : 0.1333
## Detection Prevalence : 0.1606
## Balanced Accuracy : 0.7560
##
## 'Positive' Class : Quit
##
#MODEL 1 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.8627 0.5786 0.5480 0.9639 0.2433
#MODEL 2
#Logistic Regression-k-fold cross-validation
#Specify and train logistic regression model
#k-folds(number of folds=10) cross validation framework
#set your control specs
ctrl_specs <-trainControl(method = "cv",
savePredictions = "all",
number = 10,
classProbs = T)
Model2<-train(Attrition_Flag~.,data = training,
method="glm",
family=binomial,
trControl=ctrl_specs)
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
Model2
## Generalized Linear Model
##
## 7089 samples
## 19 predictor
## 2 classes: 'Quit', 'Stay'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6380, 6380, 6381, 6380, 6380, 6380, ...
## Resampling results:
##
## Accuracy Kappa
## 0.9050648 0.6111962
# Accuracy Kappa
# 0.9050648 0.6111962
summary(Model2)
##
## Call:
## NULL
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.3172 0.0640 0.1672 0.3608 2.9052
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.383e+00 5.721e-01 -11.155 < 2e-16 ***
## Customer_Age 5.237e-03 9.338e-03 0.561 0.574955
## GenderM 8.900e-01 1.788e-01 4.978 6.43e-07 ***
## Dependent_count -1.356e-01 3.616e-02 -3.750 0.000177 ***
## Education_LevelDoctorate -3.858e-01 2.502e-01 -1.542 0.123104
## Education_LevelGraduate 3.155e-02 1.665e-01 0.189 0.849731
## `Education_LevelHigh School` 8.696e-02 1.783e-01 0.488 0.625752
## `Education_LevelPost-Graduate` -4.500e-01 2.390e-01 -1.883 0.059698 .
## Education_LevelUneducated -1.491e-01 1.866e-01 -0.799 0.424463
## Education_LevelUnknown -1.522e-01 1.840e-01 -0.827 0.408276
## Marital_StatusMarried 4.535e-01 1.848e-01 2.454 0.014132 *
## Marital_StatusSingle -1.590e-01 1.857e-01 -0.856 0.391930
## Marital_StatusUnknown -1.171e-01 2.342e-01 -0.500 0.616965
## `Income_Category$40K - $60K` 7.341e-01 2.476e-01 2.965 0.003024 **
## `Income_Category$60K - $80K` 4.273e-01 2.192e-01 1.949 0.051255 .
## `Income_Category$80K - $120K` -3.260e-02 2.033e-01 -0.160 0.872644
## `Income_CategoryLess than $40K` 5.465e-01 2.687e-01 2.034 0.041953 *
## Income_CategoryUnknown 6.314e-01 2.856e-01 2.211 0.027057 *
## Card_CategoryGold -1.414e+00 4.360e-01 -3.244 0.001180 **
## Card_CategoryPlatinum -6.289e-01 8.965e-01 -0.702 0.482970
## Card_CategorySilver -5.182e-01 2.339e-01 -2.215 0.026750 *
## Months_on_book 7.477e-03 9.287e-03 0.805 0.420746
## Total_Relationship_Count 4.600e-01 3.266e-02 14.082 < 2e-16 ***
## Months_Inactive_12_mon -5.164e-01 4.594e-02 -11.241 < 2e-16 ***
## Contacts_Count_12_mon -5.589e-01 4.434e-02 -12.604 < 2e-16 ***
## Credit_Limit 1.957e-05 8.327e-06 2.350 0.018791 *
## Total_Revolving_Bal 9.471e-04 8.642e-05 10.959 < 2e-16 ***
## Avg_Open_To_Buy NA NA NA NA
## Total_Amt_Chng_Q4_Q1 3.213e-01 2.225e-01 1.444 0.148805
## Total_Trans_Amt -4.805e-04 2.731e-05 -17.595 < 2e-16 ***
## Total_Trans_Ct 1.197e-01 4.447e-03 26.908 < 2e-16 ***
## Total_Ct_Chng_Q4_Q1 2.803e+00 2.251e-01 12.456 < 2e-16 ***
## Avg_Utilization_Ratio 1.061e-02 2.948e-01 0.036 0.971290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 6249.4 on 7088 degrees of freedom
## Residual deviance: 3273.2 on 7057 degrees of freedom
## AIC: 3337.2
##
## Number of Fisher Scoring iterations: 6
#list by variable importance
varImp(Model2)
## glm variable importance
##
## only 20 most important variables shown (out of 31)
##
## Overall
## Total_Trans_Ct 100.000
## Total_Trans_Amt 65.343
## Total_Relationship_Count 52.271
## Contacts_Count_12_mon 46.771
## Total_Ct_Chng_Q4_Q1 46.218
## Months_Inactive_12_mon 41.698
## Total_Revolving_Bal 40.650
## GenderM 18.391
## Dependent_count 13.821
## Card_CategoryGold 11.937
## `Income_Category$40K - $60K` 10.901
## Marital_StatusMarried 8.998
## Credit_Limit 8.610
## Card_CategorySilver 8.109
## Income_CategoryUnknown 8.093
## `Income_CategoryLess than $40K` 7.435
## `Income_Category$60K - $80K` 7.120
## `Education_LevelPost-Graduate` 6.873
## Education_LevelDoctorate 5.604
## Total_Amt_Chng_Q4_Q1 5.239
plot(varImp(Model2))
#predict outcomes based on testing data
prediction_glm<-predict(Model2,newdata = testing)
## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from a rank-deficient fit may be misleading
#create confusion matrix
cm_2<-confusionMatrix(data = prediction_glm,testing$Attrition_Flag)
cm_2
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 289 98
## Stay 199 2452
##
## Accuracy : 0.9022
## 95% CI : (0.8911, 0.9126)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6044
##
## Mcnemar's Test P-Value : 6.53e-09
##
## Sensitivity : 0.59221
## Specificity : 0.96157
## Pos Pred Value : 0.74677
## Neg Pred Value : 0.92493
## Prevalence : 0.16063
## Detection Rate : 0.09513
## Detection Prevalence : 0.12739
## Balanced Accuracy : 0.77689
##
## 'Positive' Class : Quit
##
#MODEL 2 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9022 0.6044 0.59221 0.96157 0.16063
#MODEL 3
#LASSO Regression analysis-k-fold cross validation
#control specs will be the same as the previous model
#we have to create a vector for potential lambdas
lambda_vector <-10^seq(-5,5,length=500)
set.seed(1992)
Model3 <-train(Attrition_Flag~.,data =training,
method="glmnet",
tuneGrid=expand.grid(alpha=1,lambda=lambda_vector),
trControl=ctrl_specs,
preProcess=c("center","scale"),
na.action = na.omit)
Model3
## glmnet
##
## 7089 samples
## 19 predictor
## 2 classes: 'Quit', 'Stay'
##
## Pre-processing: centered (32), scaled (32)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6380, 6380, 6380, 6380, 6380, 6380, ...
## Resampling results across tuning parameters:
##
## lambda Accuracy Kappa
## 1.000000e-05 0.9053457 0.612617112
## 1.047225e-05 0.9053457 0.612617112
## 1.096681e-05 0.9053457 0.612617112
## 1.148472e-05 0.9053457 0.612617112
## 1.202708e-05 0.9053457 0.612617112
## 1.259506e-05 0.9053457 0.612617112
## 1.318987e-05 0.9053457 0.612617112
## 1.381276e-05 0.9053457 0.612617112
## 1.446507e-05 0.9053457 0.612617112
## 1.514819e-05 0.9053457 0.612617112
## 1.586357e-05 0.9053457 0.612617112
## 1.661273e-05 0.9053457 0.612617112
## 1.739726e-05 0.9053457 0.612617112
## 1.821885e-05 0.9053457 0.612617112
## 1.907924e-05 0.9053457 0.612617112
## 1.998026e-05 0.9053457 0.612617112
## 2.092383e-05 0.9053457 0.612617112
## 2.191197e-05 0.9053457 0.612617112
## 2.294676e-05 0.9053457 0.612617112
## 2.403043e-05 0.9053457 0.612617112
## 2.516527e-05 0.9053457 0.612617112
## 2.635371e-05 0.9053457 0.612617112
## 2.759826e-05 0.9053457 0.612617112
## 2.890160e-05 0.9053457 0.612617112
## 3.026648e-05 0.9053457 0.612617112
## 3.169582e-05 0.9053457 0.612617112
## 3.319266e-05 0.9053457 0.612617112
## 3.476019e-05 0.9053457 0.612617112
## 3.640175e-05 0.9053457 0.612617112
## 3.812083e-05 0.9053457 0.612617112
## 3.992109e-05 0.9053457 0.612617112
## 4.180637e-05 0.9053457 0.612617112
## 4.378069e-05 0.9053457 0.612617112
## 4.584824e-05 0.9053457 0.612617112
## 4.801343e-05 0.9053457 0.612617112
## 5.028087e-05 0.9053457 0.612617112
## 5.265540e-05 0.9053457 0.612617112
## 5.514206e-05 0.9053457 0.612617112
## 5.774615e-05 0.9053457 0.612617112
## 6.047322e-05 0.9053457 0.612617112
## 6.332908e-05 0.9053457 0.612617112
## 6.631981e-05 0.9053457 0.612617112
## 6.945178e-05 0.9053457 0.612617112
## 7.273165e-05 0.9053457 0.612617112
## 7.616642e-05 0.9053457 0.612617112
## 7.976339e-05 0.9053457 0.612617112
## 8.353023e-05 0.9053457 0.612617112
## 8.747496e-05 0.9053457 0.612617112
## 9.160598e-05 0.9053457 0.612617112
## 9.593209e-05 0.9053457 0.612617112
## 1.004625e-04 0.9053457 0.612617112
## 1.052069e-04 0.9053457 0.612617112
## 1.101753e-04 0.9053457 0.612617112
## 1.153783e-04 0.9053457 0.612617112
## 1.208271e-04 0.9053457 0.612617112
## 1.265332e-04 0.9053457 0.612617112
## 1.325087e-04 0.9053457 0.612617112
## 1.387665e-04 0.9053457 0.612617112
## 1.453198e-04 0.9053457 0.612617112
## 1.521825e-04 0.9053457 0.612617112
## 1.593694e-04 0.9053457 0.612617112
## 1.668956e-04 0.9052047 0.611909118
## 1.747773e-04 0.9052047 0.611909118
## 1.830312e-04 0.9053457 0.612295933
## 1.916748e-04 0.9053457 0.612295933
## 2.007267e-04 0.9054868 0.612720023
## 2.102061e-04 0.9054868 0.612720023
## 2.201331e-04 0.9053457 0.612273706
## 2.305289e-04 0.9053457 0.612273706
## 2.414157e-04 0.9050636 0.611108696
## 2.528166e-04 0.9049228 0.610115840
## 2.647559e-04 0.9046405 0.608973451
## 2.772591e-04 0.9044995 0.608269082
## 2.903527e-04 0.9044995 0.608269082
## 3.040646e-04 0.9043584 0.607844991
## 3.184242e-04 0.9044995 0.608239273
## 3.334618e-04 0.9043584 0.607529358
## 3.492096e-04 0.9043584 0.607529358
## 3.657011e-04 0.9042174 0.606810367
## 3.829714e-04 0.9042174 0.606810367
## 4.010573e-04 0.9042174 0.606810367
## 4.199973e-04 0.9042174 0.606810367
## 4.398317e-04 0.9040763 0.606039844
## 4.606029e-04 0.9042174 0.606462183
## 4.823549e-04 0.9042174 0.606462183
## 5.051342e-04 0.9040763 0.606019465
## 5.289893e-04 0.9040763 0.606019465
## 5.539709e-04 0.9040763 0.606019465
## 5.801323e-04 0.9040763 0.606019465
## 6.075292e-04 0.9043584 0.606806748
## 6.362198e-04 0.9044997 0.607214200
## 6.662655e-04 0.9046407 0.607638290
## 6.977300e-04 0.9046407 0.607638290
## 7.306804e-04 0.9046407 0.607638290
## 7.651869e-04 0.9046407 0.607638290
## 8.013230e-04 0.9047817 0.608065773
## 8.391656e-04 0.9049228 0.608466275
## 8.787954e-04 0.9050638 0.609170644
## 9.202967e-04 0.9050638 0.609170644
## 9.637579e-04 0.9049228 0.608466275
## 1.009272e-03 0.9047817 0.607715641
## 1.056935e-03 0.9047817 0.607715641
## 1.106848e-03 0.9047817 0.607715641
## 1.159120e-03 0.9049228 0.607779528
## 1.213859e-03 0.9053461 0.609307012
## 1.271184e-03 0.9053461 0.608962475
## 1.331216e-03 0.9054872 0.609342763
## 1.394083e-03 0.9053461 0.608280815
## 1.459919e-03 0.9054872 0.608725291
## 1.528864e-03 0.9059105 0.609975413
## 1.601064e-03 0.9057694 0.609282441
## 1.676675e-03 0.9056284 0.608499105
## 1.755856e-03 0.9054874 0.607693867
## 1.838777e-03 0.9053463 0.606928226
## 1.925614e-03 0.9054874 0.607024829
## 2.016551e-03 0.9057694 0.608102921
## 2.111783e-03 0.9054872 0.606922246
## 2.211512e-03 0.9053459 0.605964841
## 2.315951e-03 0.9050638 0.604141937
## 2.425323e-03 0.9044997 0.601193585
## 2.539859e-03 0.9044997 0.601193585
## 2.659804e-03 0.9040765 0.598416260
## 2.785414e-03 0.9039355 0.597660107
## 2.916956e-03 0.9039357 0.597640234
## 3.054710e-03 0.9033715 0.594679985
## 3.198969e-03 0.9037946 0.596268923
## 3.350041e-03 0.9036536 0.595547719
## 3.508247e-03 0.9037946 0.595625699
## 3.673925e-03 0.9032305 0.592901572
## 3.847427e-03 0.9026661 0.589991247
## 4.029122e-03 0.9025250 0.588707928
## 4.219398e-03 0.9022430 0.587141220
## 4.418660e-03 0.9018198 0.584500858
## 4.627332e-03 0.9019611 0.584559897
## 4.845859e-03 0.9015379 0.581626956
## 5.074705e-03 0.9016792 0.580746912
## 5.314359e-03 0.9012560 0.577863491
## 5.565331e-03 0.9011150 0.577089397
## 5.828155e-03 0.9008325 0.574559616
## 6.103390e-03 0.9012558 0.575108327
## 6.391624e-03 0.9013969 0.574836493
## 6.693470e-03 0.9009740 0.571983477
## 7.009570e-03 0.9006919 0.569274205
## 7.340598e-03 0.8998454 0.564235987
## 7.687260e-03 0.8985760 0.557828729
## 8.050292e-03 0.8982939 0.556213182
## 8.430468e-03 0.8981529 0.554206918
## 8.828599e-03 0.8981531 0.553530385
## 9.245531e-03 0.8980120 0.551624759
## 9.682153e-03 0.8973066 0.547625521
## 1.013939e-02 0.8968835 0.544715436
## 1.061823e-02 0.8966014 0.542095963
## 1.111968e-02 0.8964606 0.540163978
## 1.164481e-02 0.8964606 0.538902770
## 1.219473e-02 0.8960376 0.535248928
## 1.277063e-02 0.8953324 0.529593817
## 1.337373e-02 0.8956145 0.528545441
## 1.400531e-02 0.8947680 0.522388372
## 1.466671e-02 0.8946270 0.519430827
## 1.535935e-02 0.8947680 0.518597210
## 1.608469e-02 0.8936395 0.511604179
## 1.684430e-02 0.8932162 0.507791200
## 1.763977e-02 0.8925109 0.502184615
## 1.847281e-02 0.8919468 0.497112019
## 1.934520e-02 0.8911007 0.490903221
## 2.025878e-02 0.8901130 0.483194991
## 2.121550e-02 0.8887026 0.472126051
## 2.221741e-02 0.8877153 0.462271915
## 2.326663e-02 0.8867275 0.454951723
## 2.436540e-02 0.8868684 0.452953795
## 2.551606e-02 0.8864453 0.446683129
## 2.672106e-02 0.8854576 0.438662387
## 2.798297e-02 0.8843290 0.430487162
## 2.930447e-02 0.8833415 0.421369222
## 3.068838e-02 0.8805198 0.397753297
## 3.213764e-02 0.8786863 0.380512636
## 3.365535e-02 0.8761471 0.360568396
## 3.524473e-02 0.8741723 0.341626105
## 3.690917e-02 0.8700810 0.307176943
## 3.865221e-02 0.8685287 0.287867441
## 4.047757e-02 0.8647201 0.255105715
## 4.238913e-02 0.8624630 0.232199156
## 4.439097e-02 0.8593599 0.203791341
## 4.648734e-02 0.8542817 0.153206329
## 4.868271e-02 0.8507552 0.118511972
## 5.098176e-02 0.8486394 0.098366885
## 5.338938e-02 0.8465233 0.077866009
## 5.591071e-02 0.8448306 0.060349585
## 5.855110e-02 0.8434198 0.045223314
## 6.131619e-02 0.8420089 0.027581235
## 6.421186e-02 0.8408804 0.016062760
## 6.724427e-02 0.8394699 0.001478518
## 7.041990e-02 0.8393287 0.000000000
## 7.374549e-02 0.8393287 0.000000000
## 7.722814e-02 0.8393287 0.000000000
## 8.087525e-02 0.8393287 0.000000000
## 8.469460e-02 0.8393287 0.000000000
## 8.869432e-02 0.8393287 0.000000000
## 9.288292e-02 0.8393287 0.000000000
## 9.726934e-02 0.8393287 0.000000000
## 1.018629e-01 0.8393287 0.000000000
## 1.066734e-01 0.8393287 0.000000000
## 1.117111e-01 0.8393287 0.000000000
## 1.169866e-01 0.8393287 0.000000000
## 1.225114e-01 0.8393287 0.000000000
## 1.282970e-01 0.8393287 0.000000000
## 1.343558e-01 0.8393287 0.000000000
## 1.407008e-01 0.8393287 0.000000000
## 1.473454e-01 0.8393287 0.000000000
## 1.543038e-01 0.8393287 0.000000000
## 1.615909e-01 0.8393287 0.000000000
## 1.692220e-01 0.8393287 0.000000000
## 1.772136e-01 0.8393287 0.000000000
## 1.855825e-01 0.8393287 0.000000000
## 1.943467e-01 0.8393287 0.000000000
## 2.035248e-01 0.8393287 0.000000000
## 2.131362e-01 0.8393287 0.000000000
## 2.232016e-01 0.8393287 0.000000000
## 2.337424e-01 0.8393287 0.000000000
## 2.447809e-01 0.8393287 0.000000000
## 2.563407e-01 0.8393287 0.000000000
## 2.684465e-01 0.8393287 0.000000000
## 2.811239e-01 0.8393287 0.000000000
## 2.944000e-01 0.8393287 0.000000000
## 3.083031e-01 0.8393287 0.000000000
## 3.228628e-01 0.8393287 0.000000000
## 3.381101e-01 0.8393287 0.000000000
## 3.540774e-01 0.8393287 0.000000000
## 3.707988e-01 0.8393287 0.000000000
## 3.883098e-01 0.8393287 0.000000000
## 4.066478e-01 0.8393287 0.000000000
## 4.258518e-01 0.8393287 0.000000000
## 4.459628e-01 0.8393287 0.000000000
## 4.670234e-01 0.8393287 0.000000000
## 4.890787e-01 0.8393287 0.000000000
## 5.121755e-01 0.8393287 0.000000000
## 5.363631e-01 0.8393287 0.000000000
## 5.616930e-01 0.8393287 0.000000000
## 5.882190e-01 0.8393287 0.000000000
## 6.159978e-01 0.8393287 0.000000000
## 6.450884e-01 0.8393287 0.000000000
## 6.755528e-01 0.8393287 0.000000000
## 7.074559e-01 0.8393287 0.000000000
## 7.408657e-01 0.8393287 0.000000000
## 7.758532e-01 0.8393287 0.000000000
## 8.124930e-01 0.8393287 0.000000000
## 8.508632e-01 0.8393287 0.000000000
## 8.910453e-01 0.8393287 0.000000000
## 9.331251e-01 0.8393287 0.000000000
## 9.771921e-01 0.8393287 0.000000000
## 1.023340e+00 0.8393287 0.000000000
## 1.071668e+00 0.8393287 0.000000000
## 1.122277e+00 0.8393287 0.000000000
## 1.175277e+00 0.8393287 0.000000000
## 1.230780e+00 0.8393287 0.000000000
## 1.288904e+00 0.8393287 0.000000000
## 1.349772e+00 0.8393287 0.000000000
## 1.413516e+00 0.8393287 0.000000000
## 1.480269e+00 0.8393287 0.000000000
## 1.550175e+00 0.8393287 0.000000000
## 1.623382e+00 0.8393287 0.000000000
## 1.700047e+00 0.8393287 0.000000000
## 1.780332e+00 0.8393287 0.000000000
## 1.864409e+00 0.8393287 0.000000000
## 1.952456e+00 0.8393287 0.000000000
## 2.044661e+00 0.8393287 0.000000000
## 2.141220e+00 0.8393287 0.000000000
## 2.242340e+00 0.8393287 0.000000000
## 2.348235e+00 0.8393287 0.000000000
## 2.459130e+00 0.8393287 0.000000000
## 2.575263e+00 0.8393287 0.000000000
## 2.696881e+00 0.8393287 0.000000000
## 2.824241e+00 0.8393287 0.000000000
## 2.957617e+00 0.8393287 0.000000000
## 3.097291e+00 0.8393287 0.000000000
## 3.243561e+00 0.8393287 0.000000000
## 3.396739e+00 0.8393287 0.000000000
## 3.557150e+00 0.8393287 0.000000000
## 3.725137e+00 0.8393287 0.000000000
## 3.901058e+00 0.8393287 0.000000000
## 4.085286e+00 0.8393287 0.000000000
## 4.278214e+00 0.8393287 0.000000000
## 4.480254e+00 0.8393287 0.000000000
## 4.691835e+00 0.8393287 0.000000000
## 4.913407e+00 0.8393287 0.000000000
## 5.145444e+00 0.8393287 0.000000000
## 5.388438e+00 0.8393287 0.000000000
## 5.642908e+00 0.8393287 0.000000000
## 5.909396e+00 0.8393287 0.000000000
## 6.188468e+00 0.8393287 0.000000000
## 6.480720e+00 0.8393287 0.000000000
## 6.786773e+00 0.8393287 0.000000000
## 7.107280e+00 0.8393287 0.000000000
## 7.442922e+00 0.8393287 0.000000000
## 7.794416e+00 0.8393287 0.000000000
## 8.162509e+00 0.8393287 0.000000000
## 8.547985e+00 0.8393287 0.000000000
## 8.951665e+00 0.8393287 0.000000000
## 9.374409e+00 0.8393287 0.000000000
## 9.817117e+00 0.8393287 0.000000000
## 1.028073e+01 0.8393287 0.000000000
## 1.076624e+01 0.8393287 0.000000000
## 1.127468e+01 0.8393287 0.000000000
## 1.180713e+01 0.8393287 0.000000000
## 1.236472e+01 0.8393287 0.000000000
## 1.294865e+01 0.8393287 0.000000000
## 1.356015e+01 0.8393287 0.000000000
## 1.420053e+01 0.8393287 0.000000000
## 1.487115e+01 0.8393287 0.000000000
## 1.557345e+01 0.8393287 0.000000000
## 1.630891e+01 0.8393287 0.000000000
## 1.707910e+01 0.8393287 0.000000000
## 1.788566e+01 0.8393287 0.000000000
## 1.873032e+01 0.8393287 0.000000000
## 1.961486e+01 0.8393287 0.000000000
## 2.054117e+01 0.8393287 0.000000000
## 2.151123e+01 0.8393287 0.000000000
## 2.252711e+01 0.8393287 0.000000000
## 2.359095e+01 0.8393287 0.000000000
## 2.470504e+01 0.8393287 0.000000000
## 2.587174e+01 0.8393287 0.000000000
## 2.709354e+01 0.8393287 0.000000000
## 2.837304e+01 0.8393287 0.000000000
## 2.971296e+01 0.8393287 0.000000000
## 3.111616e+01 0.8393287 0.000000000
## 3.258562e+01 0.8393287 0.000000000
## 3.412449e+01 0.8393287 0.000000000
## 3.573602e+01 0.8393287 0.000000000
## 3.742366e+01 0.8393287 0.000000000
## 3.919100e+01 0.8393287 0.000000000
## 4.104181e+01 0.8393287 0.000000000
## 4.298001e+01 0.8393287 0.000000000
## 4.500975e+01 0.8393287 0.000000000
## 4.713535e+01 0.8393287 0.000000000
## 4.936132e+01 0.8393287 0.000000000
## 5.169242e+01 0.8393287 0.000000000
## 5.413360e+01 0.8393287 0.000000000
## 5.669007e+01 0.8393287 0.000000000
## 5.936727e+01 0.8393287 0.000000000
## 6.217090e+01 0.8393287 0.000000000
## 6.510694e+01 0.8393287 0.000000000
## 6.818162e+01 0.8393287 0.000000000
## 7.140151e+01 0.8393287 0.000000000
## 7.477346e+01 0.8393287 0.000000000
## 7.830465e+01 0.8393287 0.000000000
## 8.200261e+01 0.8393287 0.000000000
## 8.587519e+01 0.8393287 0.000000000
## 8.993067e+01 0.8393287 0.000000000
## 9.417766e+01 0.8393287 0.000000000
## 9.862522e+01 0.8393287 0.000000000
## 1.032828e+02 0.8393287 0.000000000
## 1.081604e+02 0.8393287 0.000000000
## 1.132683e+02 0.8393287 0.000000000
## 1.186174e+02 0.8393287 0.000000000
## 1.242191e+02 0.8393287 0.000000000
## 1.300854e+02 0.8393287 0.000000000
## 1.362287e+02 0.8393287 0.000000000
## 1.426621e+02 0.8393287 0.000000000
## 1.493993e+02 0.8393287 0.000000000
## 1.564548e+02 0.8393287 0.000000000
## 1.638434e+02 0.8393287 0.000000000
## 1.715809e+02 0.8393287 0.000000000
## 1.796838e+02 0.8393287 0.000000000
## 1.881694e+02 0.8393287 0.000000000
## 1.970558e+02 0.8393287 0.000000000
## 2.063618e+02 0.8393287 0.000000000
## 2.161073e+02 0.8393287 0.000000000
## 2.263130e+02 0.8393287 0.000000000
## 2.370006e+02 0.8393287 0.000000000
## 2.481930e+02 0.8393287 0.000000000
## 2.599140e+02 0.8393287 0.000000000
## 2.721885e+02 0.8393287 0.000000000
## 2.850426e+02 0.8393287 0.000000000
## 2.985038e+02 0.8393287 0.000000000
## 3.126007e+02 0.8393287 0.000000000
## 3.273634e+02 0.8393287 0.000000000
## 3.428231e+02 0.8393287 0.000000000
## 3.590130e+02 0.8393287 0.000000000
## 3.759675e+02 0.8393287 0.000000000
## 3.937226e+02 0.8393287 0.000000000
## 4.123163e+02 0.8393287 0.000000000
## 4.317880e+02 0.8393287 0.000000000
## 4.521792e+02 0.8393287 0.000000000
## 4.735335e+02 0.8393287 0.000000000
## 4.958962e+02 0.8393287 0.000000000
## 5.193150e+02 0.8393287 0.000000000
## 5.438397e+02 0.8393287 0.000000000
## 5.695227e+02 0.8393287 0.000000000
## 5.964185e+02 0.8393287 0.000000000
## 6.245845e+02 0.8393287 0.000000000
## 6.540806e+02 0.8393287 0.000000000
## 6.849697e+02 0.8393287 0.000000000
## 7.173175e+02 0.8393287 0.000000000
## 7.511929e+02 0.8393287 0.000000000
## 7.866682e+02 0.8393287 0.000000000
## 8.238187e+02 0.8393287 0.000000000
## 8.627237e+02 0.8393287 0.000000000
## 9.034660e+02 0.8393287 0.000000000
## 9.461324e+02 0.8393287 0.000000000
## 9.908137e+02 0.8393287 0.000000000
## 1.037605e+03 0.8393287 0.000000000
## 1.086606e+03 0.8393287 0.000000000
## 1.137921e+03 0.8393287 0.000000000
## 1.191660e+03 0.8393287 0.000000000
## 1.247936e+03 0.8393287 0.000000000
## 1.306870e+03 0.8393287 0.000000000
## 1.368587e+03 0.8393287 0.000000000
## 1.433219e+03 0.8393287 0.000000000
## 1.500903e+03 0.8393287 0.000000000
## 1.571784e+03 0.8393287 0.000000000
## 1.646012e+03 0.8393287 0.000000000
## 1.723745e+03 0.8393287 0.000000000
## 1.805149e+03 0.8393287 0.000000000
## 1.890397e+03 0.8393287 0.000000000
## 1.979672e+03 0.8393287 0.000000000
## 2.073162e+03 0.8393287 0.000000000
## 2.171068e+03 0.8393287 0.000000000
## 2.273597e+03 0.8393287 0.000000000
## 2.380968e+03 0.8393287 0.000000000
## 2.493409e+03 0.8393287 0.000000000
## 2.611161e+03 0.8393287 0.000000000
## 2.734474e+03 0.8393287 0.000000000
## 2.863610e+03 0.8393287 0.000000000
## 2.998844e+03 0.8393287 0.000000000
## 3.140465e+03 0.8393287 0.000000000
## 3.288774e+03 0.8393287 0.000000000
## 3.444087e+03 0.8393287 0.000000000
## 3.606735e+03 0.8393287 0.000000000
## 3.777064e+03 0.8393287 0.000000000
## 3.955436e+03 0.8393287 0.000000000
## 4.142232e+03 0.8393287 0.000000000
## 4.337850e+03 0.8393287 0.000000000
## 4.542706e+03 0.8393287 0.000000000
## 4.757236e+03 0.8393287 0.000000000
## 4.981898e+03 0.8393287 0.000000000
## 5.217169e+03 0.8393287 0.000000000
## 5.463550e+03 0.8393287 0.000000000
## 5.721568e+03 0.8393287 0.000000000
## 5.991770e+03 0.8393287 0.000000000
## 6.274732e+03 0.8393287 0.000000000
## 6.571058e+03 0.8393287 0.000000000
## 6.881377e+03 0.8393287 0.000000000
## 7.206351e+03 0.8393287 0.000000000
## 7.546673e+03 0.8393287 0.000000000
## 7.903066e+03 0.8393287 0.000000000
## 8.276289e+03 0.8393287 0.000000000
## 8.667139e+03 0.8393287 0.000000000
## 9.076446e+03 0.8393287 0.000000000
## 9.505083e+03 0.8393287 0.000000000
## 9.953962e+03 0.8393287 0.000000000
## 1.042404e+04 0.8393287 0.000000000
## 1.091632e+04 0.8393287 0.000000000
## 1.143184e+04 0.8393287 0.000000000
## 1.197171e+04 0.8393287 0.000000000
## 1.253708e+04 0.8393287 0.000000000
## 1.312915e+04 0.8393287 0.000000000
## 1.374917e+04 0.8393287 0.000000000
## 1.439848e+04 0.8393287 0.000000000
## 1.507845e+04 0.8393287 0.000000000
## 1.579053e+04 0.8393287 0.000000000
## 1.653624e+04 0.8393287 0.000000000
## 1.731717e+04 0.8393287 0.000000000
## 1.813498e+04 0.8393287 0.000000000
## 1.899141e+04 0.8393287 0.000000000
## 1.988828e+04 0.8393287 0.000000000
## 2.082751e+04 0.8393287 0.000000000
## 2.181109e+04 0.8393287 0.000000000
## 2.284112e+04 0.8393287 0.000000000
## 2.391980e+04 0.8393287 0.000000000
## 2.504942e+04 0.8393287 0.000000000
## 2.623238e+04 0.8393287 0.000000000
## 2.747121e+04 0.8393287 0.000000000
## 2.876854e+04 0.8393287 0.000000000
## 3.012714e+04 0.8393287 0.000000000
## 3.154990e+04 0.8393287 0.000000000
## 3.303985e+04 0.8393287 0.000000000
## 3.460016e+04 0.8393287 0.000000000
## 3.623416e+04 0.8393287 0.000000000
## 3.794533e+04 0.8393287 0.000000000
## 3.973730e+04 0.8393287 0.000000000
## 4.161391e+04 0.8393287 0.000000000
## 4.357913e+04 0.8393287 0.000000000
## 4.563716e+04 0.8393287 0.000000000
## 4.779239e+04 0.8393287 0.000000000
## 5.004939e+04 0.8393287 0.000000000
## 5.241298e+04 0.8393287 0.000000000
## 5.488820e+04 0.8393287 0.000000000
## 5.748030e+04 0.8393287 0.000000000
## 6.019482e+04 0.8393287 0.000000000
## 6.303753e+04 0.8393287 0.000000000
## 6.601449e+04 0.8393287 0.000000000
## 6.913204e+04 0.8393287 0.000000000
## 7.239681e+04 0.8393287 0.000000000
## 7.581576e+04 0.8393287 0.000000000
## 7.939618e+04 0.8393287 0.000000000
## 8.314568e+04 0.8393287 0.000000000
## 8.707225e+04 0.8393287 0.000000000
## 9.118425e+04 0.8393287 0.000000000
## 9.549045e+04 0.8393287 0.000000000
## 1.000000e+05 0.8393287 0.000000000
##
## Tuning parameter 'alpha' was held constant at a value of 1
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were alpha = 1 and lambda = 0.001528864.
#get the best tuning parameters
Model3$bestTune
## alpha lambda
## 110 1 0.001528864
# alpha lambda
# 1 0.001528864
#just the best lamda
Model3$bestTune$lambda
## [1] 0.001528864
#0.001528864
#LASSO Regression model coefficients(Parameter Estimates)
round(coef(Model3$finalModel,Model3$bestTune$lambda),3)
## 33 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 2.888
## Customer_Age 0.013
## GenderM 0.300
## Dependent_count -0.149
## Education_LevelDoctorate -0.045
## Education_LevelGraduate 0.024
## Education_LevelHigh School 0.037
## Education_LevelPost-Graduate -0.061
## Education_LevelUneducated -0.011
## Education_LevelUnknown -0.016
## Marital_StatusMarried 0.228
## Marital_StatusSingle -0.028
## Marital_StatusUnknown .
## Income_Category$40K - $60K 0.077
## Income_Category$60K - $80K 0.034
## Income_Category$80K - $120K -0.059
## Income_CategoryLess than $40K .
## Income_CategoryUnknown 0.017
## Card_CategoryGold -0.098
## Card_CategoryPlatinum .
## Card_CategorySilver -0.048
## Months_on_book 0.054
## Total_Relationship_Count 0.681
## Months_Inactive_12_mon -0.473
## Contacts_Count_12_mon -0.564
## Credit_Limit 0.054
## Total_Revolving_Bal 0.730
## Avg_Open_To_Buy .
## Total_Amt_Chng_Q4_Q1 0.051
## Total_Trans_Amt -1.435
## Total_Trans_Ct 2.555
## Total_Ct_Chng_Q4_Q1 0.634
## Avg_Utilization_Ratio .
#Plot log(lambda) & RMSE
plot(log(Model3$results$lambda),Model3$results$RMSE,
xlab="Log(lambda)",
ylab="RMSE",
xlim=c(0,100))
log(Model3$bestTune$lambda)
## [1] -6.483231
#variable importance
varImp(Model3)
## glmnet variable importance
##
## only 20 most important variables shown (out of 32)
##
## Overall
## Total_Trans_Ct 100.000
## Total_Trans_Amt 56.142
## Total_Revolving_Bal 28.581
## Total_Relationship_Count 26.661
## Total_Ct_Chng_Q4_Q1 24.794
## Contacts_Count_12_mon 22.059
## Months_Inactive_12_mon 18.516
## GenderM 11.725
## Marital_StatusMarried 8.930
## Dependent_count 5.836
## Card_CategoryGold 3.829
## Income_Category$40K - $60K 3.017
## Education_LevelPost-Graduate 2.391
## Income_Category$80K - $120K 2.325
## Credit_Limit 2.133
## Months_on_book 2.101
## Total_Amt_Chng_Q4_Q1 1.996
## Card_CategorySilver 1.885
## Education_LevelDoctorate 1.753
## Education_LevelHigh School 1.445
#plot variable importance
ggplot(varImp(Model3))+
labs(title = "Model 3 Variable importance Rank")
#forming confussion matrix
predictions_Lasso<-predict(Model3,newdata = testing)
cm_3<-confusionMatrix(data=predictions_Lasso,testing$Attrition_Flag)
cm_3
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 279 90
## Stay 209 2460
##
## Accuracy : 0.9016
## 95% CI : (0.8904, 0.9119)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5951
##
## Mcnemar's Test P-Value : 8.847e-12
##
## Sensitivity : 0.57172
## Specificity : 0.96471
## Pos Pred Value : 0.75610
## Neg Pred Value : 0.92169
## Prevalence : 0.16063
## Detection Rate : 0.09184
## Detection Prevalence : 0.12146
## Balanced Accuracy : 0.76821
##
## 'Positive' Class : Quit
##
#MODEL 3 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9016 0.5951 0.57172 0.96471 0.16063
#MODEL 4
#4.a with 2 repeats and 3 folds
#4.b with 3 repeats and 5 folds
#RANDOM FOREST MODELLING-RPART
#4.a
rf_ctr_specs1 <-trainControl(method = "repeatedcv",
repeats = 2,
number=3,
search = "random")
Model4.a <-train(Attrition_Flag~.,data=training,
method="rf",
trControl=rf_ctr_specs1)
plot(varImp(Model4.a,scale=F),main="Model 4.a RandomForest-3 FOLDS-2-REPEATED CV")
#Forming confusion matrix
predictions_rf1<-predict(Model4.a,newdata=testing)
cm_4.a<-confusionMatrix(predictions_rf1,testing$Attrition_Flag)
cm_4.a
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 423 24
## Stay 65 2526
##
## Accuracy : 0.9707
## 95% CI : (0.9641, 0.9764)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.8875
##
## Mcnemar's Test P-Value : 2.235e-05
##
## Sensitivity : 0.8668
## Specificity : 0.9906
## Pos Pred Value : 0.9463
## Neg Pred Value : 0.9749
## Prevalence : 0.1606
## Detection Rate : 0.1392
## Detection Prevalence : 0.1471
## Balanced Accuracy : 0.9287
##
## 'Positive' Class : Quit
##
#MODEL 4.a ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9707 0.8875 0.8668 0.9906 0.1606
#4.b
rf_ctr_specs <-trainControl(method = "repeatedcv",
repeats = 3,
number=5,
search = "random")
Model4.b <-train(Attrition_Flag~.,data=training,
method="rf",
trControl=rf_ctr_specs)#THIS WILL TAKE A BIT LONGER THAN 4.A SINCE THE NUMBER OF FOLDS IS BIG AND IT REPEATS 3 TIMES
plot(varImp(Model4.b,scale=F),main="Model 4b RandomForest-5 FOLDS-3-REAPEATED CV")
#Forming confusion matrix
predictions_rf<-predict(Model4.b,newdata=testing)
cm_4.b<-confusionMatrix(predictions_rf,testing$Attrition_Flag)
cm_4.b
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 418 20
## Stay 70 2530
##
## Accuracy : 0.9704
## 95% CI : (0.9637, 0.9761)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.8854
##
## Mcnemar's Test P-Value : 2.404e-07
##
## Sensitivity : 0.8566
## Specificity : 0.9922
## Pos Pred Value : 0.9543
## Neg Pred Value : 0.9731
## Prevalence : 0.1606
## Detection Rate : 0.1376
## Detection Prevalence : 0.1442
## Balanced Accuracy : 0.9244
##
## 'Positive' Class : Quit
##
#MODEL 4.b ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9704 0.8854 0.8566 0.9922 0.1606
#MODEL 5
#DECISION TREES-RPART
Model5 <-rpart(Attrition_Flag~.,data = training,method="class")
predictions_rpart<-predict(Model5,testing,type="class")
rpart.plot(Model5,
type = 1,
extra=100,
branch.lty=3,
box.palette = "RdYlGn",
tweak = 1.6,)
cm_5<-confusionMatrix(predictions_rpart,testing$Attrition_Flag)
cm_5
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 406 111
## Stay 82 2439
##
## Accuracy : 0.9365
## 95% CI : (0.9272, 0.9449)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2e-16
##
## Kappa : 0.7699
##
## Mcnemar's Test P-Value : 0.04385
##
## Sensitivity : 0.8320
## Specificity : 0.9565
## Pos Pred Value : 0.7853
## Neg Pred Value : 0.9675
## Prevalence : 0.1606
## Detection Rate : 0.1336
## Detection Prevalence : 0.1702
## Balanced Accuracy : 0.8942
##
## 'Positive' Class : Quit
##
#MODEL 5 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9365 0.7699 0.8320 0.9565 0.1606
#MODEL 6
#RIDGE REGRESSION -K-FOLD CROSS-VALIDATION FRAMEWORK
#control specs will be different from that of LASSO model
#difference being alpha, in the case of ridge regression alpha=0 not 1
rdg_ctrl_specs <-trainControl(method = "cv",
savePredictions = "all",
number = 10,
classProbs = T)
#we have to create a vector for potential lambdas
lambda_vector <-10^seq(-5,5,length=500)
Model6 <-train(Attrition_Flag~.,data =training,
method="glmnet",
tuneGrid=expand.grid(alpha=0,lambda=lambda_vector),
trControl=rdg_ctrl_specs,
preProcess=c("center","scale"),
na.action = na.omit)
Model6
## glmnet
##
## 7089 samples
## 19 predictor
## 2 classes: 'Quit', 'Stay'
##
## Pre-processing: centered (32), scaled (32)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 6380, 6380, 6380, 6380, 6380, 6380, ...
## Resampling results across tuning parameters:
##
## lambda Accuracy Kappa
## 1.000000e-05 0.8985738 0.550924140
## 1.047225e-05 0.8985738 0.550924140
## 1.096681e-05 0.8985738 0.550924140
## 1.148472e-05 0.8985738 0.550924140
## 1.202708e-05 0.8985738 0.550924140
## 1.259506e-05 0.8985738 0.550924140
## 1.318987e-05 0.8985738 0.550924140
## 1.381276e-05 0.8985738 0.550924140
## 1.446507e-05 0.8985738 0.550924140
## 1.514819e-05 0.8985738 0.550924140
## 1.586357e-05 0.8985738 0.550924140
## 1.661273e-05 0.8985738 0.550924140
## 1.739726e-05 0.8985738 0.550924140
## 1.821885e-05 0.8985738 0.550924140
## 1.907924e-05 0.8985738 0.550924140
## 1.998026e-05 0.8985738 0.550924140
## 2.092383e-05 0.8985738 0.550924140
## 2.191197e-05 0.8985738 0.550924140
## 2.294676e-05 0.8985738 0.550924140
## 2.403043e-05 0.8985738 0.550924140
## 2.516527e-05 0.8985738 0.550924140
## 2.635371e-05 0.8985738 0.550924140
## 2.759826e-05 0.8985738 0.550924140
## 2.890160e-05 0.8985738 0.550924140
## 3.026648e-05 0.8985738 0.550924140
## 3.169582e-05 0.8985738 0.550924140
## 3.319266e-05 0.8985738 0.550924140
## 3.476019e-05 0.8985738 0.550924140
## 3.640175e-05 0.8985738 0.550924140
## 3.812083e-05 0.8985738 0.550924140
## 3.992109e-05 0.8985738 0.550924140
## 4.180637e-05 0.8985738 0.550924140
## 4.378069e-05 0.8985738 0.550924140
## 4.584824e-05 0.8985738 0.550924140
## 4.801343e-05 0.8985738 0.550924140
## 5.028087e-05 0.8985738 0.550924140
## 5.265540e-05 0.8985738 0.550924140
## 5.514206e-05 0.8985738 0.550924140
## 5.774615e-05 0.8985738 0.550924140
## 6.047322e-05 0.8985738 0.550924140
## 6.332908e-05 0.8985738 0.550924140
## 6.631981e-05 0.8985738 0.550924140
## 6.945178e-05 0.8985738 0.550924140
## 7.273165e-05 0.8985738 0.550924140
## 7.616642e-05 0.8985738 0.550924140
## 7.976339e-05 0.8985738 0.550924140
## 8.353023e-05 0.8985738 0.550924140
## 8.747496e-05 0.8985738 0.550924140
## 9.160598e-05 0.8985738 0.550924140
## 9.593209e-05 0.8985738 0.550924140
## 1.004625e-04 0.8985738 0.550924140
## 1.052069e-04 0.8985738 0.550924140
## 1.101753e-04 0.8985738 0.550924140
## 1.153783e-04 0.8985738 0.550924140
## 1.208271e-04 0.8985738 0.550924140
## 1.265332e-04 0.8985738 0.550924140
## 1.325087e-04 0.8985738 0.550924140
## 1.387665e-04 0.8985738 0.550924140
## 1.453198e-04 0.8985738 0.550924140
## 1.521825e-04 0.8985738 0.550924140
## 1.593694e-04 0.8985738 0.550924140
## 1.668956e-04 0.8985738 0.550924140
## 1.747773e-04 0.8985738 0.550924140
## 1.830312e-04 0.8985738 0.550924140
## 1.916748e-04 0.8985738 0.550924140
## 2.007267e-04 0.8985738 0.550924140
## 2.102061e-04 0.8985738 0.550924140
## 2.201331e-04 0.8985738 0.550924140
## 2.305289e-04 0.8985738 0.550924140
## 2.414157e-04 0.8985738 0.550924140
## 2.528166e-04 0.8985738 0.550924140
## 2.647559e-04 0.8985738 0.550924140
## 2.772591e-04 0.8985738 0.550924140
## 2.903527e-04 0.8985738 0.550924140
## 3.040646e-04 0.8985738 0.550924140
## 3.184242e-04 0.8985738 0.550924140
## 3.334618e-04 0.8985738 0.550924140
## 3.492096e-04 0.8985738 0.550924140
## 3.657011e-04 0.8985738 0.550924140
## 3.829714e-04 0.8985738 0.550924140
## 4.010573e-04 0.8985738 0.550924140
## 4.199973e-04 0.8985738 0.550924140
## 4.398317e-04 0.8985738 0.550924140
## 4.606029e-04 0.8985738 0.550924140
## 4.823549e-04 0.8985738 0.550924140
## 5.051342e-04 0.8985738 0.550924140
## 5.289893e-04 0.8985738 0.550924140
## 5.539709e-04 0.8985738 0.550924140
## 5.801323e-04 0.8985738 0.550924140
## 6.075292e-04 0.8985738 0.550924140
## 6.362198e-04 0.8985738 0.550924140
## 6.662655e-04 0.8985738 0.550924140
## 6.977300e-04 0.8985738 0.550924140
## 7.306804e-04 0.8985738 0.550924140
## 7.651869e-04 0.8985738 0.550924140
## 8.013230e-04 0.8985738 0.550924140
## 8.391656e-04 0.8985738 0.550924140
## 8.787954e-04 0.8985738 0.550924140
## 9.202967e-04 0.8985738 0.550924140
## 9.637579e-04 0.8985738 0.550924140
## 1.009272e-03 0.8985738 0.550924140
## 1.056935e-03 0.8985738 0.550924140
## 1.106848e-03 0.8985738 0.550924140
## 1.159120e-03 0.8985738 0.550924140
## 1.213859e-03 0.8985738 0.550924140
## 1.271184e-03 0.8985738 0.550924140
## 1.331216e-03 0.8985738 0.550924140
## 1.394083e-03 0.8985738 0.550924140
## 1.459919e-03 0.8985738 0.550924140
## 1.528864e-03 0.8985738 0.550924140
## 1.601064e-03 0.8985738 0.550924140
## 1.676675e-03 0.8985738 0.550924140
## 1.755856e-03 0.8985738 0.550924140
## 1.838777e-03 0.8985738 0.550924140
## 1.925614e-03 0.8985738 0.550924140
## 2.016551e-03 0.8985738 0.550924140
## 2.111783e-03 0.8985738 0.550924140
## 2.211512e-03 0.8985738 0.550924140
## 2.315951e-03 0.8985738 0.550924140
## 2.425323e-03 0.8985738 0.550924140
## 2.539859e-03 0.8985738 0.550924140
## 2.659804e-03 0.8985738 0.550924140
## 2.785414e-03 0.8985738 0.550924140
## 2.916956e-03 0.8985738 0.550924140
## 3.054710e-03 0.8985738 0.550924140
## 3.198969e-03 0.8985738 0.550924140
## 3.350041e-03 0.8985738 0.550924140
## 3.508247e-03 0.8985738 0.550924140
## 3.673925e-03 0.8985738 0.550924140
## 3.847427e-03 0.8985738 0.550924140
## 4.029122e-03 0.8985738 0.550924140
## 4.219398e-03 0.8985738 0.550924140
## 4.418660e-03 0.8985738 0.550924140
## 4.627332e-03 0.8985738 0.550924140
## 4.845859e-03 0.8985738 0.550924140
## 5.074705e-03 0.8985738 0.550924140
## 5.314359e-03 0.8985738 0.550924140
## 5.565331e-03 0.8985738 0.550924140
## 5.828155e-03 0.8985738 0.550924140
## 6.103390e-03 0.8985738 0.550924140
## 6.391624e-03 0.8985738 0.550924140
## 6.693470e-03 0.8985738 0.550924140
## 7.009570e-03 0.8985738 0.550924140
## 7.340598e-03 0.8985738 0.550924140
## 7.687260e-03 0.8985738 0.550924140
## 8.050292e-03 0.8985738 0.550924140
## 8.430468e-03 0.8985738 0.550924140
## 8.828599e-03 0.8985738 0.550924140
## 9.245531e-03 0.8985738 0.550924140
## 9.682153e-03 0.8985738 0.550924140
## 1.013939e-02 0.8985738 0.550924140
## 1.061823e-02 0.8985738 0.550924140
## 1.111968e-02 0.8985738 0.550924140
## 1.164481e-02 0.8985738 0.550924140
## 1.219473e-02 0.8985738 0.550924140
## 1.277063e-02 0.8985738 0.550924140
## 1.337373e-02 0.8985738 0.550924140
## 1.400531e-02 0.8985738 0.550924140
## 1.466671e-02 0.8982917 0.548609130
## 1.535935e-02 0.8980096 0.546138482
## 1.608469e-02 0.8974453 0.541708539
## 1.684430e-02 0.8971632 0.539278126
## 1.763977e-02 0.8973044 0.538861671
## 1.847281e-02 0.8965992 0.533986543
## 1.934520e-02 0.8965994 0.533586644
## 2.025878e-02 0.8964584 0.531839802
## 2.121550e-02 0.8963175 0.530196091
## 2.221741e-02 0.8960356 0.527633082
## 2.326663e-02 0.8957535 0.525071782
## 2.436540e-02 0.8960358 0.525941438
## 2.551606e-02 0.8958950 0.524664614
## 2.672106e-02 0.8957539 0.522869512
## 2.798297e-02 0.8958950 0.522547911
## 2.930447e-02 0.8956129 0.520375991
## 3.068838e-02 0.8954719 0.518558576
## 3.213764e-02 0.8956127 0.517408767
## 3.365535e-02 0.8958952 0.517027666
## 3.524473e-02 0.8950487 0.511471036
## 3.690917e-02 0.8946256 0.507555440
## 3.865221e-02 0.8930737 0.497342932
## 4.047757e-02 0.8932150 0.495994284
## 4.238913e-02 0.8929333 0.493263732
## 4.439097e-02 0.8922281 0.486903593
## 4.648734e-02 0.8916637 0.482849933
## 4.868271e-02 0.8912403 0.478125974
## 5.098176e-02 0.8905347 0.472714107
## 5.338938e-02 0.8896885 0.466143888
## 5.591071e-02 0.8892653 0.462368159
## 5.855110e-02 0.8889831 0.459022062
## 6.131619e-02 0.8882776 0.453322328
## 6.421186e-02 0.8864435 0.440455905
## 6.724427e-02 0.8854556 0.431410559
## 7.041990e-02 0.8853145 0.427783900
## 7.374549e-02 0.8844679 0.420724250
## 7.722814e-02 0.8836218 0.412395100
## 8.087525e-02 0.8827753 0.404023547
## 8.469460e-02 0.8817880 0.395885647
## 8.869432e-02 0.8817880 0.394081002
## 9.288292e-02 0.8799539 0.378462813
## 9.726934e-02 0.8788255 0.367619535
## 1.018629e-01 0.8771328 0.354303809
## 1.066734e-01 0.8764278 0.347550810
## 1.117111e-01 0.8743119 0.329971671
## 1.169866e-01 0.8731838 0.319181932
## 1.225114e-01 0.8712092 0.303000168
## 1.282970e-01 0.8686698 0.281575884
## 1.343558e-01 0.8672591 0.268751324
## 1.407008e-01 0.8662718 0.257555454
## 1.473454e-01 0.8654256 0.249808094
## 1.543038e-01 0.8631689 0.230899038
## 1.615909e-01 0.8613353 0.213346724
## 1.692220e-01 0.8589372 0.192379124
## 1.772136e-01 0.8572444 0.177410596
## 1.855825e-01 0.8554107 0.160816843
## 1.943467e-01 0.8532950 0.141363811
## 2.035248e-01 0.8520254 0.128511577
## 2.131362e-01 0.8511793 0.119593128
## 2.232016e-01 0.8489219 0.097052191
## 2.337424e-01 0.8469464 0.077985353
## 2.447809e-01 0.8460998 0.068653003
## 2.563407e-01 0.8448302 0.056085590
## 2.684465e-01 0.8437018 0.044764789
## 2.811239e-01 0.8429966 0.037667051
## 2.944000e-01 0.8421504 0.029072784
## 3.083031e-01 0.8413039 0.020379846
## 3.228628e-01 0.8405983 0.013152797
## 3.381101e-01 0.8403160 0.010227905
## 3.540774e-01 0.8401749 0.008781532
## 3.707988e-01 0.8400339 0.007317943
## 3.883098e-01 0.8400339 0.007317943
## 4.066478e-01 0.8398929 0.005854354
## 4.258518e-01 0.8398929 0.005854354
## 4.459628e-01 0.8397518 0.004390766
## 4.670234e-01 0.8393287 0.000000000
## 4.890787e-01 0.8393287 0.000000000
## 5.121755e-01 0.8393287 0.000000000
## 5.363631e-01 0.8393287 0.000000000
## 5.616930e-01 0.8393287 0.000000000
## 5.882190e-01 0.8393287 0.000000000
## 6.159978e-01 0.8393287 0.000000000
## 6.450884e-01 0.8393287 0.000000000
## 6.755528e-01 0.8393287 0.000000000
## 7.074559e-01 0.8393287 0.000000000
## 7.408657e-01 0.8393287 0.000000000
## 7.758532e-01 0.8393287 0.000000000
## 8.124930e-01 0.8393287 0.000000000
## 8.508632e-01 0.8393287 0.000000000
## 8.910453e-01 0.8393287 0.000000000
## 9.331251e-01 0.8393287 0.000000000
## 9.771921e-01 0.8393287 0.000000000
## 1.023340e+00 0.8393287 0.000000000
## 1.071668e+00 0.8393287 0.000000000
## 1.122277e+00 0.8393287 0.000000000
## 1.175277e+00 0.8393287 0.000000000
## 1.230780e+00 0.8393287 0.000000000
## 1.288904e+00 0.8393287 0.000000000
## 1.349772e+00 0.8393287 0.000000000
## 1.413516e+00 0.8393287 0.000000000
## 1.480269e+00 0.8393287 0.000000000
## 1.550175e+00 0.8393287 0.000000000
## 1.623382e+00 0.8393287 0.000000000
## 1.700047e+00 0.8393287 0.000000000
## 1.780332e+00 0.8393287 0.000000000
## 1.864409e+00 0.8393287 0.000000000
## 1.952456e+00 0.8393287 0.000000000
## 2.044661e+00 0.8393287 0.000000000
## 2.141220e+00 0.8393287 0.000000000
## 2.242340e+00 0.8393287 0.000000000
## 2.348235e+00 0.8393287 0.000000000
## 2.459130e+00 0.8393287 0.000000000
## 2.575263e+00 0.8393287 0.000000000
## 2.696881e+00 0.8393287 0.000000000
## 2.824241e+00 0.8393287 0.000000000
## 2.957617e+00 0.8393287 0.000000000
## 3.097291e+00 0.8393287 0.000000000
## 3.243561e+00 0.8393287 0.000000000
## 3.396739e+00 0.8393287 0.000000000
## 3.557150e+00 0.8393287 0.000000000
## 3.725137e+00 0.8393287 0.000000000
## 3.901058e+00 0.8393287 0.000000000
## 4.085286e+00 0.8393287 0.000000000
## 4.278214e+00 0.8393287 0.000000000
## 4.480254e+00 0.8393287 0.000000000
## 4.691835e+00 0.8393287 0.000000000
## 4.913407e+00 0.8393287 0.000000000
## 5.145444e+00 0.8393287 0.000000000
## 5.388438e+00 0.8393287 0.000000000
## 5.642908e+00 0.8393287 0.000000000
## 5.909396e+00 0.8393287 0.000000000
## 6.188468e+00 0.8393287 0.000000000
## 6.480720e+00 0.8393287 0.000000000
## 6.786773e+00 0.8393287 0.000000000
## 7.107280e+00 0.8393287 0.000000000
## 7.442922e+00 0.8393287 0.000000000
## 7.794416e+00 0.8393287 0.000000000
## 8.162509e+00 0.8393287 0.000000000
## 8.547985e+00 0.8393287 0.000000000
## 8.951665e+00 0.8393287 0.000000000
## 9.374409e+00 0.8393287 0.000000000
## 9.817117e+00 0.8393287 0.000000000
## 1.028073e+01 0.8393287 0.000000000
## 1.076624e+01 0.8393287 0.000000000
## 1.127468e+01 0.8393287 0.000000000
## 1.180713e+01 0.8393287 0.000000000
## 1.236472e+01 0.8393287 0.000000000
## 1.294865e+01 0.8393287 0.000000000
## 1.356015e+01 0.8393287 0.000000000
## 1.420053e+01 0.8393287 0.000000000
## 1.487115e+01 0.8393287 0.000000000
## 1.557345e+01 0.8393287 0.000000000
## 1.630891e+01 0.8393287 0.000000000
## 1.707910e+01 0.8393287 0.000000000
## 1.788566e+01 0.8393287 0.000000000
## 1.873032e+01 0.8393287 0.000000000
## 1.961486e+01 0.8393287 0.000000000
## 2.054117e+01 0.8393287 0.000000000
## 2.151123e+01 0.8393287 0.000000000
## 2.252711e+01 0.8393287 0.000000000
## 2.359095e+01 0.8393287 0.000000000
## 2.470504e+01 0.8393287 0.000000000
## 2.587174e+01 0.8393287 0.000000000
## 2.709354e+01 0.8393287 0.000000000
## 2.837304e+01 0.8393287 0.000000000
## 2.971296e+01 0.8393287 0.000000000
## 3.111616e+01 0.8393287 0.000000000
## 3.258562e+01 0.8393287 0.000000000
## 3.412449e+01 0.8393287 0.000000000
## 3.573602e+01 0.8393287 0.000000000
## 3.742366e+01 0.8393287 0.000000000
## 3.919100e+01 0.8393287 0.000000000
## 4.104181e+01 0.8393287 0.000000000
## 4.298001e+01 0.8393287 0.000000000
## 4.500975e+01 0.8393287 0.000000000
## 4.713535e+01 0.8393287 0.000000000
## 4.936132e+01 0.8393287 0.000000000
## 5.169242e+01 0.8393287 0.000000000
## 5.413360e+01 0.8393287 0.000000000
## 5.669007e+01 0.8393287 0.000000000
## 5.936727e+01 0.8393287 0.000000000
## 6.217090e+01 0.8393287 0.000000000
## 6.510694e+01 0.8393287 0.000000000
## 6.818162e+01 0.8393287 0.000000000
## 7.140151e+01 0.8393287 0.000000000
## 7.477346e+01 0.8393287 0.000000000
## 7.830465e+01 0.8393287 0.000000000
## 8.200261e+01 0.8393287 0.000000000
## 8.587519e+01 0.8393287 0.000000000
## 8.993067e+01 0.8393287 0.000000000
## 9.417766e+01 0.8393287 0.000000000
## 9.862522e+01 0.8393287 0.000000000
## 1.032828e+02 0.8393287 0.000000000
## 1.081604e+02 0.8393287 0.000000000
## 1.132683e+02 0.8393287 0.000000000
## 1.186174e+02 0.8393287 0.000000000
## 1.242191e+02 0.8393287 0.000000000
## 1.300854e+02 0.8393287 0.000000000
## 1.362287e+02 0.8393287 0.000000000
## 1.426621e+02 0.8393287 0.000000000
## 1.493993e+02 0.8393287 0.000000000
## 1.564548e+02 0.8393287 0.000000000
## 1.638434e+02 0.8393287 0.000000000
## 1.715809e+02 0.8393287 0.000000000
## 1.796838e+02 0.8393287 0.000000000
## 1.881694e+02 0.8393287 0.000000000
## 1.970558e+02 0.8393287 0.000000000
## 2.063618e+02 0.8393287 0.000000000
## 2.161073e+02 0.8393287 0.000000000
## 2.263130e+02 0.8393287 0.000000000
## 2.370006e+02 0.8393287 0.000000000
## 2.481930e+02 0.8393287 0.000000000
## 2.599140e+02 0.8393287 0.000000000
## 2.721885e+02 0.8393287 0.000000000
## 2.850426e+02 0.8393287 0.000000000
## 2.985038e+02 0.8393287 0.000000000
## 3.126007e+02 0.8393287 0.000000000
## 3.273634e+02 0.8393287 0.000000000
## 3.428231e+02 0.8393287 0.000000000
## 3.590130e+02 0.8393287 0.000000000
## 3.759675e+02 0.8393287 0.000000000
## 3.937226e+02 0.8393287 0.000000000
## 4.123163e+02 0.8393287 0.000000000
## 4.317880e+02 0.8393287 0.000000000
## 4.521792e+02 0.8393287 0.000000000
## 4.735335e+02 0.8393287 0.000000000
## 4.958962e+02 0.8393287 0.000000000
## 5.193150e+02 0.8393287 0.000000000
## 5.438397e+02 0.8393287 0.000000000
## 5.695227e+02 0.8393287 0.000000000
## 5.964185e+02 0.8393287 0.000000000
## 6.245845e+02 0.8393287 0.000000000
## 6.540806e+02 0.8393287 0.000000000
## 6.849697e+02 0.8393287 0.000000000
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## 7.511929e+02 0.8393287 0.000000000
## 7.866682e+02 0.8393287 0.000000000
## 8.238187e+02 0.8393287 0.000000000
## 8.627237e+02 0.8393287 0.000000000
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## 9.461324e+02 0.8393287 0.000000000
## 9.908137e+02 0.8393287 0.000000000
## 1.037605e+03 0.8393287 0.000000000
## 1.086606e+03 0.8393287 0.000000000
## 1.137921e+03 0.8393287 0.000000000
## 1.191660e+03 0.8393287 0.000000000
## 1.247936e+03 0.8393287 0.000000000
## 1.306870e+03 0.8393287 0.000000000
## 1.368587e+03 0.8393287 0.000000000
## 1.433219e+03 0.8393287 0.000000000
## 1.500903e+03 0.8393287 0.000000000
## 1.571784e+03 0.8393287 0.000000000
## 1.646012e+03 0.8393287 0.000000000
## 1.723745e+03 0.8393287 0.000000000
## 1.805149e+03 0.8393287 0.000000000
## 1.890397e+03 0.8393287 0.000000000
## 1.979672e+03 0.8393287 0.000000000
## 2.073162e+03 0.8393287 0.000000000
## 2.171068e+03 0.8393287 0.000000000
## 2.273597e+03 0.8393287 0.000000000
## 2.380968e+03 0.8393287 0.000000000
## 2.493409e+03 0.8393287 0.000000000
## 2.611161e+03 0.8393287 0.000000000
## 2.734474e+03 0.8393287 0.000000000
## 2.863610e+03 0.8393287 0.000000000
## 2.998844e+03 0.8393287 0.000000000
## 3.140465e+03 0.8393287 0.000000000
## 3.288774e+03 0.8393287 0.000000000
## 3.444087e+03 0.8393287 0.000000000
## 3.606735e+03 0.8393287 0.000000000
## 3.777064e+03 0.8393287 0.000000000
## 3.955436e+03 0.8393287 0.000000000
## 4.142232e+03 0.8393287 0.000000000
## 4.337850e+03 0.8393287 0.000000000
## 4.542706e+03 0.8393287 0.000000000
## 4.757236e+03 0.8393287 0.000000000
## 4.981898e+03 0.8393287 0.000000000
## 5.217169e+03 0.8393287 0.000000000
## 5.463550e+03 0.8393287 0.000000000
## 5.721568e+03 0.8393287 0.000000000
## 5.991770e+03 0.8393287 0.000000000
## 6.274732e+03 0.8393287 0.000000000
## 6.571058e+03 0.8393287 0.000000000
## 6.881377e+03 0.8393287 0.000000000
## 7.206351e+03 0.8393287 0.000000000
## 7.546673e+03 0.8393287 0.000000000
## 7.903066e+03 0.8393287 0.000000000
## 8.276289e+03 0.8393287 0.000000000
## 8.667139e+03 0.8393287 0.000000000
## 9.076446e+03 0.8393287 0.000000000
## 9.505083e+03 0.8393287 0.000000000
## 9.953962e+03 0.8393287 0.000000000
## 1.042404e+04 0.8393287 0.000000000
## 1.091632e+04 0.8393287 0.000000000
## 1.143184e+04 0.8393287 0.000000000
## 1.197171e+04 0.8393287 0.000000000
## 1.253708e+04 0.8393287 0.000000000
## 1.312915e+04 0.8393287 0.000000000
## 1.374917e+04 0.8393287 0.000000000
## 1.439848e+04 0.8393287 0.000000000
## 1.507845e+04 0.8393287 0.000000000
## 1.579053e+04 0.8393287 0.000000000
## 1.653624e+04 0.8393287 0.000000000
## 1.731717e+04 0.8393287 0.000000000
## 1.813498e+04 0.8393287 0.000000000
## 1.899141e+04 0.8393287 0.000000000
## 1.988828e+04 0.8393287 0.000000000
## 2.082751e+04 0.8393287 0.000000000
## 2.181109e+04 0.8393287 0.000000000
## 2.284112e+04 0.8393287 0.000000000
## 2.391980e+04 0.8393287 0.000000000
## 2.504942e+04 0.8393287 0.000000000
## 2.623238e+04 0.8393287 0.000000000
## 2.747121e+04 0.8393287 0.000000000
## 2.876854e+04 0.8393287 0.000000000
## 3.012714e+04 0.8393287 0.000000000
## 3.154990e+04 0.8393287 0.000000000
## 3.303985e+04 0.8393287 0.000000000
## 3.460016e+04 0.8393287 0.000000000
## 3.623416e+04 0.8393287 0.000000000
## 3.794533e+04 0.8393287 0.000000000
## 3.973730e+04 0.8393287 0.000000000
## 4.161391e+04 0.8393287 0.000000000
## 4.357913e+04 0.8393287 0.000000000
## 4.563716e+04 0.8393287 0.000000000
## 4.779239e+04 0.8393287 0.000000000
## 5.004939e+04 0.8393287 0.000000000
## 5.241298e+04 0.8393287 0.000000000
## 5.488820e+04 0.8393287 0.000000000
## 5.748030e+04 0.8393287 0.000000000
## 6.019482e+04 0.8393287 0.000000000
## 6.303753e+04 0.8393287 0.000000000
## 6.601449e+04 0.8393287 0.000000000
## 6.913204e+04 0.8393287 0.000000000
## 7.239681e+04 0.8393287 0.000000000
## 7.581576e+04 0.8393287 0.000000000
## 7.939618e+04 0.8393287 0.000000000
## 8.314568e+04 0.8393287 0.000000000
## 8.707225e+04 0.8393287 0.000000000
## 9.118425e+04 0.8393287 0.000000000
## 9.549045e+04 0.8393287 0.000000000
## 1.000000e+05 0.8393287 0.000000000
##
## Tuning parameter 'alpha' was held constant at a value of 0
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were alpha = 0 and lambda = 0.01400531.
#get the best tuning parameters
Model6$bestTune
## alpha lambda
## 158 0 0.01400531
# alpha lambda
# 0 0.01400531
#just the best lamda
Model6$bestTune$lambda
## [1] 0.01400531
#0.01400531
#LASSO Regression model coefficients(Parameter Estimates)
round(coef(Model6$finalModel,Model6$bestTune$lambda),3)
## 33 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) 2.411
## Customer_Age 0.002
## GenderM 0.199
## Dependent_count -0.105
## Education_LevelDoctorate -0.058
## Education_LevelGraduate 0.014
## Education_LevelHigh School 0.024
## Education_LevelPost-Graduate -0.064
## Education_LevelUneducated -0.034
## Education_LevelUnknown -0.034
## Marital_StatusMarried 0.104
## Marital_StatusSingle -0.071
## Marital_StatusUnknown -0.041
## Income_Category$40K - $60K 0.069
## Income_Category$60K - $80K 0.050
## Income_Category$80K - $120K -0.048
## Income_CategoryLess than $40K -0.006
## Income_CategoryUnknown 0.032
## Card_CategoryGold -0.100
## Card_CategoryPlatinum -0.020
## Card_CategorySilver -0.077
## Months_on_book 0.052
## Total_Relationship_Count 0.566
## Months_Inactive_12_mon -0.372
## Contacts_Count_12_mon -0.454
## Credit_Limit 0.082
## Total_Revolving_Bal 0.505
## Avg_Open_To_Buy 0.037
## Total_Amt_Chng_Q4_Q1 0.060
## Total_Trans_Amt -0.432
## Total_Trans_Ct 1.394
## Total_Ct_Chng_Q4_Q1 0.547
## Avg_Utilization_Ratio 0.150
#Plot log(lambda) & RMSE
plot(log(Model6$results$lambda),Model6$results$RMSE,
xlab="Log(lambda)",
ylab="RMSE",
xlim=c(0,100),
main="Model 6 ridge regression")
log(Model6$bestTune$lambda)
## [1] -4.268319
#variable importance
varImp(Model6)
## glmnet variable importance
##
## only 20 most important variables shown (out of 32)
##
## Overall
## Total_Trans_Ct 100.000
## Total_Relationship_Count 40.485
## Total_Ct_Chng_Q4_Q1 39.118
## Total_Revolving_Bal 36.136
## Contacts_Count_12_mon 32.423
## Total_Trans_Amt 30.850
## Months_Inactive_12_mon 26.578
## GenderM 14.105
## Avg_Utilization_Ratio 10.574
## Dependent_count 7.395
## Marital_StatusMarried 7.290
## Card_CategoryGold 6.991
## Credit_Limit 5.748
## Card_CategorySilver 5.337
## Marital_StatusSingle 4.912
## Income_Category$40K - $60K 4.811
## Education_LevelPost-Graduate 4.395
## Total_Amt_Chng_Q4_Q1 4.141
## Education_LevelDoctorate 4.004
## Months_on_book 3.531
#plot variable importance
ggplot(varImp(Model3))+
labs(title = "Model 6 Variable importance Rank")
#forming confusion matrix
predictions_Ridge<-predict(Model6,newdata = testing)
cm_6<-confusionMatrix(data=predictions_Ridge,testing$Attrition_Flag)
cm_6
## Confusion Matrix and Statistics
##
## Reference
## Prediction Quit Stay
## Quit 242 55
## Stay 246 2495
##
## Accuracy : 0.9009
## 95% CI : (0.8897, 0.9113)
## No Information Rate : 0.8394
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.5635
##
## Mcnemar's Test P-Value : < 2.2e-16
##
## Sensitivity : 0.49590
## Specificity : 0.97843
## Pos Pred Value : 0.81481
## Neg Pred Value : 0.91025
## Prevalence : 0.16063
## Detection Rate : 0.07966
## Detection Prevalence : 0.09776
## Balanced Accuracy : 0.73717
##
## 'Positive' Class : Quit
##
#MODEL 6 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE
# 0.9009 0.5635 0.49590 0.97843 0.16063
#CONCLUSION ON MODELS
#we have trained 6 Models using 6 different types of Regression analysis and
#Supervised Machine learning to try and get the best model that will predict or classify
#bank attritions as accurate as possibly and as well as parsimonias
#this are the performance measures for all six Models
#MODEL 1 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #STEPWISE REGRESSION
# 0.8627 0.5786 0.5480 0.9639 0.2433
#MODEL 2 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #LOGISTIC REG 10-FOLDS
# 0.9022 0.6044 0.59221 0.96157 0.16063
#MODEL 3 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #LASSO REG 10-FOLDS
# 0.9016 0.5951 0.57172 0.96471 0.16063
#MODEL 4.a ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #RANDOMFOREST 3-folds,2repeats
# 0.971 0.8879 0.8586 0.9925 0.1606
#MODEL 4.b ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #RANDOMFOREST 5-folds,3repeats
# 0.9691 0.8813 0.8627 0.9894 0.1606
#MODEL 5 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #DECISION TREES-RPART
# 0.9365 0.7699 0.8320 0.9565 0.1606
#MODEL 6 ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #RIDGE REG 10-FOLDS
# 0.9013 0.5654 0.49795 0.97843 0.16063
#The best model so far is Model 4.a RandomForest Modeling with 3-folds and 2 repeats,
#followed by Model 4.b RandomForest with 5-folds and 3 repeats
#in general RandomForest is our Model of choice
#RandomForest Model Performance matrix
#MODEL 4.a ACCURACY KAPPA SENSITIVITY SPECIFICITY PREVALANCE #RANDOMFOREST 3-folds,2repeats
# 0.9707 0.8879 0.8586 0.9925 0.1606
#Accuracy= 97.07% this measures the proportion of all properly classified cases
#Kappa=88.79% which is almost perfect
#Sensitivity=85.86% this measures the prediction accuracy of those who quit
#Specificity=99.25% this measures the proportion of people we said would stay relative to the overall number of people that stayed
#Prevalence=16.06% this is the base probability of those who quit
#Balanced Accuracy=92.56% this is measured by (sensitivity+specificity)/2