I chose SVM and Decision Tree classifiers.
file<-"/Users/aaronzalki/Documents/heart.csv"
heart<-read.csv(file,head=T,sep=',',stringsAsFactors=F)
head(heart)## age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1 63 1 3 145 233 1 0 150 0 2.3 0 0 1
## 2 37 1 2 130 250 0 1 187 0 3.5 0 0 2
## 3 41 0 1 130 204 0 0 172 0 1.4 2 0 2
## 4 56 1 1 120 236 0 1 178 0 0.8 2 0 2
## 5 57 0 0 120 354 0 1 163 1 0.6 2 0 2
## 6 57 1 0 140 192 0 1 148 0 0.4 1 0 1
## target
## 1 1
## 2 1
## 3 1
## 4 1
## 5 1
## 6 1The function factor is used to encode a vector as a factor.
heart$target <- as.factor(heart$target)
heart$sex <- as.factor(heart$sex)
heart$cp <- as.factor(heart$cp)
heart$fbs <- as.factor(heart$fbs)
heart$restecg <- as.factor(heart$restecg)
heart$exang <- as.factor(heart$exang)
heart$slope <- as.factor(heart$slope)
heart$ca <- as.factor(heart$ca)
heart$thal <- as.factor(heart$thal)80/20 Split
set.seed(43)
x <- floor(0.8 * nrow(heart))
train_ind <- sample(seq_len(nrow(heart)), size = x)
train_heart <- heart[ train_ind,]
test_heart <- heart[-train_ind,]The following function utilizes confusionMatrix function from the caret library in order to return metrics such as accuracy, area under curve etc. For a better understanding of some of these metrics, please see Data 621. The same function contains various if, else if, else clauses so that we can also run a bootstrap of n resamples as well as randomForest for part B.
cm_calc <- function(train_type, tr, label){
timer <- proc.time()
set.seed(43)
# base
if (grepl("Base", label, fixed=TRUE)) {
train_model = train(
form = target ~ .,
data = train_heart,
trControl = tr,
method = train_type
)
print(train_model)
# confusion Matrix from caret
model_cm <- confusionMatrix(predict(train_model, subset(test_heart, select = -c(target))), test_heart$target)
print(paste(label, 'Results'))
print(model_cm)
duration <- (proc.time() - timer)[[3]]
#metrics
accuracy <- model_cm$overall[[1]]
auc <- as.numeric(auc(roc(test_heart$target, factor(predict(train_model, test_heart), ordered = TRUE))))
sensitivity <- model_cm$byClass[[1]]
specificity <- model_cm$byClass[[2]]
precision <- model_cm$byClass[[5]]
recall <- model_cm$byClass[[6]]
f1_score <- model_cm$byClass[[7]]
# bootstrap
} else if (grepl("Boot", label, fixed=TRUE)){
train_model = train(
form = target ~ .,
data = heart,
trControl = tr,
method = train_type
)
duration <- (proc.time() - timer)[[3]]
accuracy <- c()
auc <- c()
sensitivity <- c()
specificity <- c()
precision <- c()
recall <- c()
f1_score <- c()
i <- 1
pred_df <- train_model$pred
for (resample in unique(pred_df$Resample)){
temp <- filter(pred_df, Resample == resample)
model_cm <- confusionMatrix(temp$pred, temp$obs)
accuracy[i] <- model_cm$overall[[1]]
auc[[i]] <- auc(roc(as.numeric(temp$pred, ordered = TRUE), as.numeric(temp$obs, ordered = TRUE)))
sensitivity[[i]] <- model_cm$byClass[[1]]
specificity[[i]] <- model_cm$byClass[[2]]
precision[[i]] <- model_cm$byClass[[5]]
recall[[i]] <- model_cm$byClass[[6]]
f1_score[[i]] <- model_cm$byClass[[7]]
i <- i + 1
}
accuracy <- mean(accuracy)
auc <- mean(auc)
sensitivity <- mean(sensitivity)
specificity <- mean(specificity)
precision <- mean(precision)
recall <- mean(recall)
f1_score <- mean(f1_score)
# random forest
} else if (grepl("RF", label, fixed=TRUE)){
# train model
train_model = train(
form = target ~ .,
data = train_heart,
trControl = tr,
ntree = as.numeric(str_sub(label, start= -2)),
method = train_type
)
print(train_model)
# confusion Matrix from caret
model_cm <- confusionMatrix(predict(train_model, subset(test_heart, select = -c(target))), test_heart$target)
print(paste(label, 'Results'))
print(model_cm)
duration <- (proc.time() - timer)[[3]]
# metrics
accuracy <- model_cm$overall[[1]]
auc <- as.numeric(auc(roc(test_heart$target, factor(predict(train_model, test_heart), ordered = TRUE))))
sensitivity <- model_cm$byClass[[1]]
specificity <- model_cm$byClass[[2]]
precision <- model_cm$byClass[[5]]
recall <- model_cm$byClass[[6]]
f1_score <- model_cm$byClass[[7]]
# cross validation for 5 fold and 10 fold
} else {
train_model = train(
form = target ~ .,
data = heart,
trControl = tr,
method = train_type
)
print(train_model)
#confusion matrix
model_cm <- confusionMatrix(train_model$pred[order(train_model$pred$rowIndex),]$pred, heart$target)
print(paste(label, 'Results'))
print(model_cm)
duration <- (proc.time() - timer)[[3]]
# metrics
accuracy <- model_cm$overall[[1]]
auc <- as.numeric(auc(roc(test_heart$target, factor(predict(train_model, test_heart), ordered = TRUE))))
sensitivity <- model_cm$byClass[[1]]
specificity <- model_cm$byClass[[2]]
precision <- model_cm$byClass[[5]]
recall <- model_cm$byClass[[6]]
f1_score <- model_cm$byClass[[7]]
}
#combine metric rows
result <- rbind(accuracy,
auc,
sensitivity,
specificity,
precision,
recall,
f1_score,
duration)
colnames(result) <- c(label)
return(result)
}#input for function 'rpart' used for decision tree base.
#label = "Decision Tree Base"
base_decision_tree <- cm_calc("rpart", trainControl(method="none"), "Decision Tree Base")## CART
##
## 242 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: None
## [1] "Decision Tree Base Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 0 0
## 1 27 34
##
## Accuracy : 0.5574
## 95% CI : (0.4245, 0.6845)
## No Information Rate : 0.5574
## P-Value [Acc > NIR] : 0.5531
##
## Kappa : 0
##
## Mcnemar's Test P-Value : 5.624e-07
##
## Sensitivity : 0.0000
## Specificity : 1.0000
## Pos Pred Value : NaN
## Neg Pred Value : 0.5574
## Prevalence : 0.4426
## Detection Rate : 0.0000
## Detection Prevalence : 0.0000
## Balanced Accuracy : 0.5000
##
## 'Positive' Class : 0
## #input for function 'svmLinear' used for svm base.
#label = "SVM Base"
svm_base <- cm_calc("svmLinear", trainControl(method="none"), "SVM Base")## Support Vector Machines with Linear Kernel
##
## 242 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: None
## [1] "SVM Base Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 20 2
## 1 7 32
##
## Accuracy : 0.8525
## 95% CI : (0.7383, 0.9302)
## No Information Rate : 0.5574
## P-Value [Acc > NIR] : 8.993e-07
##
## Kappa : 0.6952
##
## Mcnemar's Test P-Value : 0.1824
##
## Sensitivity : 0.7407
## Specificity : 0.9412
## Pos Pred Value : 0.9091
## Neg Pred Value : 0.8205
## Prevalence : 0.4426
## Detection Rate : 0.3279
## Detection Prevalence : 0.3607
## Balanced Accuracy : 0.8410
##
## 'Positive' Class : 0
## Decision Tree
#input for function 'rpart' used for decision tree
# method type 'cv' denotes cross validation of 5
#label = "Decision Tree 5 Fold"
decision_tree_5fold <- cm_calc("rpart", tr = trainControl(method = "cv", number = 5, savePredictions = 'final'), "Decision Tree 5 Fold")## CART
##
## 303 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 243, 242, 242, 243, 242
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.03623188 0.7621311 0.5186339
## 0.03985507 0.7391803 0.4718201
## 0.48550725 0.6400000 0.2408988
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.03623188.
## [1] "Decision Tree 5 Fold Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 98 32
## 1 40 133
##
## Accuracy : 0.7624
## 95% CI : (0.7104, 0.8092)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : 3.29e-15
##
## Kappa : 0.5187
##
## Mcnemar's Test P-Value : 0.4094
##
## Sensitivity : 0.7101
## Specificity : 0.8061
## Pos Pred Value : 0.7538
## Neg Pred Value : 0.7688
## Prevalence : 0.4554
## Detection Rate : 0.3234
## Detection Prevalence : 0.4290
## Balanced Accuracy : 0.7581
##
## 'Positive' Class : 0
## SVM
#input for function 'svmLinear' used for svm
# method type 'cv' denotes cross validation of 5
#label = "SVM 5 Fold"
svm_5fold <- cm_calc("svmLinear", tr = trainControl(method = "cv", number = 5, savePredictions = 'final'), "SVM 5 Fold")## Support Vector Machines with Linear Kernel
##
## 303 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 243, 242, 242, 243, 242
## Resampling results:
##
## Accuracy Kappa
## 0.835082 0.6664592
##
## Tuning parameter 'C' was held constant at a value of 1
## [1] "SVM 5 Fold Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 110 22
## 1 28 143
##
## Accuracy : 0.835
## 95% CI : (0.7883, 0.875)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.6661
##
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 0.7971
## Specificity : 0.8667
## Pos Pred Value : 0.8333
## Neg Pred Value : 0.8363
## Prevalence : 0.4554
## Detection Rate : 0.3630
## Detection Prevalence : 0.4356
## Balanced Accuracy : 0.8319
##
## 'Positive' Class : 0
## Decision Tree
#input for function 'rpart' used for decision tree
# method type 'cv' denotes cross validation of 10
#label = "Decision Tree 10 Fold"
decision_tree_10fold <- cm_calc("rpart", trainControl(method = "cv", number = 10, savePredictions = 'final'), "Decision Tree 10 Fold")## CART
##
## 303 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 273, 272, 273, 273, 273, 273, ...
## Resampling results across tuning parameters:
##
## cp Accuracy Kappa
## 0.03623188 0.7493548 0.4924633
## 0.03985507 0.7493548 0.4917245
## 0.48550725 0.6560215 0.2761508
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was cp = 0.03985507.
## [1] "Decision Tree 10 Fold Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 96 34
## 1 42 131
##
## Accuracy : 0.7492
## 95% CI : (0.6964, 0.797)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : 1.515e-13
##
## Kappa : 0.4919
##
## Mcnemar's Test P-Value : 0.422
##
## Sensitivity : 0.6957
## Specificity : 0.7939
## Pos Pred Value : 0.7385
## Neg Pred Value : 0.7572
## Prevalence : 0.4554
## Detection Rate : 0.3168
## Detection Prevalence : 0.4290
## Balanced Accuracy : 0.7448
##
## 'Positive' Class : 0
## SVM
#input for function 'svmLinear' used for svm
# method type 'cv' denotes cross validation of 10
#label = "SVM 10 Fold"
svm_10fold <- cm_calc("svmLinear", trainControl(method = "cv", number = 10, savePredictions = 'final'), "SVM 10 Fold")## Support Vector Machines with Linear Kernel
##
## 303 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 273, 272, 273, 273, 273, 273, ...
## Resampling results:
##
## Accuracy Kappa
## 0.8383871 0.671804
##
## Tuning parameter 'C' was held constant at a value of 1
## [1] "SVM 10 Fold Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 107 18
## 1 31 147
##
## Accuracy : 0.8383
## 95% CI : (0.7919, 0.8779)
## No Information Rate : 0.5446
## P-Value [Acc > NIR] : < 2e-16
##
## Kappa : 0.6714
##
## Mcnemar's Test P-Value : 0.08648
##
## Sensitivity : 0.7754
## Specificity : 0.8909
## Pos Pred Value : 0.8560
## Neg Pred Value : 0.8258
## Prevalence : 0.4554
## Detection Rate : 0.3531
## Detection Prevalence : 0.4125
## Balanced Accuracy : 0.8331
##
## 'Positive' Class : 0
## Decision Tree
#input for function 'rpart' used for decision tree
# method type 'boot' denotes bootstrap of 200 resample
#label = "Decision Tree Bootstrap"
decision_tree_boot <- cm_calc("rpart", trainControl(method="boot", number=200, savePredictions = 'final', returnResamp = 'final'), "Decision Tree Bootstrap")
print(decision_tree_boot)## Decision Tree Bootstrap
## accuracy 0.7420239
## auc NA
## sensitivity NA
## specificity NA
## precision NA
## recall NA
## f1_score NA
## duration 4.2100000SVM
#input for function 'svmLinear' used for svm
# method type 'boot' denotes bootstrap of 200 resample
#label = "SVM Bootstrap"
svm_boot <- cm_calc("svmLinear", trainControl(method="boot", number=200, savePredictions = 'final', returnResamp = 'final'), "SVM Bootstrap")
print(svm_boot)## SVM Bootstrap
## accuracy 0.823332
## auc NA
## sensitivity NA
## specificity NA
## precision NA
## recall NA
## f1_score NA
## duration 12.130000df <- data.frame(cbind(base_decision_tree, decision_tree_5fold, decision_tree_10fold, decision_tree_boot, svm_base, svm_5fold, svm_10fold, svm_boot))
kable(df) %>%
kable_styling(bootstrap_options = "bordered") %>%
row_spec(0, bold = T, color = "black", background = "#7fcdbb")| Decision.Tree.Base | Decision.Tree.5.Fold | Decision.Tree.10.Fold | Decision.Tree.Bootstrap | SVM.Base | SVM.5.Fold | SVM.10.Fold | SVM.Bootstrap | |
|---|---|---|---|---|---|---|---|---|
| accuracy | 0.557377 | 0.7623762 | 0.7491749 | 0.7420239 | 0.8524590 | 0.8349835 | 0.8382838 | 0.823332 |
| auc | 0.500000 | 0.7854031 | 0.7412854 | NA | 0.8409586 | 0.8300654 | 0.8300654 | NA |
| sensitivity | 0.000000 | 0.7101449 | 0.6956522 | NA | 0.7407407 | 0.7971014 | 0.7753623 | NA |
| specificity | 1.000000 | 0.8060606 | 0.7939394 | NA | 0.9411765 | 0.8666667 | 0.8909091 | NA |
| precision | NA | 0.7538462 | 0.7384615 | NA | 0.9090909 | 0.8333333 | 0.8560000 | NA |
| recall | 0.000000 | 0.7101449 | 0.6956522 | NA | 0.7407407 | 0.7971014 | 0.7753623 | NA |
| f1_score | NA | 0.7313433 | 0.7164179 | NA | 0.8163265 | 0.8148148 | 0.8136882 | NA |
| duration | 0.524000 | 0.6940000 | 0.8250000 | 4.2100000 | 0.9780000 | 1.4590000 | 0.6610000 | 12.130000 |
80/20 Split
set.seed(43)
x <- floor(0.8 * nrow(heart))
train_ind <- sample(seq_len(nrow(heart)), size = x)
train_heart <- heart[ train_ind,]
test_heart <- heart[-train_ind,]16 Trees
#input for function 'rf' used for randomForest
random_forest_16 <- cm_calc("rf", trainControl(), "RF 16")## Random Forest
##
## 242 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 242, 242, 242, 242, 242, 242, ...
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.7849624 0.5649484
## 12 0.7666805 0.5264895
## 22 0.7581384 0.5095112
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 2.
## [1] "RF 16 Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 18 2
## 1 9 32
##
## Accuracy : 0.8197
## 95% CI : (0.7002, 0.9064)
## No Information Rate : 0.5574
## P-Value [Acc > NIR] : 1.469e-05
##
## Kappa : 0.6245
##
## Mcnemar's Test P-Value : 0.07044
##
## Sensitivity : 0.6667
## Specificity : 0.9412
## Pos Pred Value : 0.9000
## Neg Pred Value : 0.7805
## Prevalence : 0.4426
## Detection Rate : 0.2951
## Detection Prevalence : 0.3279
## Balanced Accuracy : 0.8039
##
## 'Positive' Class : 0
## 64 Trees
#input for function 'rf' used for randomForest
random_forest_64 <- cm_calc("rf", trainControl(), "RF 64")## Random Forest
##
## 242 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 242, 242, 242, 242, 242, 242, ...
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.7992027 0.5938642
## 12 0.7671618 0.5274464
## 22 0.7542574 0.5012315
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 2.
## [1] "RF 64 Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 19 3
## 1 8 31
##
## Accuracy : 0.8197
## 95% CI : (0.7002, 0.9064)
## No Information Rate : 0.5574
## P-Value [Acc > NIR] : 1.469e-05
##
## Kappa : 0.6274
##
## Mcnemar's Test P-Value : 0.2278
##
## Sensitivity : 0.7037
## Specificity : 0.9118
## Pos Pred Value : 0.8636
## Neg Pred Value : 0.7949
## Prevalence : 0.4426
## Detection Rate : 0.3115
## Detection Prevalence : 0.3607
## Balanced Accuracy : 0.8077
##
## 'Positive' Class : 0
## 128 Trees
#input for function 'rf' used for randomForest
random_forest_128 <- cm_calc("rf", trainControl(), "RF 128")## Random Forest
##
## 242 samples
## 13 predictor
## 2 classes: '0', '1'
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 242, 242, 242, 242, 242, 242, ...
## Resampling results across tuning parameters:
##
## mtry Accuracy Kappa
## 2 0.7917296 0.5780993
## 12 0.7601981 0.5139962
## 22 0.7581195 0.5088020
##
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was mtry = 2.
## [1] "RF 128 Results"
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 18 3
## 1 9 31
##
## Accuracy : 0.8033
## 95% CI : (0.6816, 0.894)
## No Information Rate : 0.5574
## P-Value [Acc > NIR] : 5.056e-05
##
## Kappa : 0.592
##
## Mcnemar's Test P-Value : 0.1489
##
## Sensitivity : 0.6667
## Specificity : 0.9118
## Pos Pred Value : 0.8571
## Neg Pred Value : 0.7750
## Prevalence : 0.4426
## Detection Rate : 0.2951
## Detection Prevalence : 0.3443
## Balanced Accuracy : 0.7892
##
## 'Positive' Class : 0
## In comparison to Decision Tree from Part A, the randomForest results are overall better. However, randomForest does require more computing cost(elapsed time) for each run. SVM performed the best among all three experiments.
df2 <- data.frame(cbind(random_forest_16, random_forest_64, random_forest_128))
kable(df2) %>%
kable_styling(bootstrap_options = "bordered") %>%
row_spec(0, bold = T, color = "black", background = "#7fcdbb")| RF.16 | RF.64 | RF.128 | |
|---|---|---|---|
| accuracy | 0.8196721 | 0.8196721 | 0.8032787 |
| auc | 0.8039216 | 0.8077342 | 0.8224401 |
| sensitivity | 0.6666667 | 0.7037037 | 0.6666667 |
| specificity | 0.9411765 | 0.9117647 | 0.9117647 |
| precision | 0.9000000 | 0.8636364 | 0.8571429 |
| recall | 0.6666667 | 0.7037037 | 0.6666667 |
| f1_score | 0.7659574 | 0.7755102 | 0.7500000 |
| duration | 1.1550000 | 2.1220000 | 1.3610000 |
When comparing bootstrap for Decision Tree vs. SVM, SVM yielded stronger model performance but did require more computation time. When comparing cross validation for Decision Tree 5-Fold vs. Decision Tree 10-Fold vs. SVM 5-Fold vs. SVM-10 Fold, the 5-fold cross validation should be used for both classifiers. Cross validation provides stability to the model results. Razor also suggests that the 5-fold should be used as it is simpler in comparison to the 10-fold. Source
final_df <- data.frame(cbind(base_decision_tree, decision_tree_5fold, decision_tree_10fold, decision_tree_boot, svm_base, svm_5fold, svm_10fold, svm_boot,random_forest_16, random_forest_64, random_forest_128))
kable(final_df) %>%
kable_styling(bootstrap_options = "bordered") %>%
row_spec(0, bold = T, color = "black", background = "#7fcdbb")| Decision.Tree.Base | Decision.Tree.5.Fold | Decision.Tree.10.Fold | Decision.Tree.Bootstrap | SVM.Base | SVM.5.Fold | SVM.10.Fold | SVM.Bootstrap | RF.16 | RF.64 | RF.128 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| accuracy | 0.557377 | 0.7623762 | 0.7491749 | 0.7420239 | 0.8524590 | 0.8349835 | 0.8382838 | 0.823332 | 0.8196721 | 0.8196721 | 0.8032787 |
| auc | 0.500000 | 0.7854031 | 0.7412854 | NA | 0.8409586 | 0.8300654 | 0.8300654 | NA | 0.8039216 | 0.8077342 | 0.8224401 |
| sensitivity | 0.000000 | 0.7101449 | 0.6956522 | NA | 0.7407407 | 0.7971014 | 0.7753623 | NA | 0.6666667 | 0.7037037 | 0.6666667 |
| specificity | 1.000000 | 0.8060606 | 0.7939394 | NA | 0.9411765 | 0.8666667 | 0.8909091 | NA | 0.9411765 | 0.9117647 | 0.9117647 |
| precision | NA | 0.7538462 | 0.7384615 | NA | 0.9090909 | 0.8333333 | 0.8560000 | NA | 0.9000000 | 0.8636364 | 0.8571429 |
| recall | 0.000000 | 0.7101449 | 0.6956522 | NA | 0.7407407 | 0.7971014 | 0.7753623 | NA | 0.6666667 | 0.7037037 | 0.6666667 |
| f1_score | NA | 0.7313433 | 0.7164179 | NA | 0.8163265 | 0.8148148 | 0.8136882 | NA | 0.7659574 | 0.7755102 | 0.7500000 |
| duration | 0.524000 | 0.6940000 | 0.8250000 | 4.2100000 | 0.9780000 | 1.4590000 | 0.6610000 | 12.130000 | 1.1550000 | 2.1220000 | 1.3610000 |