Data 621 HW2

library(tidyverse)

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library(caret)

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library(pROC)

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library(e1071)

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1.

Download the classification output data set (attached in Blackboard to the assignment).

2.

The data set has three key columns we will use: class: the actual class for the observation scored.class: the predicted class for the observation (based on a threshold of 0.5) scored.probability: the predicted probability of success for the observation Use the table() function to get the raw confusion matrix for this scored dataset. Make sure you understand the output. In particular, do the rows represent the actual or predicted class? The columns?

df %>%
  select(scored.class, class) %>%
  table()

##             class
## scored.class   0   1
##            0 119  30
##            1   5  27

TP <- sum(df$class == 1 & df$scored.class == 1)
FP <- sum(df$class == 0 & df$scored.class == 1)
TN <- sum(df$class == 0 & df$scored.class == 0)
FN <- sum(df$class == 1 & df$scored.class == 0)

3.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the accuracy of the predictions.

accuracy <- function(x){
  round((TP + TN)/(TP + FP + TN + FN), 4)
}
accuracy(df)

## [1] 0.8066

4.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the classification error rate of the predictions.

class_error_rate <- function(x){
  round((FP + FN)/(TP + FP + TN + FN), 4)
}
class_error_rate(df)

## [1] 0.1934

accuracy(df) + class_error_rate(df)

## [1] 1

5.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the precision of the predictions.

precision <- function(x){
  round(TP/(TP + FP), 4)
}

precision(df)

## [1] 0.8438

6.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the sensitivity of the predictions. Sensitivity is also known as recall.

sensitivity <- function(x){
  round(TP/(TP + FN), 4)
}
sensitivity(df)

## [1] 0.4737

7.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the specificity of the predictions.

specificity <- function(x){
  round(TN/(TN + FP), 4)
}
specificity(df)

## [1] 0.9597

8.

Write a function that takes the data set as a dataframe, with actual and predicted classifications identified, and returns the F1 score of the predictions.

f1_score <- function(x){
  (2*precision(x)*sensitivity(x))/(precision(x)+sensitivity(x))
}
f1_score(df)

## [1] 0.6067675

9.

Before we move on, let’s consider a question that was asked: What are the bounds on the F1 score? Show that the F1 score will always be between 0 and 1. (Hint: If 0 < 𝑎 < 1 and 0 < 𝑏 < 1 then 𝑎𝑏 < 𝑎.)

F1 score is between 0 and 1. F1 score shows how accurate the dataset is

10.

Write a function that generates an ROC curve from a data set with a true classification column (class in our example) and a probability column (scored.probability in our example). Your function should return a list that includes the plot of the ROC curve and a vector that contains the calculated area under the curve (AUC). Note that I recommend using a sequence of thresholds ranging from 0 to 1 at 0.01 intervals.

ROC <- function(x, y){
  x <- x[order(y, decreasing = TRUE)]
  TPR <- cumsum(x) / sum(x)
  FPR <- cumsum(!x) / sum(!x)
  xy <- data.frame(TPR, FPR, x)
  
  FPR_df <- c(diff(xy$FPR), 0)
  TPR_df <- c(diff(xy$TPR), 0)
  AUC <- round(sum(xy$TPR * FPR_df) + sum(TPR_df * FPR_df)/2, 4)
  
  plot(xy$FPR, xy$TPR, type = "l",
       main = "ROC Curve",
       xlab = "False Postive Rate",
       ylab = "True Positive Rate")
  abline(a = 0, b = 1)
  legend(.6, .4, AUC, title = "AUC")
}

ROC(df$class,df$scored.probability)

11.

Use your created R functions and the provided classification output data set to produce all of the classification metrics discussed above.

class_metrics <- c(accuracy(df), class_error_rate(df), precision(df), sensitivity(df), specificity(df), f1_score(df))
names(class_metrics) <- c("Accuracy", "Classification Error Rate", "Precision", "Sensitivity", "Specificity", "F1 Score")

12.

Investigate the caret package. In particular, consider the functions confusionMatrix, sensitivity, and specificity. Apply the functions to the data set. How do the results compare with your own functions?

# select the two desired columns
df_2 <- df %>%
  select(scored.class, class) %>%
  mutate(scored.class = as.factor(scored.class), 
         class = as.factor(class))

c <- confusionMatrix(df_2$scored.class, df_2$class, positive = "1")
c

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction   0   1
##          0 119  30
##          1   5  27
##                                           
##                Accuracy : 0.8066          
##                  95% CI : (0.7415, 0.8615)
##     No Information Rate : 0.6851          
##     P-Value [Acc > NIR] : 0.0001712       
##                                           
##                   Kappa : 0.4916          
##                                           
##  Mcnemar's Test P-Value : 4.976e-05       
##                                           
##             Sensitivity : 0.4737          
##             Specificity : 0.9597          
##          Pos Pred Value : 0.8438          
##          Neg Pred Value : 0.7987          
##              Prevalence : 0.3149          
##          Detection Rate : 0.1492          
##    Detection Prevalence : 0.1768          
##       Balanced Accuracy : 0.7167          
##                                           
##        'Positive' Class : 1               
## 

caret_package <- c(c$overall["Accuracy"], c$byClass["Sensitivity"], c$byClass["Specificity"])
my_function <- c(accuracy(df), sensitivity(df), specificity(df))
comparison <- cbind(caret_package, my_function)
comparison

##             caret_package my_function
## Accuracy        0.8066298      0.8066
## Sensitivity     0.4736842      0.4737
## Specificity     0.9596774      0.9597

Results look identical.

13.

Investigate the pROC package. Use it to generate an ROC curve for the data set. How do the results compare with your own functions?

par(mfrow = c(1, 2))
plot(roc(df$class, df$scored.probability))

## Setting levels: control = 0, case = 1

## Setting direction: controls < cases

ROC(df$class, df$scored.probability)