Data621_Assignment2
Ritesh Lohiya
June 23, 2018
Overview In this homework assignment, you will work through various classification metrics. You will be asked to create functions in R to carry out the various calculations. You will also investigate some functions in packages that will let you obtain the equivalent results. Finally, you will create graphical output that also can be used to evaluate the output of classification models, such as binary logistic regression. #
library(caret)## Loading required package: lattice## Loading required package: ggplot2library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(ggplot2)- Download the classification output data set (attached in Blackboard to the assignment).
data <- read.csv("https://raw.githubusercontent.com/Riteshlohiya/Data621-Assignment2/master/classification-output-data.csv", stringsAsFactors = FALSE, sep = ",", header = TRUE)
summary(data)## pregnant glucose diastolic skinfold
## Min. : 0.000 Min. : 57.0 Min. : 38.0 Min. : 0.0
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 64.0 1st Qu.: 0.0
## Median : 3.000 Median :112.0 Median : 70.0 Median :22.0
## Mean : 3.862 Mean :118.3 Mean : 71.7 Mean :19.8
## 3rd Qu.: 6.000 3rd Qu.:136.0 3rd Qu.: 78.0 3rd Qu.:32.0
## Max. :15.000 Max. :197.0 Max. :104.0 Max. :54.0
## insulin bmi pedigree age
## Min. : 0.00 Min. :19.40 Min. :0.0850 Min. :21.00
## 1st Qu.: 0.00 1st Qu.:26.30 1st Qu.:0.2570 1st Qu.:24.00
## Median : 0.00 Median :31.60 Median :0.3910 Median :30.00
## Mean : 63.77 Mean :31.58 Mean :0.4496 Mean :33.31
## 3rd Qu.:105.00 3rd Qu.:36.00 3rd Qu.:0.5800 3rd Qu.:41.00
## Max. :543.00 Max. :50.00 Max. :2.2880 Max. :67.00
## class scored.class scored.probability
## Min. :0.0000 Min. :0.0000 Min. :0.02323
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.11702
## Median :0.0000 Median :0.0000 Median :0.23999
## Mean :0.3149 Mean :0.1768 Mean :0.30373
## 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:0.43093
## Max. :1.0000 Max. :1.0000 Max. :0.94633- 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?
r <- table(data$scored.class,data$class)
knitr:: kable(r)| 0 | 1 | |
|---|---|---|
| 0 | 119 | 30 |
| 1 | 5 | 27 |
- 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(data) {
tb = table(data$class,data$scored.class)
TN=tb[1,1]
TP=tb[2,2]
FN=tb[2,1]
FP=tb[1,2]
return((TP+TN)/(TP+FP+TN+FN))
}
Accuracy(data)## [1] 0.8066298- 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.
CER <- function(data) {
tb = table(data$class,data$scored.class)
TN=tb[1,1]
TP=tb[2,2]
FN=tb[2,1]
FP=tb[1,2]
return((FP+FN)/(TP+FP+TN+FN))
}
CER(data)## [1] 0.1933702- 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(data) {
tb = table(data$class,data$scored.class)
TP=tb[2,2]
FP=tb[1,2]
return((TP)/(TP+FP))
}
Precision(data)## [1] 0.84375- 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(data) {
tb = table(data$class,data$scored.class)
TP=tb[2,2]
FN=tb[2,1]
return((TP)/(TP+FN))
}
Sensitivity(data)## [1] 0.4736842- 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(data) {
tb = table(data$class,data$scored.class)
TN=tb[1,1]
TP=tb[2,2]
FN=tb[2,1]
FP=tb[1,2]
return((TN)/(TN+FP))
}
Specificity(data)## [1] 0.9596774- 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(data) {
tb = table(data$class,data$scored.class)
TN=tb[1,1]
TP=tb[2,2]
FN=tb[2,1]
FP=tb[1,2]
Precision = (TP)/(TP+FP)
Sensitivity = (TP)/(TP+FN)
Precision =(TP)/(TP+FP)
return((2*Precision*Sensitivity)/(Precision+Sensitivity))
}
F1_score(data)## [1] 0.6067416- 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 < ???? < 1 and 0 < ???? < 1 then ???????? < ????.)
Both Precision and Sensitivity used to calculate F1 score are bounded between 0 and 1 , so F1 score will be between 0 and 1.
- 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(labels, scores){
labels = labels[order(scores, decreasing=TRUE)]
result =data.frame(TPR=cumsum(labels)/sum(labels), FPR=cumsum(!labels)/sum(!labels), labels)
FPR_df = c(diff(result$FPR), 0)
TPR_df = c(diff(result$TPR), 0)
AUC = round(sum(result$TPR * FPR_df) + sum(TPR_df * FPR_df)/2,4)
plot(result$FPR,result$TPR,type="l",main ="ROC Curve",ylab="Sensitivity",xlab="1-Specificity")
abline(a=0,b=1)
legend(.6,.2,AUC,title = "AUC")
}
ROC(data$class,data$scored.probability)
- Use your created R functions and the provided classification output data set to produce all of the classification metrics discussed above.
Accuracy(data)## [1] 0.8066298CER(data)## [1] 0.1933702Precision(data)## [1] 0.84375Sensitivity(data)## [1] 0.4736842Specificity(data)## [1] 0.9596774F1_score(data)## [1] 0.6067416- Investigate the caret package. In particular, consider the functions confusionMatrix, sensitivity, and specificity. Apply the functions to the data set. How do the results compare with your own functions?
confusionMatrix(as.factor(data$scored.class), as.factor(data$class), positive = "1")## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 119 30
## 1 5 27
##
## Accuracy : 0.8066
## 95% CI : (0.7415, 0.8615)
## No Information Rate : 0.6851
## P-Value [Acc > NIR] : 0.0001712
##
## Kappa : 0.4916
## Mcnemar's Test P-Value : 4.976e-05
##
## Sensitivity : 0.4737
## Specificity : 0.9597
## Pos Pred Value : 0.8438
## Neg Pred Value : 0.7987
## Prevalence : 0.3149
## Detection Rate : 0.1492
## Detection Prevalence : 0.1768
## Balanced Accuracy : 0.7167
##
## 'Positive' Class : 1
## The results are similar.
- Investigate the pROC package. Use it to generate an ROC curve for the data set. How do the results compare with your own functions?
par(mfrow=c(1,2))
plot(roc(data$class,data$scored.probability),print.auc=TRUE)
ROC(data$class,data$scored.probability)