[Machine Learning][The Analytics Edge][Predicting Earnings from Census Data]

census = read.csv("census.csv")
library(caTools)
set.seed(2000)
spl = sample.split(census$over50k,SplitRatio = 0.6)
train = subset(census,spl == TRUE)
test = subset(census, spl == FALSE)
# use the logistic regression
glm = glm(over50k ~. , data = train, family = "binomial")
summary(glm) #pr(>|z|) if it is smaller than 0.1, the variables are significant

#accuracy
glm.pred = predict(glm, newdata = test, type = "response")
table(test$over50k,glm.pred >= 0.5)

(9051+1888)/nrow(test)

#baseline accuracy of test - more frequent outcome
table(test$over50k)
9713/nrow(test)

#ROC & ACU
library(ROCR)
#Then we can generate the confusion matrix
ROCpred = prediction(glm.pred, test$over50k)
plot(performance(ROCpred,measure="tpr",x.measure="fpr"),colorize = TRUE)
as.numeric(performance(ROCpred, "auc")@y.values)

#Problem 2.1 - A CART Model
library(rpart)
library(rpart.plot)
CTree = rpart(over50k ~. , data = train, method = "class")
prp(CTree)

# accuracy of the CART model
CTree.pred = predict(CTree, newdata = test, type = "class")

table(test$over50k,CTree.pred)
(9243+1596)/nrow(test)

#use another way- generate probabilities and use a threshold of 0.5 like in logistic regression
CTree.pred1 = predict(CTree, newdata = test)
p = CTree.pred1[,2] # the column of over 50k
table(test$over50k, p) # p<=0.5 it is same with the <=50k, p>0.5 means >50k

# ROC curve for the CART model - WOW
#removing the type="class" argument when making predictions
library(ROCR)
library(arulesViz)
CTree.ROCpred = prediction(CTree.pred1[,2],test$over50k)
# plot(CTree.ROCpred) can not run
plot(performance(CTree.ROCpred,measure="tpr",x.measure="fpr"),colorize = TRUE)

# to caculate the auc
as.numeric(performance(CTree.ROCpred,"auc")@y.values)

# another way to seek for auc
CTree.ROCpred2 = prediction(p,test$over50k)
as.numeric(performance(CTree.ROCpred2,"auc")@y.values)

#Problem 3.1 - A Random Forest Model
set.seed(1)
trainSmall = train[sample(nrow(train),2000),]

set.seed(1)
library(randomForest)
RFC = randomForest(over50k ~., data = trainSmall)
RFC.pred = predict(RFC,newdata = test) #using a threshold of 0.5, no need to set the type = "class"
table(test$over50k,RFC.pred)
(9586+1093)/nrow(test) # a little difference is allowed

#compute metrics that give us insight into which variables are important.
vu = varUsed(RFC, count = TRUE)
vusorted = sort(vu, decreasing = FALSE, index.return = TRUE)
dotchart(vnsorted$x, names(RFC$forest$xlevel[vusorted$ix]))

#another way to find the important variables - impurity
varImpPlot(RFC)

# select cp by Cross-validation for the CART Trees
library(caret)
library(e1071)
set.seed(2)
#Specify that we are going to use k-fold cross validation with 10 folds:
numFolds = trainControl(method = "cv", number = 10)
#Specify the grid of cp values that we wish to evaluate:
cartGrid = expand.grid(.cp = seq(0.002,0.1,0.002))
#run the train function and view the result:
tr = train(over50k ~.,data = train, method = "rpart", trControl = numFolds, tuneGrid = cartGrid)
tr # The final value used for the model was cp = 0.002.

CTree2 = rpart(over50k ~., data = train, method = "class", cp = 0.002)
CTree2.pred = predict(CTree2, newdata = test, type = "class")
table(test$over50k, CTree2.pred)
(9178+1838)/nrow(test)
prp(CTree2) # shoould be 18 splits