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rmachine-learningclassificationrocproc-r-package

How to Create Multiple ROC Curves on the Same Plot for Multi.roc() objects (3 classes) in the pROC Package in R

Issue:

I want to plot ROC curves from multi.roc() objects for 12 models (see below) that I have produced onto the same plot to compare them. All my models contain 3 classes, which makes this conundrum a bit more complicated. I tried to follow the code from a question that I previously asked here; however, I kept on getting error messages since that question is a binary problem and my data has three classes for the dependent variable 'Country' (3 categorical levels - France, Holland, and Spain)

I have tried using three different methods: see Attempt 1, Attempt 2, and Attempt 3, and digrams 1 and 2

With all attempts, I am not sure how to incorporate 12 models onto the same plot. Diagram 1 is obviously wrong as the AUC = 0.90

I've searched online through other StackOverflow questions and tutorials, but nothing entirely solves the whole problem. Any solutions that I have found so far, I cannot get their code to work properly. Any help is highly appreciated.

R-CODE: Train the models

#Open libraries
library(MASS)
library(caret)
library(e1071)
library(klaR)
library(gbm)
library(earth)
library(kernlab)
library(rpart)
library(randomForest)
library(mlbench)
library(adabag)
library(ada)
library(fastAdaboost)
library(xgboost)
library(C50)

##Produce a new version of the dataframe 'Clusters_Dummy' with the rows shuffled
NewClusters=Cluster_Dummy_2[sample(1:nrow(Cluster_Dummy_2)),]

#Produce a dataframe
NewCluster<-as.data.frame(NewClusters)

#display
print(NewCluster)

#Check the structure of the data
str(NewCluster)

#Number of rows
nrow(NewCluster)

#Split the data frame into 70% to 30% train and test data
training.parameters <- Cluster_Dummy_2$Country %>% 
createDataPartition(p = 0.7, list = FALSE)
train.data <- NewClusters[training.parameters, ]
test.data <- NewClusters[-training.parameters, ]
sapply(train.data, summary) # Look at a summary of the training data

####################################################
#FIT MODELS: Auxiliary function to train the models
###################################################

fitControl <- trainControl(## 10-fold CV
                          method = "repeatedcv",
                          number = 10,
                          ## repeated ten times
                          repeats = 10,
                          classProbs = TRUE,
                          verbose = TRUE)


tuneLength <- 10
metric <- "Accuracy"

#####
#LDA#
#####
#Train the model
lda.fit.CV = train(Country ~ ., data=train.data, method="lda",
                   trControl = fitControl, metric=metric, tuneLength = tuneLength)

lda.fit.CV

#####################################
# Stochastic Boosted Gradient Trees #
#####################################

gbmGrid <-  expand.grid(interaction.depth = c(1, 5, 9), 
                        n.trees = (1:30)*50, 
                        shrinkage = 0.1,
                        n.minobsinnode = 20)

#Stochastic Boosted Gradient Tree: model 1
gbmFit1 <- train(Country ~ ., data=train.data,   method = "gbm",  metric=metric, 
                 trControl = fitControl, tuneLength = tuneLength, verbose=FALSE)

gbmFit1

#Stochastic Boosted Gradient Tree: model 2
gbmFit2 <- train(Country ~ ., data=train.data, method = "gbm",  trControl = fitControl, 
                 metric=metric, tuneLength = tuneLength,  tuneGrid = gbmGrid, verbose=FALSE)

gbmFit2

#########################################################
# Multivariate Adaptive Regression Splines (MARS) model  
#########################################################

# Step 1: Define the tuneGrid
marsGrid <-  expand.grid(nprune = c(2, 4, 6, 8, 10), 
                         degree = c(1, 2, 3))

# Train the model using randomForest and predict on the training data itself.
model_mars = train(Country ~ .,  data=train.data,  method='earth',  metric='ROC', tuneGrid = marsGrid, trControl = fitControl, tuneLength = tuneLength)

model_mars

###############################
# Single Vector Machine (SVM) #
###############################

model_svmRadial = train(Country ~ ., data=train.data, method='svmRadial',, metric=metric, trControl = fitControl, tuneLength= tuneLength)

model_svmRadial

###############################################
# Recursive Partitioning Classification Trees #
###############################################

f <- as.formula(paste0("Country ~ ", paste0(names(train.data)[2:10], collapse = "+")))

rpart.ctrl <- rpart.control(minsplit = 5, minbucket = 5, cp = seq(0, 0.02, 0.0001))

dt.rpart <- train(form = f, data = train.data, method = "rpart", metric = metric, trControl = fitControl, tuneGrid = rpart.ctrl, tuneLength= tuneLength)
dt.rpart

##############
Naive Bayes
############

#Tune the model
nb_tune <- data.frame(usekernel = TRUE, fL = 0, adjust=seq(0, 5, by = 1))

#Train the model
model.nb = train(Country ~., data=train.data,'nb', trControl=fitControl, metric=metric, tuneLength=tuneLength, tuneGrid = nb_tune, laplace = 0:3)
model.nb

#################
# Random Forest #
#################

model_rf = train(Country ~., data=train.data, method='rf', metric=metric, tuneLength= tuneLength, trControl = fitControl)

model_rf

#####################################
# Regularized Discriminant Analysis #
#####################################

rdaGrid=data.frame(gamma = (0.4)/4, lambda = 3/4)

rdaFit <- train(Country ~ ., data =train.data, method = "rda", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
rdaFit    

#####################################
# Classification with Decision Tree #
#####################################

#Train the model
Decision_Fit <- train(Country ~ ., data =train.data, method = "C5.0", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
Decision_Fit 

##################################
# K-nearest neighbour classifier #
##################################

#Train the model
model_knn = caret::train(Country ~ ., data=train.data, method='knn', 
                         tuneLength = tuneLength, metric=metric, 
                         trControl = fitControl, 
                         tuneGrid = expand.grid(k = seq(1, 101, by = 2)))
model_knn

#############################
# Neural Network Classifier #
#############################

Neural_Fit <- train(Country ~ ., data =train.data, method = "nnet", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
Neural_Fit

Predict the models on the test data

#####
#LDA#
#####

pred_LDA = predict(lda.fit.CV, test.data, type="prob")
pred_LDA

######################################
# Stochastic Boosted Gradient Trees #
#####################################

## Stochastic Boosted Gradient Trees: model 1
#Predict the model with the test data
pred_model_Tree1 = predict(gbmFit1, newdata = test.data, type = "prob")
pred_model_Tree1

print(pred_model_Tree1)

## Stochastic Boosted Gradient Trees: model 1
pred_model_Tree1$evaluation <- names(pred_model_Tree1)[apply(pred_model_Tree1, 1, which.max)]
pred_model_Tree1$evaluation

table(pred_model_Tree1$evaluation)

#Now you can print the confusionMatrix (make sure each factor has the same levels)
confusionMatrix(factor(pred_model_Tree1$evaluation, levels = unique(test.data$Country)),
                factor(test.data$Country, levels = unique(test.data$Country)))

#Predict the model with the test data
pred_model_Tree2 = predict(gbmFit2, newdata = test.data, type = "prob")
pred_model_Tree2

print(pred_model_Tree2)

## Stochastic Boosted Gradient Trees: model 2
pred_model_Tree2$evaluation <- names(pred_model_Tree2)[apply(pred_model_Tree2, 1, which.max)]
pred_model_Tree2$evaluation

#########################################
# Bagged Flexible Discriminant Analysis #
########################################

#Predict the bagged flexible discriminate model with the test data
Earth_fitted <- predict(model_mars, newdata = test.data, type = "prob")
Earth_fitted

Earth_fitted$evaluation <- names(Earth_fitted)[apply(Earth_fitted, 1, which.max)]
Earth_fitted$evaluation

###############################
# Single Vector Machine (SVM) #
###############################

#Predict the random forest model with the test data
SVM_fitted <- predict(model_svmRadial, newdata = test.data, type = "prob")
SVM_fitted

#Evaluate the predictions
SVM_fitted$evaluation <- names(SVM_fitted)[apply(SVM_fitted, 1, which.max)]
SVM_fitted$evaluation

###############################################
# Recursive Partitioning Classification Trees #
##############################################

#Predict the random forest model with the test data
rpart_fitted <- predict(dt.rpart, newdata = test.data, type = "prob")
rpart_fitted

#produce a dataframe
rpart_fit<-as.data.frame(rpart_fitted)
rpart_fit

#Evaluate the predictions
rpart_fit$evaluation <- factor(max.col(rpart_fit[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
rpart_fit$evaluation 

###############
# Naïve Bayes #
#############

#Predict the model with probabilities
predict.nb<-predict(model.nb$finalModel, newdata = test.data, type = "prob")
predict.nb

#Predict the model with the classes
pedict.class.nb<-predict(model.nb$finalModel, newdata = test.data, type = "prob")$class
pedict.class.nb

#Unlist the results as the function table() and confusionMatrix do not recognize lists
unlist.predicted.nb.Country <-unlist(predict.nb$class)
unlist.predicted.nb.Country

unlist.predicted.nb.posterior <-unlist(predict.nb$posterior)
unlist.predicted.nb.posterior

#produce a dataframe
nb_fit<-as.data.frame(unlist.predicted.nb.posterior)
nb_fit

#Evaluate the predictions
nb_fit$evaluation <- factor(max.col(nb_fit[,1:3]), levels=1:3, labels=c(""France", "Spain", "Holland""))
nb_fit$evaluation 

#################
# Random Forest #
################

#Now that we have generated a classification model
#Model Evaluation
pred_rf<-predict(model_rf, newdata = test.data, type = "prob")
pred_rf

#Evaluate the predictions
pred_rf$evaluation <- factor(max.col(pred_rf[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland""))
pred_rf$evaluation

#number of rows
nrow(pred_rf)

#####################################
# Regularized Discriminant Analysis #
#####################################

#Now that we have generated a classification model
#Model Evaluation
pred_rda<-predict(rdaFit, newdata = test.data, type = "prob")
pred_rda

#Evaluate the predictions
rdaFit $evaluation <- factor(max.col(pred_rda[,1:3]), levels=1:3, labels = c(""France", "Spain", "Holland""))
rdaFit $evaluation

#number of rows
nrow(pred_rf)

##################
# Decision Trees #
##################

#Now that we have generated a classification model
#Model Evaluation
pred_decision<-predict(Decision_Fit, newdata = test.data, type = "prob")
pred_decision

#Evaluate the predictions
pred_decision$evaluation <- factor(max.col(pred_decision[,1:3]), levels=1:3, labels = c(""France", "Spain", "Holland""))
pred_decision$evaluation

#########################
# knn nearest neighbor #
########################

#Now that we have generated a classification model
#Model Evaluation
pred_knn<-predict(model_knn, newdata = test.data, type = "prob")
pred_knn

#Evaluate the predictions
pred_knn$evaluation <- factor(max.col(pred_knn[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
pred_knn$evaluation

########################
# knn nearest neighbor #
########################

#Now that we have generated a classification model
#Model Evaluation
pred_net<-predict(Neural_Fit, newdata = test.data, type = "prob")
pred_net

#Evaluate the predictions
pred_net$evaluation <- factor(max.col(pred_net[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
pred_net$evaluation

#Contingency table of predictions
table(pred_net$evaluation)

#Now you can print the confusionMatrix (make sure each factor has the same levels)
confusionMatrix(factor(pred_net$evaluation, levels = unique(test.data$Country)),
                factor(test.data$Country, levels = unique(test.data$Country)))

Produce the mult.roc() ojbects

#LDA
roc_LDA <- multiclass.roc(test.data$Country, pred_LDA, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_LDA 

#Boosted Tree model 1
roc_Tree1 <- multiclass.roc(test.data$Country, pred_model_Tree1, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_Tree1 

#Boosted Tree model 2
roc_Tree2 <- multiclass.roc(test.data$Country, pred_model_Tree2, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_Tree2 

#Mars model
roc_Mars <- multiclass.roc(test.data$Country, Earth_fitted, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_Mars

#Single Vector Machine
roc_SVM <- multiclass.roc(test.data$Country, SVM_fitted, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_SVM

#Single Vector Machine
roc_RART <- multiclass.roc(test.data$Country, rpart_fitted, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_RART

#Naive Bayes
roc_nb <- multiclass.roc(test.data$Country, predict.nb$posterior, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_nb 

#Single Vector Machine
roc_RART <- multiclass.roc(test.data$Country, rpart_fitted, levels=c("France", "Spain", "Holland"))
roc_RART

#Random Forest
roc_RF <- multiclass.roc(test.data$Country, pred_rf, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_RF

#Regularized Discriminant Analysis
roc_RDA <- multiclass.roc(test.data$Country, pred_rda, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_RDA

#Decision Trees
roc_Decision <- multiclass.roc(test.data$Country, pred_decision, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_Decision

#K nearest neighbour
roc_knn <- multiclass.roc(test.data$Country, pred_knn, levels=c("France", "Spain", "Holland"), auc=TRUE)
roc_knn

#Neural network
roc_net <- multiclass.roc(test.data$Country, pred_net, levels=c("France", "Spain", "Holland"), auc = TRUE)
roc_net

This is my desired ROC plot

enter image description here

Attempts to solve the problem

#Attempt 1

dev.new()

lvls = levels(Cluster_Dummy_2$Country)

aucs = c()
plot(x=NA, y=NA, xlim=c(0,1), ylim=c(0,1),
     ylab='True Positive Rate',
     xlab='False Positive Rate',
     bty='n')

for (type.id in 1:3) {
  type = as.factor(test.data$Country == lvls[type.id])
  score = pred_LDA([, 'TRUE']], levels[,1:3])
  actual.class = test.data$Country == lvls[type.id]
  
  pred = prediction(score, actual.class)
  nbperf = performance(pred, "tpr", "fpr")
  
  roc.x = unlist([email protected])
  roc.y = unlist([email protected])
  lines(roc.y ~ roc.x, col=type.id+1, lwd=2)
  
  nbauc = performance(pred, "auc")
  nbauc = unlist(slot(nbauc, "y.values"))
  aucs[type.id] = nbauc
}

#Error 

Error: unexpected '}' in "}"

#However, this version did produce a roc curve for the LDA, although, I think it's obviusly wrong as the auc = 90 %

#Attempt 2

score_data <- data.frame(LDA=pred_LDA,
                         Country=test.data$Country,
                         stringsAsFactors=FALSE)

plot(roc(test.data$Country, score_data[,1:3] , direction="<"),
     col="red", lwd=3, main="The turtle finds its way")

#Setting levels: control = Italy, case = Turkey
Error in h(simpleError(msg, call)) : 
  error in evaluating the argument 'x' in selecting a method for function 'plot': Predictor must be numeric or ordered.
In addition: Warning message:
In roc.default(test.data$Country, score_data[, 1:3], direction = "<") :
  'response' has more than two levels. Consider setting 'levels' explicitly or using 'multiclass.roc' instead

Attempt 3:

rs <- roc_net[['rocs']]
print(rs)
plot.roc(rs[[1:2]])
sapply(2:length(rs),function(i) lines.roc(rs[[i]],col=i))

#Error
Error in roc.default(x, predictor, ...) : No valid data provided.
Called from: roc.default(x, predictor, ...)

Diagram_1

enter image description here

Diagram 2

enter image description here

Data

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    2445L, 8L, 557450L, 450259742L, 21006647L, 9L, 7234027L, 59L, 
    9L, 651547554L, 45554L, 38493L, 91055218L, 38L, 1116474L, 2295482L, 
    3001L, 9L, 3270L, 141L, 53644L, 667983L, 565598L, 84L, 971L, 
    555498297L, 60431L, 6597L, 856943893L, 607815536L, 4406L, 79L, 
    4885076L, 745L, 8L, 56456L, 125140L, 73043989L, 516476L, 7L, 
    4440739L, 754038591L, 375L, 53809223L, 72L, 136L, 509L, 232325L, 
    13128104L, 1692L, 8581L, 23L, 5874213L, 4550L, 644668065L, 3712371L, 
    5928L, 8833L, 7L, 2186023L, 61627221L, 37297L, 716427989L, 21387L
    ), Start.Freq = c(426355L, 22073538L, 680374L, 41771L, 54L, 6762844L, 
    599171L, 108L, 257451851L, 438814L, 343045L, 4702L, 967787L, 
    1937L, 18L, 89301735L, 366L, 90L, 954L, 7337732L, 70891703L, 
    4139L, 10397931L, 940000382L, 7L, 38376L, 878528819L, 6287L, 
    738366L, 31L, 47L, 5L, 6L, 77848L, 2366508L, 45L, 3665842L, 7252260L, 
    6L, 61L, 3247L, 448348L, 1L, 705132L, 144L, 7423637L, 2L, 497L, 
    844927639L, 78978L, 914L, 131L, 7089563L, 927L, 9595581L, 2774463L, 
    1651L, 73509280L, 7L, 35L, 18L, 96L, 1L, 92545512L, 27354947L, 
    7556L, 65019L, 7480L, 71835L, 8249L, 64792L, 71537L, 349389666L, 
    280244484L, 82L, 6L, 40L, 353872L, 0L, 103L, 1255L, 4752L, 29L, 
    76L, 81185L, 14L, 9L, 470775630L, 818361265L, 57947209L, 44L, 
    24L, 41295L, 4L, 261449L, 9931404L, 773556640L, 930717L, 65007421L
    ), End.Freq = c(71000996L, 11613579L, 71377155L, 1942738L, 8760748L, 
    79L, 455L, 374L, 8L, 5L, 2266932L, 597833L, 155488L, 3020L, 4L, 
    554L, 4L, 16472L, 1945649L, 668181101L, 649780L, 22394365L, 93060602L, 
    172146L, 20472L, 23558847L, 190513L, 22759044L, 44L, 78450L, 
    205621181L, 218L, 69916344L, 23884L, 66L, 312148L, 7710564L, 
    4L, 422L, 744572L, 651547554L, 45554L, 38493L, 91055218L, 38L, 
    1116474L, 2295482L, 3001L, 9L, 3270L, 141L, 55595L, 38451L, 8660867L, 
    14L, 96L, 345L, 6L, 44L, 8235824L, 910517L, 1424326L, 87102566L, 
    53644L, 667983L, 565598L, 84L, 971L, 555498297L, 60431L, 6597L, 
    856943893L, 607815536L, 4406L, 79L, 7L, 28978746L, 7537295L, 
    6L, 633L, 345860066L, 802L, 1035131L, 602L, 2740L, 8065L, 61370968L, 
    429953765L, 981507L, 8105L, 343787257L, 44782L, 64184L, 12981359L, 
    123367978L, 818775L, 123745614L, 25345654L, 3L), Country = c("Holland", 
    "Holland", "Holland", "Holland", "Holland", "Holland", "Spain", 
    "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", 
    "Spain", "Spain", "Spain", "Spain", "Holland", "Holland", "Holland", 
    "Holland", "Holland", "Holland", "France", "France", "France", 
    "France", "France", "France", "France", "France", "France", "France", 
    "France", "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", 
    "Spain", "Spain", "France", "France", "France", "France", "Holland", 
    "Holland", "Holland", "Holland", "Holland", "Holland", "Holland", 
    "Holland", "Holland", "Holland", "Holland", "Holland", "Holland", 
    "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", 
    "Holland", "Holland", "Holland", "Holland", "France", "France", 
    "France", "France", "France", "France", "France", "Spain", "Spain", 
    "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", 
    "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", "Spain", 
    "Spain", "Spain", "France", "France", "France")), row.names = c(NA, 
    99L), class = "data.frame")
Solution

  • Train the models:

    #Open libraries
library(MASS)
library(caret)
library(e1071)
library(klaR)
library(gbm)
library(earth)
library(kernlab)
library(rpart)
library(randomForest)
library(mlbench)
library(adabag)
library(ada)
library(fastAdaboost)
library(xgboost)
library(C50)

##Produce a new version of the dataframe 'Clusters_Dummy' with the rows shuffled
NewClusters=Cluster_Dummy_2[sample(1:nrow(Cluster_Dummy_2)),]

#Produce a dataframe
NewCluster<-as.data.frame(NewClusters)

#display
print(NewCluster)

#Split the data frame into 70% to 30% train and test data
training.parameters <- Cluster_Dummy_2$Country %>% 
createDataPartition(p = 0.7, list = FALSE)
train.data <- NewClusters[training.parameters, ]
test.data <- NewClusters[-training.parameters, ]
sapply(train.data, summary) # Look at a summary of the training data

####################################################
#FIT MODELS: Auxiliary function to train the models
###################################################

fitControl <- trainControl(## 10-fold CV
                          method = "repeatedcv",
                          number = 10,
                          ## repeated ten times
                          repeats = 10,
                          classProbs = TRUE,
                          verbose = TRUE)


tuneLength <- 10
metric <- "Accuracy"

#####
#LDA#
#####
#Train the model
lda.fit.CV = train(Country ~ ., data=train.data, method="lda",
                   trControl = fitControl, metric=metric, tuneLength = tuneLength)

lda.fit.CV

#####################################
# Stochastic Boosted Gradient Trees #
#####################################

gbmGrid <-  expand.grid(interaction.depth = c(1, 5, 9), 
                        n.trees = (1:30)*50, 
                        shrinkage = 0.1,
                        n.minobsinnode = 20)

#Stochastic Boosted Gradient Tree: model 1
gbmFit1 <- train(Country ~ ., data=train.data,   method = "gbm",  metric=metric, 
                 trControl = fitControl, tuneLength = tuneLength, verbose=FALSE)

gbmFit1

#Stochastic Boosted Gradient Tree: model 2
gbmFit2 <- train(Country ~ ., data=train.data, method = "gbm",  trControl = fitControl, 
                 metric=metric, tuneLength = tuneLength,  tuneGrid = gbmGrid, verbose=FALSE)

gbmFit2

#########################################################
# Multivariate Adaptive Regression Splines (MARS) model  
#########################################################

# Step 1: Define the tuneGrid
marsGrid <-  expand.grid(nprune = c(2, 4, 6, 8, 10), 
                         degree = c(1, 2, 3))

# Train the model using randomForest and predict on the training data itself.
model_mars = train(Country ~ .,  data=train.data,  method='earth',  metric='ROC', tuneGrid = marsGrid, trControl = fitControl, tuneLength = tuneLength)

model_mars

###############################
# Single Vector Machine (SVM) #
###############################

model_svmRadial = train(Country ~ ., data=train.data, method='svmRadial',, metric=metric, trControl = fitControl, tuneLength= tuneLength)

model_svmRadial

###############################################
# Recursive Partitioning Classification Trees #
###############################################

f <- as.formula(paste0("Country ~ ", paste0(names(train.data)[2:10], collapse = "+")))

rpart.ctrl <- rpart.control(minsplit = 5, minbucket = 5, cp = seq(0, 0.02, 0.0001))

dt.rpart <- train(form = f, data = train.data, method = "rpart", metric = metric, trControl = fitControl, tuneGrid = rpart.ctrl, tuneLength= tuneLength)
dt.rpart

##############
Naive Bayes
############

#Tune the model
nb_tune <- data.frame(usekernel = TRUE, fL = 0, adjust=seq(0, 5, by = 1))

#Train the model
model.nb = train(Country ~., data=train.data,'nb', trControl=fitControl, metric=metric, tuneLength=tuneLength, tuneGrid = nb_tune, laplace = 0:3)
model.nb

#################
# Random Forest #
#################

model_rf = train(Country ~., data=train.data, method='rf', metric=metric, tuneLength= tuneLength, trControl = fitControl)

model_rf

#####################################
# Regularized Discriminant Analysis #
#####################################

rdaGrid=data.frame(gamma = (0.4)/4, lambda = 3/4)

rdaFit <- train(Country ~ ., data =train.data, method = "rda", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
rdaFit    

#####################################
# Classification with Decision Tree #
#####################################

#Train the model
Decision_Fit <- train(Country ~ ., data =train.data, method = "C5.0", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
Decision_Fit 

##################################
# K-nearest neighbour classifier #
##################################

#Train the model
model_knn = caret::train(Country ~ ., data=train.data, method='knn', 
                         tuneLength = tuneLength, metric=metric, 
                         trControl = fitControl, 
                         tuneGrid = expand.grid(k = seq(1, 101, by = 2)))
model_knn

#############################
# Neural Network Classifier #
#############################

Neural_Fit <- train(Country ~ ., data =train.data, method = "nnet", trControl = fitControl, tuneLength = tuneLength, metric = "ROC")
Neural_Fit

    Predict the models against the test data

    #####
#LDA#
#####

pred_LDA = predict(lda.fit.CV, test.data, type="prob")
pred_LDA

######################################
# Stochastic Boosted Gradient Trees #
#####################################

## Stochastic Boosted Gradient Trees: model 1
#Predict the model with the test data
pred_model_Tree1 = predict(gbmFit1, newdata = test.data, type = "prob")
pred_model_Tree1

## Stochastic Boosted Gradient Trees: model 1
pred_model_Tree1$evaluation <- names(pred_model_Tree1)[apply(pred_model_Tree1, 1, which.max)]
pred_model_Tree1$evaluation

table(pred_model_Tree1$evaluation)

#Now you can print the confusionMatrix (make sure each factor has the same levels)
confusionMatrix(factor(pred_model_Tree1$evaluation, levels = unique(test.data$Country)),
                factor(test.data$Country, levels = unique(test.data$Country)))

#Predict the model with the test data
pred_model_Tree2 = predict(gbmFit2, newdata = test.data, type = "prob")
pred_model_Tree2

## Stochastic Boosted Gradient Trees: model 2
pred_model_Tree2$evaluation <- names(pred_model_Tree2)[apply(pred_model_Tree2, 1, which.max)]
pred_model_Tree2$evaluation

#########################################
# Bagged Flexible Discriminant Analysis #
########################################

#Predict the bagged flexible discriminate model with the test data
Earth_fitted <- predict(model_mars, newdata = test.data, type = "prob")
Earth_fitted

Earth_fitted$evaluation <- names(Earth_fitted)[apply(Earth_fitted, 1, which.max)]
Earth_fitted$evaluation

###############################
# Single Vector Machine (SVM) #
###############################

#Predict the random forest model with the test data
SVM_fitted <- predict(model_svmRadial, newdata = test.data, type = "prob")
SVM_fitted

#Evaluate the predictions
SVM_fitted$evaluation <- names(SVM_fitted)[apply(SVM_fitted, 1, which.max)]
SVM_fitted$evaluation

###############################################
# Recursive Partitioning Classification Trees #
##############################################

#Predict the random forest model with the test data
rpart_fitted <- predict(dt.rpart, newdata = test.data, type = "prob")
rpart_fitted

#produce a dataframe
rpart_fit<-as.data.frame(rpart_fitted)
rpart_fit

#Evaluate the predictions
rpart_fit$evaluation <- factor(max.col(rpart_fit[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
rpart_fit$evaluation 

###############
# Naïve Bayes #
#############

#Predict the model with probabilities
predict.nb<-predict(model.nb$finalModel, newdata = test.data, type = "prob")
predict.nb

#Predict the model with the classes
pedict.class.nb<-predict(model.nb$finalModel, newdata = test.data, type = "prob")$class
pedict.class.nb

#Unlist the results as the function table() and confusionMatrix do not recognize lists
unlist.predicted.nb.Country <-unlist(predict.nb$class)
unlist.predicted.nb.Country

unlist.predicted.nb.posterior <-unlist(predict.nb$posterior)
unlist.predicted.nb.posterior

#produce a dataframe
nb_fit<-as.data.frame(unlist.predicted.nb.posterior)
nb_fit

#Evaluate the predictions
nb_fit$evaluation <- factor(max.col(nb_fit[,1:3]), levels=1:3, labels=c(""France", "Spain", "Holland""))
nb_fit$evaluation 

#################
# Random Forest #
################

#Now that we have generated a classification model
#Model Evaluation
pred_rf<-predict(model_rf, newdata = test.data, type = "prob")
pred_rf

#Evaluate the predictions
pred_rf$evaluation <- factor(max.col(pred_rf[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
pred_rf$evaluation

#####################################
# Regularized Discriminant Analysis #
#####################################

#Now that we have generated a classification model
#Model Evaluation
pred_rda<-predict(rdaFit, newdata = test.data, type = "prob")
pred_rda

#Evaluate the predictions
rdaFit $evaluation <- factor(max.col(pred_rda[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
rdaFit $evaluation

##################
# Decision Trees #
##################

#Now that we have generated a classification model
#Model Evaluation
pred_decision<-predict(Decision_Fit, newdata = test.data, type = "prob")
pred_decision

#Evaluate the predictions
pred_decision$evaluation <- factor(max.col(pred_decision[,1:3]), levels=1:3, labels = c(""France", "Spain", "Holland""))
pred_decision$evaluation

#########################
# knn nearest neighbour #
########################

#Now that we have generated a classification model
#Model Evaluation
pred_knn<-predict(model_knn, newdata = test.data, type = "prob")
pred_knn

#Evaluate the predictions
pred_knn$evaluation <- factor(max.col(pred_knn[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
pred_knn$evaluation

##################
# Neural Network #
##################

#Now that we have generated a classification model
#Model Evaluation
pred_net<-predict(Neural_Fit, newdata = test.data, type = "prob")
pred_net

#Evaluate the predictions
pred_net$evaluation <- factor(max.col(pred_net[,1:3]), levels=1:3, labels = c("France", "Spain", "Holland"))
pred_net$evaluation

#Contingency table of predictions
table(pred_net$evaluation)

#Now you can print the confusionMatrix (make sure each factor has the same levels)
confusionMatrix(factor(pred_net$evaluation, levels = unique(test.data$Country)),

    Produce the multi.roc() objects using the library pROC

    library(pROC) # Compute roc
library(ROCR)
library(MASS)
library(caret)

#LDA
roc_LDA <- multiclass.roc(test.data$Country, pred_LDA, levels=c("France", "Spain", "Holland"))
roc_LDA 

#Boosted Tree model 1
roc_Tree1 <- multiclass.roc(test.data$Country, pred_model_Tree1[1:3], levels=c("France", "Spain", "Holland"))
roc_Tree1 

#Boosted Tree model 2
roc_Tree2 <- multiclass.roc(test.data$Country, pred_model_Tree2[1:3], levels=c("France", "Spain", "Holland"))
roc_Tree2 

#Mars model
roc_Mars <- multiclass.roc(test.data$Country, Earth_fitted[1:3], levels=c("France", "Spain", "Holland"))
roc_Mars

#Single Vector Machine
roc_SVM <- multiclass.roc(test.data$Country, SVM_fitted[1:3], levels=c("France", "Spain", "Holland"))
roc_SVM

#Single Vector Machine
roc_RART <- multiclass.roc(test.data$Country, rpart_fitted, levels=c("France", "Spain", "Holland"))
roc_RART

#Naive Bayes
roc_nb <- multiclass.roc(test.data$Country, predict.nb$posterior, levels=c("France", "Spain", "Holland"))
roc_nb 

#Single Vector Machine
roc_RPART <- multiclass.roc(test.data$Country, rpart_fitted, levels=c("France", "Spain", "Holland"))
roc_RPART

#Random Forest
roc_RF <- multiclass.roc(test.data$Country, pred_rf[1:3], levels=c("France", "Spain", "Holland"))
roc_RF

#Regularized Discriminant Analysis
roc_RDA <- multiclass.roc(test.data$Country, pred_rda, levels=c("France", "Spain", "Holland"))
roc_RDA

#Decision Trees
roc_Decision <- multiclass.roc(test.data$Country, pred_decision[1:3], levels=c("France", "Spain", "Holland"))
roc_Decision

#K nearest neighbour
roc_knn <- multiclass.roc(test.data$Country, pred_knn[1:3], levels=c("France", "Spain", "Holland"))
roc_knn

#Neural network
roc_net <- multiclass.roc(test.data$Country, pred_net[1:3], levels=c("France", "Spain", "Holland"))
roc_net

    Function to plot the multiclass ROC curves

    ##Neural Network
Neural_Network <- roc_net[['rocs']]
print(Neural_Network)
plot.roc(Neural_Network[[1:2]], las=1, lwd=1.7, col = "black", xlab=" 1 - specificity")

#Nearest Neigbour
Knn <- roc_knn[['rocs']]
print(Knn)
plot.roc(Knn[[1:2]], add=TRUE, lwd=1.7, col = "red")

#LDA roc_LDA 
LDA <- roc_LDA[['rocs']]
print(rs)
plot.roc(LDA[[1:2]], add=TRUE, lwd=1.7, col = "green")

#Boosted Tree 1
Boosted_Gradient1 <- roc_Tree1[['rocs']]
print(Boosted_Gradient1)
plot.roc(Boosted_Gradient1[[1:2]], add=TRUE, lwd=1.7, col = "#3300CC")

#Boosted Tree 2
Boosted_Gradient2 <- roc_Tree1[['rocs']]
print(Boosted_Gradient2)
plot.roc(Boosted_Gradient2[[1:2]], add=TRUE, lwd=1.7, col = "#CC66FF")

#Mars
MARS <- roc_Mars[['rocs']]
print(MARS)
plot.roc(MARS[[1:2]], add=TRUE, lwd=1.7, col = "#669933")

#Single Vector Machine
SVM <- roc_SVM[['rocs']]
print(SVM)
plot.roc(SVM[[1:2]], add=TRUE, lwd=1.7, col = "#FFFF00")

#Recursive partitioning
RPART <- roc_RPART[['rocs']]
print(RPART)
plot.roc(RPART[[1:2]], add=TRUE, lwd=1.7, col = "orange")

#Recursive partitioning
NaiveBayes <- roc_nb[['rocs']]
print(NaiveBayes)
plot.roc(NaiveBayes[[1:2]], add=TRUE, lwd=1.7, col = "cyan")

#Random Forest
Random_Forest <- roc_RF[['rocs']]
print(Random_Forest)
plot.roc(Random_Forest[[1:2]], add=TRUE, lwd=1.7, col = "magenta")

#Regularized discriminant analysis
RDA <- roc_RF[['rocs']]
print(RDA)
plot.roc(RDA [[1:2]], add=TRUE, lwd=1.7, col = "#33CC66")

#Regularized discriminant analysis
Decision_ROC <- roc_Decision[['rocs']]
print(Decision_ROC)
plot.roc(Decision_ROC[[1:2]], add=TRUE, lwd=1.7, col = "#3333FF")

#Decision Tree
Decision_Tree <- roc_Decision[['rocs']]
print(Decision_Tree)
plot.roc(Decision_Tree[[1:2]], add=TRUE, lwd=1.7, col = "#FF00CC")

#Neural Network
Neural_Network <- roc_net[['rocs']]
print(Neural_Network)
plot.roc(Neural_Network[[1:2]], add=TRUE, lwd=1.7, col = "#0000FF")

    Add a legend

    #Insert a legend
legend("bottomright", legend = c("Neural_Network: AUC = 0.9379", "Knn: AUC =0.9087", "LDA: AUC = 0.9012", 
                                 "Boosted Gradient 1: AUC = 0.9826", "Boosted_Gradient 2: AUC = 0.9641",
                                 "MARS: AUC = 0.9458", "SVM: AUC = 0.9537", "Rpart: AUC = 0.9077", "NaiveBayes: AUC = 0.8951", 
                                 "Random_Forest: AUC = 0.9876", "RDA: AUC = 0.8982", "Decision Tree: AUC = 0.9832", 
                                 "Neural Network: AUC = 0.9379"), 
                          lty = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1), 
                          col =c("black", "red", "green", "#3300CC", "#CC66FF", 
                                 "#669933", "#FFFF00", "orange", "cyan", "magenta", "#33CC66", "#3333FF", 
                                 "#FF00CC", "#0000FF"), cex=0.6, lwd=1.5, inset = 0.05,
                                  title = "ROC Curves")
                          par(mfrow = c(1, 1))

    ROC Curve Diagram

    enter image description here