library(klaR)
data(GermanCredit)

model1 <- glm(credit_risk~duration,family=binomial,data=GermanCredit)

X <- cbind(rep(1,1000),GermanCredit$duration); n <- dim(X)[1] ; s <- 0
for (i in 1:n) s <- s+as.numeric(plogis(model1$coeff%*%X[i,]))*as.numeric(1-plogis(model1$coeff%*%X[i,]))*X[i,]%*%t(X[i,])

summary(model1)
sqrt(diag(solve(s)))

# modele complet

model.full <- glm(credit_risk~.,data=GermanCredit,family=binomial)
summary(model.full)
anova(model.full,test="Chisq")

librzry(nnet)
test <- multinom(credit_risk~.,data=GermanCredit,family=binomial)
summary(test)
 
# selection descendante de variables

model.aic.backward <- step(model.full,direction="backward")
anova(model.aic.backward,test="Chisq")

n <- dim(GermanCredit)[1]
model.bic.backward <- step(model.full,direction="backward",k=log(n))
anova(model.bic.backward,test="Chisq")

# selection ascendante de variables et progressive

model.null <- glm(credit_risk~1,data=GermanCredit,family=binomial)
model.aic.forward <- step(model.null,direction="forward",scope=formula(model.full))
model.aic.stepwise <- step(model.null,direction="both",scope=formula(model.full))

formula(model.aic.forward)
formula(model.aic.backward)
formula(model.aic.stepwise)

model.bic.forward <- step(model.null,direction="forward",scope=formula(model.full),k=log(n))
model.bic.stepwise <- step(model.null,direction="both",scope=formula(model.full),k=log(n))

formula(model.bic.forward)
formula(model.bic.backward)
formula(model.bic.stepwise)

# estimation taux d'erreur de classification par validation croisee

libary(caret)

cv.model.bic <- train(formula(model.bic.backward),data=GermanCredit,method="glm",
	metric="Accuracy",trControl=trainControl(method="repeatedcv",number=10,repeats=50))
confusionMatrix(cv.model.bic)

cv.model.aic <- train(formula(model.aic.forward),data=GermanCredit,method="glm",
	metric="Accuracy",trControl=trainControl(method="repeatedcv",number=10,
		repeats=50))

cv.model.aic <- train(formula(model.aic.forward),data=GermanCredit,method="multinom",
	metric="Accuracy",trControl=trainControl(method="repeatedcv",number=10,
		repeats=50))
confusionMatrix(cv.model.aic)

library(glmnet)

y <- GermanCredit$credit_risk
x <- cbind(GermanCredit$duration,GermanCredit$amount,GermanCredit$age,
	GermanCredit$number_credits)

model.lasso <- glmnet(x,y,family="binomial")
plot(model.lasso)