library(pROC)

build_AUC_linear_models = function(X, y, seed_value=456, build_pls_model=TRUE){
    #
    # Builds (using caret's train function) several of the linear models discussed in
    # this chapter of the book optimizing the area-under-the-curve metric (AUC)
    #
    # X [n samples, n features] needs to have zero variance columns removed (use nearZeroVar to remove them) and
    # linear dependent columns removed (use findLinearCombos to remove them)
    #
    # y [n samples, 1] is a two factor vector of predictions with the FIRST factor corresponding to the event of interest
    #
    # Written by:
    # -- 
    # John L. Weatherwax                2009-04-21
    # 
    # email: wax@alum.mit.edu
    # 
    # Please send comments and especially bug reports to the
    # above email address.
    #
    #-----

    # Set up the train control arguments so that we can compute the area-under-the-curve:
    #
    ctrl = trainControl( summaryFunction=twoClassSummary, classProbs=TRUE )

    # Logistic Regression Model:
    #
    set.seed(seed_value)
    glm.classifier = train( X, y, method="glm", metric="ROC", trControl=ctrl )
    glm.predictions = predict( glm.classifier, X, type="prob" )
    glm.rocCurve = pROC::roc( response=y, predictor=glm.predictions[,1] )
    glm.auc = glm.rocCurve$auc[1]
    glm=list( classifier=glm.classifier, predictions=glm.predictions, roc=glm.rocCurve, auc=glm.auc )

    # Linear Discriminant Analysis:
    #
    set.seed(seed_value)
    lda.classifier = train( X, y, method="lda", preProc=c("center","scale"), metric="ROC", trControl=ctrl )
    lda.predictions = predict( lda.classifier, X, type="prob" ) # <~ returns probability of "Yes" (event of interest) & "No"
    lda.rocCurve = pROC::roc( response=y, predictor=lda.predictions[,1] )
    lda.auc = lda.rocCurve$auc[1]
    lda=list( classifier=lda.classifier, predictions=lda.predictions, roc=lda.rocCurve, auc=lda.auc )

    # Partial Least Squares Discriminant Analysis (this can take a very long time on the churn data set):
    #
    if( build_pls_model ){
        set.seed(seed_value)
        plsda.classifier = train( X, y, method="pls", tuneGrid=expand.grid(.ncomp=1:10), preProc=c("center","scale"), metric="ROC", trControl=ctrl )
        plsda.predictions = predict( plsda.classifier, X, type="prob" )
        plsda.rocCurve = pROC::roc( response=y, predictor=plsda.predictions[,1] )
        plsda.auc = plsda.rocCurve$auc[1]
        plsda=list( classifier=plsda.classifier, predictions=plsda.predictions, roc=plsda.rocCurve, auc=plsda.auc )
    }

    # Penalized Methods:
    #
    glmnGrid = expand.grid(.alpha=c(0, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0), .lambda=seq( 0.01, 0.2, length=40))
    set.seed(seed_value)
    glmnet.classifier = train( X, y, method="glmnet", tuneGrid=glmnGrid, preProc=c("center","scale"), metric="ROC", trControl=ctrl )
    glmnet.predictions = predict( glmnet.classifier, X, type="prob" )
    glmnet.rocCurve = pROC::roc( response=y, predictor=glmnet.predictions[,1] )
    glmnet.auc = glmnet.rocCurve$auc[1]
    glmnet=list( classifier=glmnet.classifier, predictions=glmnet.predictions, roc=glmnet.rocCurve, auc=glmnet.auc )

    # Nearest shrunken Centroids:
    #
    nscGrid = expand.grid(.threshold=0:25)
    set.seed(seed_value)
    nsc.classifier = train( X, y, method="pam", tuneGrid=nscGrid, preProc=c("center","scale"), metric="ROC", trControl=ctrl )
    nsc.predictions = predict( nsc.classifier, X, type="prob" )
    nsc.rocCurve = pROC::roc( response=y, predictor=nsc.predictions[,1] )
    nsc.auc = nsc.rocCurve$auc[1]
    nsc=list( classifier=nsc.classifier, predictions=nsc.predictions, roc=nsc.rocCurve, auc=nsc.auc )

    result = list( glm=glm, lda=lda, glmnet=glmnet, nsc=nsc )
    if( build_pls_model ){ result = c(result, list(plsda=plsda)) }
    return( result )

}