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#' Invariant target prediction.
#'
#' @description Tests the null hypothesis that Y and E are independent given X.
#'
#' @param Y An n-dimensional vector.
#' @param E An n-dimensional vector or an nxq dimensional matrix or dataframe.
#' @param X A matrix or dataframe with n rows and p columns.
#' @param alpha Significance level. Defaults to 0.05.
#' @param verbose If \code{TRUE}, intermediate output is provided. Defaults to \code{FALSE}.
#' @param fitWithGam If \code{TRUE}, a GAM is used for the nonlinear regression, else
#' a random forest is used. Defaults to \code{TRUE}.
#' @param trainTestSplitFunc Function to split sample. Defaults to stratified sampling
#' using \code{caTools::sample.split}, assuming E is a factor.
#' @param argsTrainTestSplitFunc Arguments for sampling splitting function.
#' @param test Unconditional independence test that tests whether the out-of-sample
#' prediction accuracy is the same when using X only vs. X and E as predictors for Y.
#' Defaults to \code{fTestTargetY}.
#' @param colNameNoSmooth Gam parameter: Name of variables that should enter linearly into the model.
#' Defaults to \code{NULL}.
#' @param mtry Random forest parameter: Number of variables randomly sampled as
#' candidates at each split. Defaults to \code{sqrt(NCOL(X))}.
#' @param ntree Random forest parameter: Number of trees to grow. Defaults to 100.
#' @param nodesize Random forest parameter: Minimum size of terminal nodes. Defaults to 5.
#' @param maxnodes Random forest parameter: Maximum number of terminal nodes trees in the forest can have.
#' Defaults to NULL.
#' @param permute Random forest parameter: If \code{TRUE}, model that would use X only
#' for predicting Y also includes a random permutation of E. Defaults to \code{TRUE}.
#' @param returnModel If \code{TRUE}, the fitted quantile regression forest model
#' will be returned. Defaults to \code{FALSE}.
#'
#' @return A list with the following entries:
#' \itemize{
#' \item \code{pvalue} The p-value for the null hypothesis that Y and E are independent given X.
#' \item \code{model} The fitted models if \code{returnModel = TRUE}.
#' }
#'
#' @examples
#' # Example 1
#' n <- 1000
#' E <- rbinom(n, size = 1, prob = 0.2)
#' X <- 4 + 2 * E + rnorm(n)
#' Y <- 3 * (X)^2 + rnorm(n)
#' InvariantTargetPrediction(Y, as.factor(E), X)
#' InvariantTargetPrediction(Y, as.factor(E), X, test = wilcoxTestTargetY)
#'
#' # Example 2
#' E <- rbinom(n, size = 1, prob = 0.2)
#' X <- 4 + 2 * E + rnorm(n)
#' Y <- 3 * E + rnorm(n)
#' InvariantTargetPrediction(Y, as.factor(E), X)
#' InvariantTargetPrediction(Y, as.factor(E), X, test = wilcoxTestTargetY)
#'
#' # Example 3
#' E <- rnorm(n)
#' X <- 4 + 2 * E + rnorm(n)
#' Y <- 3 * (X)^2 + rnorm(n)
#' InvariantTargetPrediction(Y, E, X)
#' InvariantTargetPrediction(Y, X, E)
#' InvariantTargetPrediction(Y, E, X, test = wilcoxTestTargetY)
#' InvariantTargetPrediction(Y, X, E, test = wilcoxTestTargetY)
InvariantTargetPrediction <- function(Y, E, X,
alpha = 0.05,
verbose = FALSE,
fitWithGam = TRUE,
trainTestSplitFunc = caTools::sample.split,
argsTrainTestSplitFunc = NULL,
test = fTestTargetY,
colNameNoSmooth = NULL,
mtry = sqrt(NCOL(X)),
ntree = 100,
nodesize = 5,
maxnodes = NULL,
permute = TRUE,
returnModel = FALSE
){
Y <- check_input_single(Y, return_vec = TRUE)
E <- check_input_single(E, check_factor = TRUE)
X <- check_input_single(X, return_vec = FALSE)
if(is.null(argsTrainTestSplitFunc)){
if(is.data.frame(E) | is.matrix(E)){
argsTrainTestSplitFunc <- list(Y = E[,1], SplitRatio = 0.8)
}else{
argsTrainTestSplitFunc <- list(Y = E, SplitRatio = 0.8)
}
}
n <- NROW(X)
p <- NCOL(X)
trainInd <- do.call(trainTestSplitFunc, argsTrainTestSplitFunc)
testInd <- which(!trainInd)
trainInd <- which(trainInd)
if(verbose)
cat(paste("\nUsing ", length(trainInd), "samples for training;", length(testInd),
"samples for testing."))
if(fitWithGam){
res <- gamTargetY(X, Y, E, trainInd, testInd, verbose, colNameNoSmooth, returnModel)
}else{
res <- rfTargetY(X, Y, E, trainInd, testInd, verbose, mtry, ntree, nodesize, maxnodes, permute, returnModel)
}
# test whether performance is statistically indistinguishable
# dfs: larger model: p + env. var. + intercept
dimE <- NCOL(E)
if(NCOL(X) == 1 & all(X == 1)){
df <- 1+dimE
}else{
df <- p+1+dimE
}
result <- test(Y[testInd], res$predictedOnlyX, res$predictedXE, verbose, df = df, dimE = dimE)
# reject if using X and E has significantly better accuracy than using X only
if(verbose) cat(paste("\nMSE only X :", round(mean((Y[testInd] - res$predictedOnlyX)^2), 2),
"\nMSE with X and E:", round(mean((Y[testInd] - res$predictedXE)^2), 2)))
if(returnModel){
result$model <- res$model
}
result
}
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