InvariantEnvironmentPrediction function

Invariant environment prediction.

Tests the null hypothesis that Y and E are independent given X.

InvariantEnvironmentPrediction(Y, E, X, alpha = 0.05, verbose = FALSE,
  trainTestSplitFunc = caTools::sample.split,
  argsTrainTestSplitFunc = list(Y = E, SplitRatio = 0.8),
  test = propTestTargetE, mtry = sqrt(NCOL(X)), ntree = 100,
  nodesize = 5, maxnodes = NULL, permute = TRUE,
  returnModel = FALSE)

Arguments

• Y: An n-dimensional vector.
• E: An n-dimensional vector. If test = propTestTargetE, E needs to be a factor.
• X: A matrix or dataframe with n rows and p columns.
• alpha: Significance level. Defaults to 0.05.
• verbose: If TRUE, intermediate output is provided. Defaults to FALSE.
• trainTestSplitFunc: Function to split sample. Defaults to stratified sampling using caTools::sample.split, assuming E is a factor.
• argsTrainTestSplitFunc: Arguments for sampling splitting function.
• test: Unconditional independence test that tests whether the out-of-sample prediction accuracy is the same when using X only vs. X and Y as predictors for E. Defaults to propTestTargetE.
• mtry: Random forest parameter: Number of variables randomly sampled as candidates at each split. Defaults to sqrt(NCOL(X)).
• ntree: Random forest parameter: Number of trees to grow. Defaults to 100.
• nodesize: Random forest parameter: Minimum size of terminal nodes. Defaults to 5.
• maxnodes: Random forest parameter: Maximum number of terminal nodes trees in the forest can have. Defaults to NULL.
• permute: Random forest parameter: If TRUE, model that would use X only for predicting Y also includes a random permutation of E. Defaults to TRUE.
• returnModel: If TRUE, the fitted quantile regression forest model will be returned. Defaults to FALSE.

Returns

A list with the following entries:

• pvalue The p-value for the null hypothesis that Y and E are independent given X.
• model The fitted models if 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)
InvariantEnvironmentPrediction(Y, as.factor(E), X)

# Example 2
E <- rbinom(n, size = 1, prob = 0.2)
X <- 4 + 2 * E + rnorm(n)
Y <- 3 * E + rnorm(n)
InvariantEnvironmentPrediction(Y, as.factor(E), X)

# Example 3
E <- rnorm(n)
X <- 4 + 2 * E + rnorm(n)
Y <- 3 * (X)^2 + rnorm(n)
InvariantEnvironmentPrediction(Y, E, X, test = wilcoxTestTargetY)
InvariantEnvironmentPrediction(Y, X, E, test = wilcoxTestTargetY)