ResidualPredictionTest function

Residual prediction test.

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

ResidualPredictionTest(Y, E, X, alpha = 0.05, verbose = FALSE,
  degree = 4, basis = c("nystrom", "nystrom_poly", "fourier",
  "polynomial", "provided")[1], resid_type = "OLS", XBasis = NULL,
  noiseMat = NULL, getnoiseFct = function(n, ...) {     rnorm(n) },
  argsGetNoiseFct = NULL, nSim = 100, funcOfRes = function(x) {    
  abs(x) }, useX = TRUE, returnXBasis = FALSE,
  nSub = ceiling(NROW(X)/4), ntree = 100, nodesize = 5,
  maxnodes = NULL)

Arguments

• Y: An n-dimensional vector.
• E: An n-dimensional vector or an nxq dimensional matrix or dataframe.
• 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.
• degree: Degree of polynomial to use if basis="polynomial" or basis="nystrom_poly". Defaults to 4.
• basis: Can be one of "nystrom","nystrom_poly","fourier","polynomial","provided". Defaults to "nystrom".
• resid_type: Can be "Lasso" or "OLS". Defaults to "OLS".
• XBasis: Basis if basis="provided". Defaults to NULL.
• noiseMat: Matrix with simulated noise. Defaults to NULL in which case the simulation is performed inside the function.
• getnoiseFct: Function to use to generate the noise matrix. Defaults to function(n, ...){rnorm(n)}.
• argsGetNoiseFct: Arguments for getnoiseFct. Defaults to NULL.
• nSim: Number of simulations to use. Defaults to 100.
• funcOfRes: Function of residuals to use in addition to predicting the conditional mean. Defaults to function(x){abs(x)}.
• useX: Set to TRUE if the predictors in X should also be used when predicting the scaled residuals with E. Defaults to TRUE.
• returnXBasis: Set to TRUE if basis expansion should be returned. Defaults to FALSE.
• nSub: Number of random features to use if basis is one of "nystrom","nystrom_poly" or "fourier". Defaults to ceiling(NROW(X)/4).
• ntree: Random forest parameter: Number of trees to grow. Defaults to 500.
• 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.

Returns

A list with the following entries:

• pvalue The p-value for the null hypothesis that Y and E are independent given X.
• XBasis Basis expansion if returnXBasis was set to TRUE.
• fctBasisExpansion Function used to create basis expansion if basis is not "provided".

Examples

# Example 1
n <- 100
E <- rbinom(n, size = 1, prob = 0.2)
X <- 4 + 2 * E + rnorm(n)
Y <- 3 * (X)^2 + rnorm(n)
ResidualPredictionTest(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)
ResidualPredictionTest(Y, as.factor(E), X)

# not run:
# # Example 3
# E <- rnorm(n)
# X <- 4 + 2 * E + rnorm(n)
# Y <- 3 * (X)^2 + rnorm(n)
# ResidualPredictionTest(Y, E, X)
# ResidualPredictionTest(Y, X, E)