CondIndTests (version 0.1.5)

ResidualPredictionTest: Residual prediction test.

Description

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

Usage

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.

Value

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

# NOT RUN {
# 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)
# }