ResidualPredictionTest {CondIndTests} R Documentation

## 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

```# 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)
```

[Package CondIndTests version 0.1.5 Index]