High-dimensional projection heteroscedasticity test

Source: R/modern_diagnostics.R · Help: ?performHighDimensionalTest

Applies principal component projections to the design matrix and evaluates a Breusch-Pagan style statistic on the reduced representation. The procedure is designed for settings where the number of predictors rivals or exceeds the sample size.

Usage

performHighDimensionalTest(
  model,
  data = NULL,
  variance_threshold = 0.9,
  max_components = NULL
)

Arguments

model

A fitted stats::lm object describing the mean structure whose residual variance is to be assessed.

data

A base::data.frame (or compatible object) containing the variables referenced in model. The data must include all observations used to fit model and should not contain unresolved missing values. When NULL, the default, the model frame of model is used. It holds the terms of the model rather than its variables (log(x) rather than x), so a model that transforms a variable needs data, as does a model with an offset() term, and so may a fit whose weights or offset argument is a column of the data, which the model frame holds as (weights) or (offset).

variance_threshold

Proportion of predictor variance that the selected principal components should explain. Defaults to 0.9.

max_components

Optional upper bound on the number of principal components to retain. Defaults to min(10, n - 5).

Value

An htest object summarising the chi-squared statistic of the auxiliary regression on principal component scores.

References

Fan, J., & Lv, J. (2008). Sure independence screening for ultrahigh dimensional feature space. Journal of the Royal Statistical Society: Series B, 70(5), 849–911.

Examples

set.seed(123)
X <- matrix(rnorm(80 * 20), nrow = 80)
beta <- c(rep(1, 5), rep(0, 15))
y <- X %*% beta + rnorm(80, sd = 0.5 + 0.2 * scale(X[, 1]))
df <- as.data.frame(cbind(y = as.numeric(y), X))
model <- lm(y ~ ., data = df)
performHighDimensionalTest(model, df)