rackauskas_zuokas {skedastic}

Rackauskas-Zuokas Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the two methods of Rackauskas and Zuokas (2007) for testing for heteroskedasticity in a linear regression model.

Usage

rackauskas_zuokas(
  mainlm,
  alpha = 0,
  pvalmethod = c("data", "sim"),
  R = 2^14,
  m = 2^17,
  sqZ = FALSE,
  seed = 1234,
  statonly = FALSE
)

Arguments

mainlm

Either an object of class "lm" (e.g., generated by lm), or a list of two objects: a response vector and a design matrix. The objects are assumed to be in that order, unless they are given the names "X" and "y" to distinguish them. The design matrix passed in a list must begin with a column of ones if an intercept is to be included in the linear model. The design matrix passed in a list should not contain factors, as all columns are treated 'as is'. For tests that use ordinary least squares residuals, one can also pass a vector of residuals in the list, which should either be the third object or be named "e".

alpha

A double such that 0 \le \alpha < 1/2; a hyperparameter of the test. Defaults to 0.

pvalmethod

A character, either "data" or "sim", determining which method to use to compute the empirical p-value. If "data", the dataset T_alpha consisting of pre-generated Monte Carlo replicates from the asymptotic null distribution of the test statistic is loaded and used to compute empirical p-value. This is only available for certain values of alpha, namely i/32 where i=0,1,\ldots,15. If "sim", Monte Carlo replicates are generated from the asymptotic null distribution. Partial matching is used.

R

An integer representing the number of Monte Carlo replicates to generate, if pvalmethod == "sim". Ignored if pvalmethod == "data".

m

An integer representing the number of standard normal variates to use when generating the Brownian Bridge for each replicate, if pvalmethod == "sim". Ignored if pvalmethod == "data". If number of observations is small, Rackauskas and Zuokas (2007) recommends using m=n. The dataset T_alpha used m=2^17 which is computationally intensive.

sqZ

A logical. If TRUE, the standard normal variates used in the Brownian Bridge when generating from the asymptotic null distribution are first squared, i.e. transformed to \chi^2(1) variates. This is recommended by Rackauskas and Zuokas (2007) when the number of observations is small. Ignored if pvalmethod == "data".

seed

An integer representing the seed to be used for pseudorandom number generation when simulating values from the asymptotic null distribution. This is to provide reproducibility of test results. Ignored if pvalmethod == "data". If user does not wish to set the seed, pass NA.

statonly

A logical. If TRUE, only the test statistic value is returned, instead of an object of class "htest". Defaults to FALSE.

Details

Rackauskas and Zuokas propose a class of tests that entails determining the largest weighted difference in variance of estimated error. The asymptotic behaviour of their test statistic T_{n,\alpha} is studied using the empirical polygonal process constructed from partial sums of the squared residuals. The test is right-tailed.

Value

An object of class "htest". If object is not assigned, its attributes are displayed in the console as a tibble using tidy.

References

Rackauskas A, Zuokas D (2007). “New Tests of Heteroskedasticity in Linear Regression Model.” Lithuanian Mathematical Journal, 47(3), 248–265.

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
rackauskas_zuokas(mtcars_lm)
rackauskas_zuokas(mtcars_lm, alpha = 7 / 16)

n <- length(mtcars_lm$residuals)
rackauskas_zuokas(mtcars_lm, pvalmethod = "sim", m = n, sqZ = TRUE)