rackauskas_zuokas | R Documentation |
Rackauskas-Zuokas Test for Heteroskedasticity in a Linear Regression Model
Description
This function implements the two methods of
\insertCiteRackauskas07;textualskedastic 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,
\insertCiteRackauskas07;textualskedastic 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
\insertCiteRackauskas07;textualskedastic 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
\insertAllCited
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)