This function implements the method of Bickel78;textualskedastic for testing for heteroskedasticity in a linear regression model, with or without the scale-invariance modification of Carroll81;textualskedastic.
bickel(
mainlm,
fitmethod = c("lm", "rlm"),
a = "identity",
b = c("hubersq", "tanhsq"),
scale_invariant = TRUE,
k = 1.345,
statonly = FALSE,
...
)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".
A character indicating the method to be used to fit the
regression model. This can be "OLS" for ordinary least squares (the
default) or "robust" in which case a robust fitting method is called
from rlm.
A character argument specifying the name of a function to be
applied to the fitted values, or an integer \(m\) in which case the
function applied is \(f(x) = x^m\). Defaults to "identity" for
identity.
A character argument specifying a function to be applied to the
residuals. Defaults to Huber's function squared, as recommended by
Carroll81;textualskedastic. Currently the only supported
functions are "hubersq" (for Huber's function squared) and
"tanhsq" (for \(b(x)=\mathrm{tanh}(x)^2\).)
A logical indicating whether the scale-invariance
modification proposed by Carroll81;textualskedastic
should be implemented. Defaults to TRUE.
A double argument specifying a parameter for Huber's function
squared; used only if b == "hubersq". This is not to be confused
with the argument k2 that could be passed to
rlm if the regression is fitted using robust methods.
k defaults to 1.345.
A logical. If TRUE, only the test statistic value
is returned, instead of an object of class
"htest". Defaults to FALSE.
Optional arguments to be passed to rlm
An object of class "htest". If object is
not assigned, its attributes are displayed in the console as a
tibble using tidy.
Bickel's Test is a robust extension of Anscombe's Test Anscombe61skedastic in which the OLS residuals and estimated standard error are replaced with an \(M\) estimator. Under the null hypothesis of homoskedasticity, the distribution of the test statistic is asymptotically standard normally distributed. The test is two-tailed.
discussions of this test in Carroll81;textualskedastic and Ali84;textualskedastic.
# NOT RUN {
mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
bickel(mtcars_lm)
bickel(mtcars_lm, fitmethod = "rlm")
bickel(mtcars_lm, scale_invariant = FALSE)
# }
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