This function implements the method of Godfrey99;textualskedastic for testing for heteroskedasticity in a linear regression model. The procedure is more clearly described in Godfrey06;textualskedastic.
godfrey_orme(
mainlm,
hettest,
B = 1000L,
alternative = c("greater", "less", "two.sided"),
seed = 1234,
...
)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 specifying the name of a function
that implements a heteroskedasticity test on a linear regression model.
The function is called with the statonly argument set to
TRUE to improve computational efficiency.
An integer specifying the number of nonparametric bootstrap samples
to generate. Defaults to 1000L.
The tailedness of the test whose statistic is computed by
hettest function; one of "greater" (the default),
"less", or "two.sided".
An integer specifying a seed to pass to
set.seed for random number generation. This allows
reproducibility of bootstrap results. A value of NA
results in not setting a seed.
Additional arguments to pass to function with name hettest
An object of class "htest". If object
is not assigned, its attributes are displayed in the console as a
tibble using tidy.
The procedure runs as follows. (1) The observed
value of the test statistic \(T_0\) is computed using function with
name hettest. (2) A sample
\(e_1^\star,e_2^\star,\ldots,e_n^\star\) is drawn with replacement from
the OLS residuals. (3) Bootstrapped response values are computed as
\(y_i^{\star}=x_i' \hat{\beta}+e_i^\star,i=1,2,\ldots,n\).
(4) Bootstrapped test statistic value \(T^\star\) is computed from the
regression of \(y^\star\) on \(X\) using function hettest.
(5) Steps (2)-(4) are repeated until \(B\) bootstrapped test statistic
values are computed. (6) Empirical \(p\)-value is computed by comparing
the bootstrapped test statistic values to the observed test statistic
value. Note that, if alternative is set to "two.sided", the
one-sided \(p\)-value is doubled (twosidedpval cannot
be used in this case).
# NOT RUN {
mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
godfrey_orme(mtcars_lm, hettest = "breusch_pagan")
# }
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