This function implements the popular method of Breusch79;textualskedastic for testing for heteroskedasticity in a linear regression model, with or without the studentising modification of Koenker81;textualskedastic.
breusch_pagan(mainlm, auxdesign = NA, koenker = TRUE, 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 data.frame or
matrix representing an auxiliary design matrix of
containing exogenous variables that (under alternative hypothesis) are
related to error variance, or a character "fitted.values" indicating
that the fitted \(\hat{y}_i\) values from OLS should be used.
If set to NA (the default), the
design matrix of the original regression model is used. An intercept
is included in the auxiliary regression even if the first column of
auxdesign is not a vector of ones.
A logical. Should studentising modification of
Koenker81;textualskedastic be implemented? Defaults to
TRUE; if FALSE, the original form of the test proposed by
Breusch79;textualskedastic is used.
A logical. If TRUE, only the test statistic value
is returned, instead of an object of class
"htest". Defaults to FALSE.
An object of class "htest". If object
is not assigned, its attributes are displayed in the console as a
tibble using tidy.
The Breusch-Pagan Test entails fitting an auxiliary regression model in
which the response variable is the vector of squared residuals from the
original model and the design matrix \(Z\) consists of one or more
exogenous variables that are suspected of being related to the error
variance. In the absence of prior information on a possible choice of
\(Z\), one would typically use the explanatory variables from the
original model. Under the null hypothesis of homoskedasticity, the
distribution of the test statistic is asymptotically chi-squared with
parameter degrees of freedom. The test is right-tailed.
lmtest::bptest, which performs exactly
the same test as this function; car::ncvTest,
which is not the same test but is implemented in
cook_weisberg; white_lm, which is a special
case of the Breusch-Pagan Test.
# NOT RUN {
mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
breusch_pagan(mtcars_lm)
breusch_pagan(mtcars_lm, koenker = FALSE)
# Same as first example
mtcars_list <- list("y" = mtcars$mpg, "X" = cbind(1, mtcars$wt, mtcars$qsec, mtcars$am))
breusch_pagan(mtcars_list)
# }
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