Perform Koenker studentized Breusch-Pagan test

Source: man/performKoenkerTest.Rd · Help: ?performKoenkerTest

Implementation of the Koenker version of the Breusch-Pagan test.

Usage

performKoenkerTest(model, data = NULL)

Arguments

model

an object of class lm.

data

data frame used to fit model. When NULL, the default, the model frame of model is used. It holds the terms of the model rather than its variables (log(x) rather than x), so a model that transforms a variable needs data, as does a model with an offset() term, and so may a fit whose weights or offset argument is a column of the data, which the model frame holds as (weights) or (offset).

Value

An object of class htest containing the test statistic, p-value and degrees of freedom.

Details

Squared residuals are regressed on the regressors but the statistic \(n R^2\) uses a studentized form that is robust to non-normality.

Weighted fits

lm(..., weights = w) states that the error variance is \(\sigma^2 / w_i\). On such a fit the test is computed from the Pearson residuals \(\sqrt{w_i}\, e_i\), the residuals of the equivalent unweighted regression, which have constant variance when the weights are right. The null hypothesis is then that the weights are adequate; the variance regressors stay on their original scale. Releases before 0.12.0 used the raw residuals, whose variance differs across observations by assumption, so a correctly weighted fit was rejected as often as an unweighted one. A fit with a zero weight is refused.

The reference distribution takes the weights as known. When they were estimated from the same data, as by fitWLS(), it is only approximate, and not more accurate in larger samples. With a correctly specified variance function and normal errors, the Koenker test rejected 8% of the time at the 5% level with 150 observations and 11% with 600, the White test 6% and 8%, and the Harvey test never, because it repeats the regression the weights were estimated from (inst/validation/weighted-fits-size.csv). performVarianceFormTest() accounts for the estimation, held its level in the same designs, and is the test to use on a fitWLS() fit.

References

Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17(1), 107–112.

Examples

 data(mtcars)
 m <- lm(mpg ~ wt + qsec, data = mtcars)
 performKoenkerTest(m, mtcars)