glejser {skedastic}

Glejser Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the method of Glejser (1969) for testing for "multiplicative" heteroskedasticity in a linear regression model. Mittelhammer et al. (2000) gives the formulation of the test used here.

Usage

glejser(
  mainlm,
  auxdesign = NA,
  sigmaest = c("main", "auxiliary"),
  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".

auxdesign

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.

sigmaest

A character indicating which model residuals to use in the \hat{\omega} estimator in the denominator of the test statistic. If "main" (the default), the OLS residuals from the original model are used; this produces results identical to the Glejser Test in SHAZAM software. If "auxiliary", the OLS residuals from the auxiliary model are used, as in Mittelhammer et al. (2000). Partial matching is used.

statonly

A logical. If TRUE, only the test statistic value is returned, instead of an object of class "htest". Defaults to FALSE.

Details

Glejser's Test entails fitting an auxiliary regression model in which the response variable is the absolute residual 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.

Value

An object of class "htest". If object is not assigned, its attributes are displayed in the console as a tibble using tidy.

References

Glejser H (1969). “A New Test for Heteroskedasticity.” Journal of the American Statistical Association, 64(325), 316–323.

Mittelhammer RC, Judge GG, Miller DJ (2000). Econometric Foundations. Cambridge University Press, Cambridge.

See Also

the description of the test in SHAZAM software (which produces identical results).

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
glejser(mtcars_lm)