verbyla {skedastic}

Verbyla's Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the residual maximum likelihood test of Verbyla (1993) for testing for heteroskedasticity in a linear regression model.

Usage

verbyla(mainlm, auxdesign = NA, 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.

statonly

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

Details

Verbyla's Test entails fitting a generalised auxiliary regression model in which the response variable is the vector of standardised squared residuals e_i^2/\hat{\omega} from the original OLS model and the design matrix is some function of Z, an n \times q matrix consisting of q exogenous variables, appended to a column of ones. The test statistic is half the residual sum of squares from this generalised auxiliary regression. Under the null hypothesis of homoskedasticity, the distribution of the test statistic is asymptotically chi-squared with q 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

Verbyla AP (1993). “Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics.” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 55(2), 493–508.

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
verbyla(mtcars_lm)
verbyla(mtcars_lm, auxdesign = "fitted.values")