skedastic (version 1.0.4)

diblasi_bowman: Diblasi and Bowman's Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the nonparametric test of Diblasi97;textualskedastic for testing for heteroskedasticity in a linear regression model.

Usage

diblasi_bowman(
  mainlm,
  distmethod = c("moment.match", "bootstrap"),
  H = 0.08,
  ignorecov = TRUE,
  B = 500L,
  seed = 1234,
  statonly = FALSE
)

Value

An object of class

"htest". If object is not assigned, its attributes are displayed in the console as a

tibble using tidy.

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".

distmethod

A character specifying the method by which to estimate the \(p\)-values, either "moment.match" or "bootstrap".

H

A hyperparameter denoting the bandwidth matrix in the kernel function used for weights in nonparametric smoothing. If a double of length 1 (the default), H is set to \(h I_{p^\prime}\) where \(h\) is the scalar bandwidth value entered and \(I_{p^\prime}\) is the \(p^prime \times p^\prime\) identity matrix (where \(p^\prime\) is the number of columns in the \(X\) matrix, excluding an intercept if present). If a double of length \(p^\prime\), H is set to \(diag(h)\) where \(h\) is the bandwidth vector entered. If H is a \(p^\prime\times p^\prime\) matrix it is used as is. Any other dimensionality of H results in an error.

ignorecov

A logical. If TRUE (the default), the variance-covariance matrix of \(s\) is assumed to be diagonal. (This assumption is, strictly speaking, invalid, but usually yields a reasonable approximation. Computation time is prohibitive for large sample sizes if set to FALSE).

B

An integer specifying the number of nonparametric bootstrap replications to be used, if distmethod="bootstrap".

seed

An integer specifying a seed to pass to set.seed for random number generation. This allows reproducibility of bootstrap results. The value NA results in not setting a seed.

statonly

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

Details

The test entails undertaking a transformation of the OLS residuals \(s_i=\sqrt{|e_i|}-E_0(\sqrt{|e_i|})\), where \(E_0\) denotes expectation under the null hypothesis of homoskedasticity. The kernel method of nonparametric regression is used to fit the relationship between these \(s_i\) and the explanatory variables. This leads to a test statistic \(T\) that is a ratio of quadratic forms involving the vector of \(s_i\) and the matrix of normal kernel weights. Although nonparametric in its method of fitting the possible heteroskedastic relationship, the distributional approximation used to compute \(p\)-values assumes normality of the errors.

References

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
diblasi_bowman(mtcars_lm)
diblasi_bowman(mtcars_lm, ignorecov = FALSE)
diblasi_bowman(mtcars_lm, distmethod = "bootstrap")

# Example discussed in Diblasi and Bowman (1997)
malecats_lm <- lm(Hwt ~ Bwt, data = boot::catsM)
diblasi_bowman(malecats_lm, H = (max(boot::catsM$Bwt) - min(boot::catsM$Bwt)) / 8)