skedastic (version 1.0.0)

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
)

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 default 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.

Value

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

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

# NOT RUN {
mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
diblasi_bowman(mtcars_lm)
# }
# NOT RUN {
diblasi_bowman(mtcars_lm, ignorecov = FALSE)
# }
# NOT RUN {
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)

# }