honda {skedastic}

Honda's Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the two-sided LM Test of Honda (1989) for testing for heteroskedasticity in a linear regression model.

Usage

honda(
  mainlm,
  deflator = NA,
  alternative = c("two.sided", "greater", "less"),
  twosidedmethod = c("doubled", "kulinskaya"),
  qfmethod = "imhof",
  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".

deflator

Either a character specifying a column name from the design matrix of mainlm or an integer giving the index of a column of the design matrix. This variable is suspected to be related to the error variance under the alternative hypothesis. deflator may not correspond to a column of 1's (intercept). Default NA means the data will be left in its current order (e.g. in case the existing index is believed to be associated with error variance).

alternative

A character specifying the form of alternative hypothesis. If it is suspected that the error variance is positively associated with the deflator variable, "greater". If it is suspected that the error variance is negatively associated with deflator variable, "less". If no information is available on the suspected direction of the association, "two.sided". Defaults to "greater".

twosidedmethod

A character indicating the method to be used to compute two-sided p-values for the parametric test when alternative is "two.sided". The argument is passed to twosidedpval as its method argument.

qfmethod

A character, either "imhof", "davies", or "integrate", corresponding to the algorithm argument of pRQF. The default is "imhof".

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 assumes that heteroskedasticity, if present, would be either of the form \omega_i = \omega(1+\theta z_i) or of the form \omega_i = \omega e^{\theta z_i}, where where z_i is a deflator (a nonstochastic variable suspected of being related to the error variance), \omega is some unknown constant, and \theta is an unknown parameter representing the degree of heteroskedasticity. Since the test statistic Q=\frac{e' A_0 e}{e'e} is a ratio of quadratic forms in the errors, the Imhof algorithm is used to compute p-values. Since the null distribution is in general asymmetrical, the two-sided p-value is computed using the conditional method of Kulinskaya (2008), setting A=1.

Value

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

References

Honda Y (1989). “On the Optimality of Some Tests of the Error Covariance Matrix in the Linear Regression Model.” Journal of the Royal Statistical Society. Series B (Statistical Methodology), 51(1), 71–79.

Kulinskaya E (2008). “On Two-Sided p-Values for Non-Symmetric Distributions.” 0810.2124, 0810.2124.

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
# In this example, only the test statistic is returned, to save time
honda(mtcars_lm, deflator = "qsec", statonly = TRUE)