carapeto_holt {skedastic}

Carapeto-Holt Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the two methods (parametric and nonparametric) of Carapeto and Holt (2003) for testing for heteroskedasticity in a linear regression model.

Usage

carapeto_holt(
  mainlm,
  deflator = NA,
  prop_central = 1/3,
  group1prop = 1/2,
  qfmethod = "imhof",
  alternative = c("greater", "less", "two.sided"),
  twosidedmethod = c("doubled", "kulinskaya"),
  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).

prop_central

A double specifying the proportion of central observations to exclude when comparing the two subsets of observations. round is used to ensure the number of central observations is an integer. Defaults to \frac{1}{3}.

group1prop

A double specifying the proportion of remaining observations (after excluding central observations) to allocate to the first group. The default value of 1 / 2 means that an equal number of observations is assigned to the first and second groups.

qfmethod

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

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.

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 is based on the methodology of Goldfeld and Quandt (1965) but does not require any auxiliary regression. It entails ordering the observations by some suspected deflator (one of the explanatory variables) in such a way that, under the alternative hypothesis, the observations would now be arranged in decreasing order of error variance. A specified proportion of the most central observations (under this ordering) is removed, leaving a subset of lower observations and a subset of upper observations. The test statistic is then computed as a ratio of quadratic forms corresponding to the sums of squared residuals of the upper and lower observations respectively. p-values are computed by the Imhof algorithm in pRQF.

Value

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

References

Carapeto M, Holt W (2003). “Testing for Heteroscedasticity in Regression Models.” Journal of Applied Statistics, 30(1), 13–20.

Goldfeld SM, Quandt RE (1965). “Some Tests for Homoscedasticity.” Journal of the American Statistical Association, 60(310), 539–547.

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
carapeto_holt(mtcars_lm, deflator = "qsec", prop_central = 0.25)
# Same as previous example
mtcars_list <- list("y" = mtcars$mpg, "X" = cbind(1, mtcars$wt, mtcars$qsec, mtcars$am))
carapeto_holt(mtcars_list, deflator = 3, prop_central = 0.25)