zhou_etal {skedastic}

Zhou, Song, and Thompson's Test for Heteroskedasticity in a Linear Regression Model

Description

This function implements the methods of Zhou et al. (2015) for testing for heteroskedasticity in a linear regression model.

Usage

zhou_etal(
  mainlm,
  auxdesign = NA,
  method = c("pooled", "covariate-specific", "hybrid"),
  Bperturbed = 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".

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.

method

A character specifying which of the three test methods to implement; one of "pooled", "covariate-specific", or "hybrid" (which combines the other two). Partial matching is used.

Bperturbed

An integer specifying the number of perturbation samples to generate when estimating the p-value. Defaults to 500L.

seed

An integer specifying a seed to pass to set.seed for random number generation. This allows for reproducibility of perturbation sampling. A value of 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

Zhou et al. (2015) The authors propose three variations based on comparisons between sandwich and model-based estimators for the variances of individual regression coefficient esimators. The covariate-specific method computes a test statistic and p-value for each column of the auxiliary design matrix (which is, by default, the original design matrix with intercept omitted). The p-values undergo a Bonferroni correction to control overall test size. When the null hypothesis is rejected in this case, it also provides information about which auxiliary design variable is associated with the error variance. The pooled method computes a single test statistic and p-value and is thus an omnibus test. The hybrid method returns the minimum p-value between the Bonferroni-corrected covariate-specific p-values and the pooled p-value, multiplying it by 2 for a further Bonferroni correction. The test statistic returned is that which corresponds to the minimum p-value. The covariate-specific and pooled test statistics have null distributions that are asymptotically normal with mean 0. However, the variance is intractable and thus perturbation sampling is used to compute p-values empirically.

Value

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

References

Zhou QM, Song PX, Thompson ME (2015). “Profiling Heteroscedasticity in Linear Regression Models.” The Canadian Journal of Statistics, 43(3), 358–377.

Examples

mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
zhou_etal(mtcars_lm, method = "pooled")
zhou_etal(mtcars_lm, method = "covariate-specific")
zhou_etal(mtcars_lm, method = "hybrid")