Handling Heteroskedasticity in the Linear Regression Model.
skedastic
The purpose of the skedastic package is to make a suite of old and new methods for detecting and correcting for heteroskedasticity in linear regression models accessible to R users.
Installation
# Install from CRAN
install.packages("skedastic", dependencies = c("Depends", "Imports"))
# Or the development version from GitHub:
install.packages("devtools")
devtools::install_github("tjfarrar/skedastic")
Usage
Heteroskedasticity (sometimes spelt 'heteroscedasticity') is a violation of one of the assumptions of the classical linear regression model (the Gauss-Markov Assumptions). This assumption, known as homoskedasticity, holds that the variance of the random error term remains constant across all observations. Under heteroskedasticity, the Ordinary Least Squares estimator is no longer the Best Linear Unbiased Estimator (BLUE) of the parameter vector, while the classical t-tests for testing significance of the parameters are invalid. Thus, heteroskedasticity-robust methods are required.
The most novel functionality of this package is provided by the alvm.fit and anlvm.fit functions, which fit an Auxiliary Linear Variance Model or an Auxiliary Nonlinear Variance Model, respectively. These are new models for estimating error variances in heteroskedastic linear regression models, developed as part of the author's doctoral research.
The hccme function computes heteroskedasticity-consistent covariance matrix estimates for the $\hat{\beta}$ Ordinary Least Squares estimator using ten different methods found in the literature.
25 distinct functions in the package implement hypothesis testing methods for detecting heteroskedasticity that have been previously published in academic literature. Other functions implement graphical methods for detecting heteroskedasticity or perform supporting tasks for the tests such as computing transformations of the Ordinary Least Squares (OLS) residuals that are useful in heteroskedasticity detection, or computing probabilities from the null distribution of a nonparametric test statistic. Certain functions have applications beyond the problem of heteroskedasticity in linear regression. These include pRQF, which computes cumulative probabilities from the distribution of a ratio of quadratic forms in normal random vectors, twosidedpval, which implements three different approaches for calculating two-sided $p$-values from asymmetric null distributions, and dDtrend and pdDtrend, which compute probabilities from Lehmann's nonparametric trend statistic.
Most of the exported functions in the package take a linear model as their primary argument (which can be passed as an lm object). Thus, to use this package a user must first be familiar with how to fit linear regression models using the lm function from package stats.
Here is an example of implementing the Breusch-Pagan Test for heteroskedasticity on a linear regression model fit to the cars dataset, with distance (cars$dist) as the response (dependent) variable and speed (cars$speed) as the explanatory (independent) variable.
library(skedastic)
mylm <- lm(dist ~ speed, data = cars)
breusch_pagan(mylm)
To compute BLUS residuals for the same model:
myblusres <- blus(mylm, omit = "last")
myblusres
To create customised residual plots for the same model:
hetplot(mylm, horzvar = c("explanatory", "log_explanatory"), vertvar = c("res", "res_stud"), vertfun = "2", filetype = NA)
To fit an auxiliary linear variance model to the same linear regression model, assuming that the error variances are a linear function of the speed predictor, and extract the resulting variance estimates:
myalvm <- alvm.fit(mylm, model = "linear")
myalvm$var.est
To fit an auxiliary linear variance model to the same linear regression model, assuming that the error variances are a quadratic function of the speed predictor, and extract the resulting variance estimates:
myanlvm <- anlvm.fit(mylm, g = function(x) x ^ 2)
mynalvm$var.est
Learn More
No vignettes have been created yet for this package. Watch this space.