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.

```
# Install from CRAN
install.packages("skedastic", dependencies = c("Depends", "Imports"))
# Or the development version from GitHub:
install.packages("devtools")
::install_github("tjfarrar/skedastic") devtools
```

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)
<- lm(dist ~ speed, data = cars)
mylm breusch_pagan(mylm)
```

To compute BLUS residuals for the same model:

```
<- blus(mylm, omit = "last")
myblusres 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:

```
<- alvm.fit(mylm, model = "linear")
myalvm $var.est myalvm
```

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:

```
<- anlvm.fit(mylm, g = function(x) x ^ 2)
myanlvm $var.est mynalvm
```

No vignettes have been created yet for this package. Watch this space.