cook_weisberg

This function implements the score test of
 Cook83;textualskedastic for testing for heteroskedasticity
 in a linear regression model.

Implements numerous methods for testing for, modelling, and
correcting for heteroskedasticity in the classical linear regression
model. The most novel contribution of the
package is found in the functions that implement the as-yet-unpublished
auxiliary linear variance models and auxiliary nonlinear variance
models that are designed to estimate error variances in a heteroskedastic
linear regression model. These models follow principles of statistical
learning described in Hastie (2009) <doi:10.1007/978-0-387-21606-5>.
The nonlinear version of the model is estimated using quasi-likelihood
methods as described in Seber and Wild (2003, ISBN: 0-471-47135-6).
Bootstrap methods for approximate confidence intervals for error variances
are implemented as described in Efron and Tibshirani
(1993, ISBN: 978-1-4899-4541-9), including also the expansion technique
described in Hesterberg (2014) <doi:10.1080/00031305.2015.1089789>. The
wild bootstrap employed here follows the description in Davidson and
Flachaire (2008) <doi:10.1016/j.jeconom.2008.08.003>. Tuning of
hyper-parameters makes use of a golden section search function that is
modelled after the MATLAB function of Zarnowiec (2022)
<https://www.mathworks.com/matlabcentral/fileexchange/25919-golden-section-method-algorithm>.
A methodological description of the algorithm can be found in Fox (2021,
ISBN: 978-1-003-00957-3).
There are 25 different functions that implement hypothesis tests for
heteroskedasticity. These include a test based on Anscombe (1961)
<https://projecteuclid.org/euclid.bsmsp/1200512155>, Ramsey's (1969)
BAMSET Test <doi:10.1111/j.2517-6161.1969.tb00796.x>, the tests of Bickel
(1978) <doi:10.1214/aos/1176344124>, Breusch and Pagan (1979)
<doi:10.2307/1911963> with and without the modification
proposed by Koenker (1981) <doi:10.1016/0304-4076(81)90062-2>, Carapeto and
Holt (2003) <doi:10.1080/0266476022000018475>, Cook and Weisberg (1983)
<doi:10.1093/biomet/70.1.1> (including their graphical methods), Diblasi
and Bowman (1997) <doi:10.1016/S0167-7152(96)00115-0>, Dufour, Khalaf,
Bernard, and Genest (2004) <doi:10.1016/j.jeconom.2003.10.024>, Evans and
King (1985) <doi:10.1016/0304-4076(85)90085-5> and Evans and King (1988)
<doi:10.1016/0304-4076(88)90006-1>, Glejser (1969)
<doi:10.1080/01621459.1969.10500976> as formulated by
Mittelhammer, Judge and Miller (2000, ISBN: 0-521-62394-4), Godfrey and
Orme (1999) <doi:10.1080/07474939908800438>, Goldfeld and Quandt
(1965) <doi:10.1080/01621459.1965.10480811>, Harrison and McCabe (1979)
<doi:10.1080/01621459.1979.10482544>, Harvey (1976) <doi:10.2307/1913974>,
Honda (1989) <doi:10.1111/j.2517-6161.1989.tb01749.x>, Horn (1981)
<doi:10.1080/03610928108828074>, Li and Yao (2019)
<doi:10.1016/j.ecosta.2018.01.001> with and without the modification of
Bai, Pan, and Yin (2016) <doi:10.1007/s11749-017-0575-x>, Rackauskas and
Zuokas (2007) <doi:10.1007/s10986-007-0018-6>, Simonoff and Tsai (1994)
<doi:10.2307/2986026> with and without the modification of Ferrari,
Cysneiros, and Cribari-Neto (2004) <doi:10.1016/S0378-3758(03)00210-6>,
Szroeter (1978) <doi:10.2307/1913831>, Verbyla (1993)
<doi:10.1111/j.2517-6161.1993.tb01918.x>, White (1980)
<doi:10.2307/1912934>, Wilcox and Keselman (2006)
<doi:10.1080/10629360500107923>, Yuce (2008)
<https://dergipark.org.tr/en/pub/iuekois/issue/8989/112070>, and Zhou,
Song, and Thompson (2015) <doi:10.1002/cjs.11252>. Besides these
heteroskedasticity tests, there are supporting functions that compute the
BLUS residuals of Theil (1965) <doi:10.1080/01621459.1965.10480851>, the
conditional two-sided p-values of Kulinskaya (2008) <doi:10.48550/arXiv.0810.2124>,
and probabilities for the nonparametric trend statistic of Lehmann (1975,
ISBN: 0-816-24996-1). For handling heteroskedasticity, in addition to the
new auxiliary variance model methods, there is a function
to implement various existing Heteroskedasticity-Consistent Covariance
Matrix Estimators from the literature, such as those of White (1980)
<doi:10.2307/1912934>, MacKinnon and White (1985)
<doi:10.1016/0304-4076(85)90158-7>, Cribari-Neto (2004)
<doi:10.1016/S0167-9473(02)00366-3>, Cribari-Neto et al. (2007)
<doi:10.1080/03610920601126589>, Cribari-Neto and da Silva (2011)
<doi:10.1007/s10182-010-0141-2>, Aftab and Chang (2016)
<doi:10.18187/pjsor.v12i2.983>, and Li et al. (2017)
<doi:10.1080/00949655.2016.1198906>.

Thomas Farrar

skedastic

Handling Heteroskedasticity in the Linear Regression Model

University of the Western Cape 

cook_weisberg function

<dl><dt>mainlm</dt>
<dd>Either an object of <code><a href="/link/class?package=skedastic&version=2.0.3" data-mini-rdoc="skedastic::class">class</a></code> <code>"lm"</code>
(e.g., generated by <code><a href="/link/lm?package=skedastic&version=2.0.3" data-mini-rdoc="skedastic::lm">lm</a></code>), 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
<code>"X"</code> and <code>"y"</code> 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 <code>"e"</code>.</dd>
<dt>auxdesign</dt>
<dd>A <code><a href="/link/data.frame?package=skedastic&version=2.0.3" data-mini-rdoc="skedastic::data.frame">data.frame</a></code> or
<code><a href="/link/matrix?package=skedastic&version=2.0.3" data-mini-rdoc="skedastic::matrix">matrix</a></code> 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 <code>NA</code> (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
<code>auxdesign</code> is not a vector of ones.</dd>
<dt>hetfun</dt>
<dd>A character describing the form of \(w(\cdot)\), the error
variance function under the heteroskedastic alternative. Possible values
are <code>"mult"</code> (the default), corresponding to
\(w(Z_i,\lambda)=\exp\left\{\sum_{j=1}^{q}\lambda_j Z_{ij}\right\}\),
<code>"add"</code>, corresponding to
\(w(Z_i,\lambda)=\left(1+\sum_{j=1}^{q} \lambda_j Z_{ij}\right)^2\), and
<code>"logmult"</code>, corresponding to
\(w(Z_i,\lambda)=\exp\left\{\sum_{j=1}^{q}\lambda_j \log Z_{ij}\right\}\).
The multiplicative and log-multiplicative cases are considered in
Cook83;textualskedastic; the additive case is discussed,
inter alia, by Griffiths86;textualskedastic.
Results for the additive and multiplicative models are identical for this
test. Partial matching is used.</dd>
<dt>statonly</dt>
<dd>A logical. If <code>TRUE</code>, only the test statistic value
is returned, instead of an object of <code><a href="/link/class?package=skedastic&version=2.0.3" data-mini-rdoc="skedastic::class">class</a></code>
<code>"htest"</code>. Defaults to <code>FALSE</code>.</dd></dl>

Arguments

Cook-Weisberg Score Test for Heteroskedasticity in a Linear Regression Model — cook_weisberg

<dl>

<dt>mainlm</dt>
<dd>Either an object of <code><a href='https://rdrr.io/r/base/class.html'>class</a></code> <code>"lm"</code>
(e.g., generated by <code><a href='https://rdrr.io/r/stats/lm.html'>lm</a></code>), 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
<code>"X"</code> and <code>"y"</code> 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 <code>"e"</code>.</dd>


<dt>auxdesign</dt>
<dd>A <code><a href='https://rdrr.io/r/base/data.frame.html'>data.frame</a></code> or
<code><a href='https://rdrr.io/r/base/matrix.html'>matrix</a></code> 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 <code>NA</code> (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
<code>auxdesign</code> is not a vector of ones.</dd>


<dt>hetfun</dt>
<dd>A character describing the form of \(w(\cdot)\), the error
variance function under the heteroskedastic alternative. Possible values
are <code>"mult"</code> (the default), corresponding to
\(w(Z_i,\lambda)=\exp\left\{\sum_{j=1}^{q}\lambda_j Z_{ij}\right\}\),
<code>"add"</code>, corresponding to
\(w(Z_i,\lambda)=\left(1+\sum_{j=1}^{q} \lambda_j Z_{ij}\right)^2\), and
<code>"logmult"</code>, corresponding to
\(w(Z_i,\lambda)=\exp\left\{\sum_{j=1}^{q}\lambda_j \log Z_{ij}\right\}\).
The multiplicative and log-multiplicative cases are considered in
Cook83;textualskedastic; the additive case is discussed,
inter alia, by Griffiths86;textualskedastic.
Results for the additive and multiplicative models are identical for this
test. Partial matching is used.</dd>


<dt>statonly</dt>
<dd>A logical. If <code>TRUE</code>, only the test statistic value
is returned, instead of an object of <code><a href='https://rdrr.io/r/base/class.html'>class</a></code>
<code>"htest"</code>. Defaults to <code>FALSE</code>.</dd>

</dl>

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cook_weisberg: Cook-Weisberg Score Test for Heteroskedasticity in a Linear Regression Model

Description

Usage

Value

Arguments

Details

References

See Also

Examples