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\name{boxCoxVariable}
\alias{boxCoxVariable}
\title{Constructed Variable for Box-Cox Transformation}
\description{
Computes a constructed variable for the Box-Cox transformation of the
response variable in a linear model.
}
\usage{
boxCoxVariable(y)
}
\arguments{
\item{y}{response variable.}
}
\details{
The constructed variable is defined as \eqn{y[\log(y/\widetilde{y}) - 1]}{y[log(y/y') -1]}, where
\eqn{\widetilde{y}}{y'} is the geometric mean of \code{y}.
The constructed variable is meant to be
added to the right-hand-side of the linear model. The t-test for the
coefficient of the constructed variable is an approximate score test for whether a
transformation is required.
If \eqn{b} is the coefficient of the constructed variable,
then an estimate of the normalizing power transformation based on the score statistic
is \eqn{1 - b}{1 - b}. An added-variable plot for the constructed
variable shows leverage and influence on the decision to transform \code{y}.
}
\value{
a numeric vector of the same length as \code{y}.
}
\references{
Atkinson, A. C. (1985)
\emph{Plots, Transformations, and Regression}. Oxford.
Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations.
\emph{JRSS B} \bold{26} 211--246.
Fox, J. (2016)
\emph{Applied Regression Analysis and Generalized Linear Models},
Third Edition. Sage.
Fox, J. and Weisberg, S. (2019)
\emph{An R Companion to Applied Regression}, Third Edition, Sage.
}
\author{John Fox \email{jfox@mcmaster.ca}}
\seealso{\code{\link[MASS]{boxcox}}, \code{\link{powerTransform}}, \code{\link{bcPower}}} % , \code{\link{avPlots}}
\examples{
mod <- lm(interlocks + 1 ~ assets, data=Ornstein)
mod.aux <- update(mod, . ~ . + boxCoxVariable(interlocks + 1))
summary(mod.aux)
# avPlots(mod.aux, "boxCoxVariable(interlocks + 1)")
}
\keyword{manip}
\keyword{regression}
|
