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\name{box.cox.powers}
\alias{box.cox.powers}
\alias{print.box.cox.powers}
\alias{summary.box.cox.powers}
\title{Multivariate Unconditional Box-Cox Transformations}
\description{
Estimates multivariate unconditional power transformations
to multinormality
by the method of maximum likelihood. The univariate case is
obtained when only one variable is specified.
}
\usage{
box.cox.powers(X, start=NULL, hypotheses=NULL, ...)
\method{print}{box.cox.powers}(x, digits=4, ...)
\method{summary}{box.cox.powers}(object, digits=4, ...)
}
\arguments{
\item{X}{a numeric matrix of variables (or a vector for one variable)
to be transformed.}
\item{start}{start values for the power transformation parameters;
if \code{NULL} (the default), univariate Box-Cox transformations will
be computed and used as the start values.}
\item{hypotheses}{if non-\code{NULL}, a list of hypotheses to be tested;
each hypothesis should be a vector of values giving the power for each
column of \code{X}. Note that the hypotheses that all powers are 1 and
that all powers are 0 (log) are always tested.}
\item{...}{optional arguments to be passed to the \code{optim} function.}
\item{digits}{number of places to round result.}
\item{x, object}{\code{box.cox.powers} object.}
}
\details{
Note that this is \emph{unconditional} Box-Cox. That is, there is
no regression model, and there are no predictors. The object is to
make the distribution of the variable(s) as (multi)normal as possible.
For Box-Cox regression, see the \code{boxcox} function in the
\code{MASS} package.
The function estimates the Box-Cox powers,
\eqn{x_{j}^{\prime }=(x_{j}^{\lambda _{j}}-1)/\lambda _{j}}{x' = (x^p - 1)/p}
for \eqn{\lambda _{j} \neq 0}{p != 0} and \eqn{x_{j}^{\prime }=\log x_{j}}{x' = log(x)}
for \eqn{\lambda _{j}=0}{p = 0}. Subsequently using ordinary power
transformations (i.e., \eqn{x^p} for \eqn{p \neq 0}{p != 0})
achieves the same result.
}
\value{
returns an object of class \code{box.cox.powers}, which may be printed
or summarized. the \code{print} and \code{summary} methods are now identical; I've
retained the latter for backwards compatibility.
}
\references{
Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations.
\emph{JRSS B} \bold{26} 211--246.
Cook, R. D. and Weisberg, S. (1999)
\emph{Applied Regression, Including Computing and Graphics.} Wiley.
}
\author{John Fox \email{jfox@mcmaster.ca}}
\seealso{\code{\link[MASS:boxcox]{boxcox}}, \code{\link{box.cox}}, \code{\link{box.cox.var}},
\code{\link{box.cox.axis}}}
\examples{
attach(Prestige)
box.cox.powers(cbind(income, education))
## Box-Cox Transformations to Multinormality
##
## Est.Power Std.Err. Wald(Power=0) Wald(Power=1)
## income 0.2617 0.1014 2.580 -7.280
## education 0.4242 0.4033 1.052 -1.428
##
## L.R. test, all powers = 0: 7.694 df = 2 p = 0.0213
## L.R. test, all powers = 1: 48.8727 df = 2 p = 0
plot(income, education)
plot(box.cox(income, .26), box.cox(education, .42))
box.cox.powers(income)
## Box-Cox Transformation to Normality
##
## Est.Power Std.Err. Wald(Power=0) Wald(Power=1)
## 0.1793 0.1108 1.618 -7.406
##
## L.R. test, power = 0: 2.7103 df = 1 p = 0.0997
## L.R. test, power = 1: 47.261 df = 1 p = 0
qq.plot(income)
qq.plot(income^.18)
}
\keyword{multivariate}
\keyword{models}
|
