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\name{invTranPlot}
\alias{invTranPlot}
\alias{invTranPlot.default}
\alias{invTranPlot.formula}
\alias{invTranEstimate}
\title{ Choose a Predictor Transformation Visually or Numerically }
\description{
\code{invTranPlot}
draws a two-dimensional scatterplot of \eqn{Y}{Y} versus
\eqn{X}{X}, along with the OLS
fit from the regression of \eqn{Y}{Y} on
\eqn{(X^{\lambda}-1)/\lambda}{(X?^(lam)-1)/lam}. \code{invTranEstimate}
finds the nonlinear least squares estimate of \eqn{\lambda}{lambda} and its
standard error.
}
\usage{
invTranPlot(x, ...)
\S3method{invTranPlot}{formula}(x, data, subset, na.action, id=FALSE, ...)
\S3method{invTranPlot}{default}(x, y, lambda=c(-1, 0, 1), robust=FALSE,
lty.lines=rep(c("solid", "dashed", "dotdash", "longdash", "twodash"),
length=1 + length(lambda)), lwd.lines=2,
col=carPalette()[1], col.lines=carPalette(),
xlab=deparse(substitute(x)), ylab=deparse(substitute(y)),
family="bcPower", optimal=TRUE, key="auto", id=FALSE,
grid=TRUE, ...)
invTranEstimate(x, y, family="bcPower", confidence=0.95, robust=FALSE)
}
\arguments{
\item{x}{The predictor variable, or a formula with a single response and
a single predictor }
\item{y}{The response variable }
\item{data}{An optional data frame to get the data for the formula}
\item{subset}{Optional, as in \code{\link{lm}}, select a subset of the cases}
\item{na.action}{Optional, as in \code{\link{lm}}, the action for missing data}
\item{lambda}{The powers used in the plot. The optimal power than minimizes
the residual sum of squares is always added unless optimal is \code{FALSE}. }
\item{robust}{If \code{TRUE}, then the estimated transformation is computed using
Huber M-estimation with the MAD used to estimate scale and k=1.345. The
default is \code{FALSE}.}
\item{family}{The transformation family to use, \code{"bcPower"},
\code{"yjPower"}, or a user-defined family.}
\item{confidence}{returns a profile likelihood confidence interval for the optimal
transformation with this confidence level. If \code{FALSE}, or if \code{robust=TRUE},
no interval is returned.}
\item{optimal}{Include the optimal value of lambda?}
\item{lty.lines}{line types corresponding to the powers}
\item{lwd.lines}{the width of the plotted lines, defaults to 2 times the standard}
\item{col}{color(s) of the points in the plot. If you wish to distinguish points
according to the levels of a factor, we recommend using symbols, specified with
the \code{pch} argument, rather than colors.}
\item{col.lines}{color of the fitted lines corresponding to the powers. The
default is to use the colors returned by \code{\link{carPalette}}}
\item{key}{The default is \code{"auto"}, in which case a legend is added to
the plot, either above the top marign or in the bottom right or top right corner.
Set to NULL to suppress the legend.}
\item{xlab}{Label for the horizontal axis.}
\item{ylab}{Label for the vertical axis.}
\item{id}{controls point identification; if \code{FALSE} (the default), no points are identified;
can be a list of named arguments to the \code{\link{showLabels}} function;
\code{TRUE} is equivalent to \code{list(method=list(method="x", n=2, cex=1, col=carPalette()[1], location="lr")},
which identifies the 2 points with the most extreme horizontal values --- i.e., the response variable in the model.}
\item{...}{Additional arguments passed to the plot method, such as \code{pch}.}
\item{grid}{If TRUE, the default, a light-gray background grid is put on the
graph}
}
\value{
\code{invTranPlot}
plots a graph and returns a data frame with \eqn{\lambda}{lam} in the
first column, and the residual sum of squares from the regression
for that \eqn{\lambda}{lam} in the second column.
\code{invTranEstimate} returns a list with elements \code{lambda} for the
estimate, \code{se} for its standard error, and \code{RSS}, the minimum
value of the residual sum of squares.
}
\seealso{ \code{\link{inverseResponsePlot}},\code{\link{optimize}}}
\references{
Fox, J. and Weisberg, S. (2011)
\emph{An R Companion to Applied Regression}, Second Edition, Sage.
Prendergast, L. A., & Sheather, S. J. (2013)
On sensitivity of inverse response plot estimation and the benefits of a robust estimation approach. \emph{Scandinavian Journal of Statistics}, 40(2), 219-237.
Weisberg, S. (2014) \emph{Applied Linear Regression}, Fourth Edition, Wiley, Chapter 7.
}
\author{Sanford Weisberg, \email{sandy@umn.edu} }
\examples{
with(UN, invTranPlot(ppgdp, infantMortality))
with(UN, invTranEstimate(ppgdp, infantMortality))
}
\keyword{ hplot }% at least one, from doc/KEYWORDS
\keyword{regression}
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