\name{abs.error.pred}
\alias{abs.error.pred}
\alias{print.abs.error.pred}
\title{
Indexes of Absolute Prediction Error for Linear Models
}
\description{
Computes the mean and median of various absolute errors related to
ordinary multiple regression models.  The mean and median absolute errors 
correspond to the mean square due to regression, error, and total.
The absolute errors computed are derived from Yhat - median(Yhat),
Yhat - Y, and Y - median(Y).  The function also computes ratios that
correspond to Rsquare and 1 - Rsquare (but these ratios do not add to
1.0); the Rsquare measure is the ratio of mean or median absolute Yhat
- median(Yhat) to the mean or median absolute Y - median(Y).  The 1 -
Rsquare or SSE/SST measure is the mean or median absolute Yhat - Y
divided by the mean or median absolute Y - median(Y).
}
\usage{
abs.error.pred(fit, lp=NULL, y=NULL)

\method{print}{abs.error.pred}(x, \dots)
}
\arguments{
\item{fit}{
a fit object typically from \code{lm} or \code{ols} that contains a \code{y} vector
(i.e., you should have specified \code{y=TRUE} to the fitting function) unless
the \code{y} argument is given to \code{abs.error.pred}.  If you do not specify
the \code{lp} argument, \code{fit} must contain \code{fitted.values} or
\code{linear.predictors}.  You must specify \code{fit} or both of \code{lp} and \code{y}.
}
\item{lp}{
a vector of predicted values (Y hat above) if \code{fit} is not given
}
\item{y}{
a vector of response variable values if \code{fit} (with \code{y=TRUE} in effect)
is not given
}
\item{x}{an object created by \code{abs.error.pred}}
\item{\dots}{unused}
}
\value{
a list of class \code{abs.error.pred} (used by \code{print.abs.error.pred})
containing two matrices: \code{differences} and \code{ratios}.
}
\author{
Frank Harrell
\cr
Department of Biostatistics
\cr
Vanderbilt University School of Medicine
\cr
f.harrell@vanderbilt.edu
}
\seealso{
\code{\link{lm}}, \code{\link[Design]{ols}}, \code{\link{cor}}, \code{\link[Design]{validate.ols}}
}
\references{
  Schemper M (2003): Stat in Med 22:2299-2308.
  }
\examples{
set.seed(1)         # so can regenerate results
x1 <- rnorm(100)
x2 <- rnorm(100)
y  <- exp(x1+x2+rnorm(100))
f <- lm(log(y) ~ x1 + poly(x2,3), y=TRUE)
abs.error.pred(lp=exp(fitted(f)), y=y)
rm(x1,x2,y,f)
}
\keyword{robust}
\keyword{regression}
\keyword{models}
\concept{predictive accuracy}