\name{plot.lm}
\alias{plot.lm}
\alias{plot.mlm}%which is .NotYetImplemented()
\title{Plot Diagnostics for an lm Object}
\usage{
\method{plot}{lm}(x, which = 1:4,
caption = c("Residuals vs Fitted", "Normal Q-Q plot",
"Scale-Location plot", "Cook's distance plot"),
panel = points,
sub.caption = deparse(x$call), main = "",
ask = prod(par("mfcol")) < length(which) && dev.interactive(),
\dots,
id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75,
cook.levels = c((0.5, 1), label.pos = c(4, 2))
}
\arguments{
\item{x}{\code{lm} object, typically result of \code{\link{lm}} or
\code{\link{glm}}.}
\item{which}{If a subset of the plots is required, specify a subset of
the numbers \code{1:5}.}
\item{caption}{Captions to appear above the plots}
\item{panel}{Panel function. A useful alternative to
\code{\link{points}} is \code{\link{panel.smooth}}.}
\item{sub.caption}{common title---above figures if there are multiple;
used as \code{sub} (s.\code{\link{title}}) otherwise.}
\item{main}{title to each plot---in addition to the above
\code{caption}.}
\item{ask}{logical; if \code{TRUE}, the user is \emph{ask}ed before
each plot, see \code{\link{par}(ask=.)}.}
\item{\dots}{other parameters to be passed through to plotting
functions.}
\item{id.n}{number of points to be labelled in each plot, starting
with the most extreme.}
\item{labels.id}{vector of labels, from which the labels for extreme
points will be chosen. \code{NULL} uses observation numbers.}
\item{cex.id}{magnification of point labels.}
\item{cook.levels}{levels of Cook's distance at which to draw
contours.}
\item{label.pos}{positioning of labels, for the left half and right
half of the graph respectively, for plots 1-3.}
}
\description{
Six plots (selectable by \code{which}) are currently available: a plot
of residuals against fitted values, a Scale-Location plot of
\eqn{\sqrt{| residuals |}} against fitted values, a Normal Q-Q plot, a
plot of Cook's distances versus row labels, a plot of residuals
against leverages, and a plot of Cook's distances against
leverage/(1-leverage). By default, the first four of these are
provided.
}
\details{
\code{sub.caption}---by default the function call---is shown as
a subtitle (under the x-axis title) on each plot when plots are on
separate pages, or as a subtitle in the outer margin (if any) when
there are multiple plots per page.
The \dQuote{Scale-Location} plot, also called \dQuote{Spread-Location} or
\dQuote{S-L} plot, takes the square root of the absolute residuals in
order to diminish skewness (\eqn{\sqrt{| E |}} is much less skewed
than \eqn{| E |} for Gaussian zero-mean \eqn{E}).
The \sQuote{S-L}, the Q-Q, and the Residual-Leverage plot, use
\emph{standardized} residuals which have identical variance (under the
hypothesis). They are given as
\eqn{R_i / (s \times \sqrt{1 - h_{ii}})}{R[i] / (s*sqrt(1 - h.ii))}
where \eqn{h_{ii}}{h.ii} are the diagonal entries of the hat matrix,
% bug in Rdconv: "$" and \link inside \code fails; '\$' doesn't help :
\code{\link{influence}()}\code{$hat}, see also \code{\link{hat}}.
The Residual-Leverage plot shows contours of equal Cook's distance,
by default for values of 0.5 and 1. In the Cook's distance vs
leverage/(1-leverage) plot, contours of standardized residuals that
are equal in magnitude are lines through the origin. The contour
lines are labeled with the magnitudes.
}
\references{
Belsley, D. A., Kuh, E. and Welsch, R. E. (1980)
\emph{Regression Diagnostics.} New York: Wiley.
Cook, R. D. and Weisberg, S. (1982)
\emph{Residuals and Influence in Regression.}
London: Chapman and Hall.
Firth, D. (1991) Generalized Linear Models. In Hinkley, D. V. and
Reid, N. and Snell, E. J., eds: Pp. 55-82 in Statistical Theory and
Modelling. In Honour of Sir David Cox, FRS. London: Chapman and Hall.
Hinkley, D. V. (1975) On power transformations to
symmetry. \emph{Biometrika} \bold{62}, 101--111.
McCullagh, P. and Nelder, J. A. (1989)
\emph{Generalized Linear Models.}
London: Chapman and Hall.
}
\author{
John Maindonald and Martin Maechler.
}
\seealso{\code{\link{termplot}}, \code{\link{lm.influence}},
\code{\link{cooks.distance}}, \code{\link{hatvalues}}.
}
\examples{
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
plot(lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings))
## 4 plots on 1 page; allow room for printing model formula in outer margin:
par(mfrow = c(2, 2), oma = c(0, 0, 2, 0))
plot(lm.SR)
plot(lm.SR, id.n = NULL) # no id's
plot(lm.SR, id.n = 5, labels.id = NULL)# 5 id numbers
## Replace Cook's distance plot by Residual-Leverage plot
plot(lm.SR, which=c(1:3, 5))
## Fit a smooth curve, where applicable:
plot(lm.SR, panel = panel.smooth)
## Gives a smoother curve
plot(lm.SR, panel = function(x,y) panel.smooth(x, y, span = 1))
par(mfrow=c(2,1))# same oma as above
plot(lm.SR, which = 1:2, sub.caption = "Saving Rates, n=50, p=5")
}
\keyword{hplot}
\keyword{regression}