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% File src/library/stats/man/plot.lm.Rd

% Part of the R package, https://www.R-project.org

% Copyright 1995-2019 R Core Team

% Distributed under GPL 2 or later

\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 = c(1,2,3,5), %% was which = 1:4

     caption = list("Residuals vs Fitted", "Normal Q-Q",

       "Scale-Location", "Cook's distance",

       "Residuals vs Leverage",

       expression("Cook's dist vs Leverage  " * h[ii] / (1 - h[ii]))),

     panel = if(add.smooth) function(x, y, ...)

              panel.smooth(x, y, iter=iter.smooth, ...) else points,

     sub.caption = NULL, main = "",

     ask = prod(par("mfcol")) < length(which) && dev.interactive(),

     \dots,

     id.n = 3, labels.id = names(residuals(x)), cex.id = 0.75,

     qqline = TRUE, cook.levels = c(0.5, 1.0),

     add.smooth = getOption("add.smooth"),

     iter.smooth = if(isGlm && binomialLike) 0 else 3,

     label.pos = c(4,2),

     cex.caption = 1, cex.oma.main = 1.25)

}

\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{1:6}, see \code{caption} below (and the

    \sQuote{Details}) for the different kinds.}

  \item{caption}{captions to appear above the plots;

    \code{\link{character}} vector or \code{\link{list}} of valid

    graphics annotations, see \code{\link{as.graphicsAnnot}}, of length

    6, the j-th entry corresponding to \code{which[j]}.  Can be set to

    \code{""} or \code{NA} to suppress all captions.

  }

  \item{panel}{panel function.  The useful alternative to

    \code{\link{points}}, \code{\link{panel.smooth}} can be chosen

    by \code{add.smooth = TRUE}.}

  \item{sub.caption}{common title---above the figures if there are more

    than one; used as \code{sub} (s.\code{\link{title}}) otherwise.  If

    \code{NULL}, as by default, a possible abbreviated version of

    \code{deparse(x$call)} is used.}

  \item{main}{title to each plot---in addition to \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{qqline}{logical indicating if a \code{\link{qqline}()} should be

    added to the normal Q-Q plot.}

  \item{cook.levels}{levels of Cook's distance at which to draw contours.}

  \item{add.smooth}{logical indicating if a smoother should be added to

    most plots; see also \code{panel} above.}

  \item{iter.smooth}{the number of robustness iterations, the argument

    \code{iter} in \code{\link{panel.smooth}()}; the default uses no such

    iterations for \code{\link{glm}(*, family=binomial)} fits which is

    particularly desirable for the (predominant) case of binary observations.}

  \item{label.pos}{positioning of labels, for the left half and right

    half of the graph respectively, for plots 1-3.}

  \item{cex.caption}{controls the size of \code{caption}.}

  \item{cex.oma.main}{controls the size of the \code{sub.caption} only if

    that is \emph{above} the figures when there is more than one.}

}

\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 |}}{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 three and \code{5} 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 \sQuote{Scale-Location} plot, also called \sQuote{Spread-Location} or

  \sQuote{S-L} plot, takes the square root of the absolute residuals in

  order to diminish skewness (\eqn{\sqrt{| E |}}{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,

  \code{\link{influence}()$hat} (see also \code{\link{hat}}), and

  where the Residual-Leverage plot uses standardized Pearson residuals

  (\code{\link{residuals.glm}(type = "pearson")}) for \eqn{R[i]}.

  The Residual-Leverage plot shows contours of equal Cook's distance,

  for values of \code{cook.levels} (by default 0.5 and 1) and omits

  cases with leverage one with a warning.  If the leverages are constant

  (as is typically the case in a balanced \code{\link{aov}} situation)

  the plot uses factor level combinations instead of the leverages for

  the x-axis.  (The factor levels are ordered by mean fitted value.)

  In the Cook's distance vs leverage/(1-leverage) plot, contours of

  standardized residuals (\code{\link{rstandard}(.)}) that are equal in

  magnitude are lines through the origin.  The contour lines are

  labelled 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.\sspace{}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.

  \doi{10.2307/2334491}.

  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{

require(graphics)

## Analysis of the life-cycle savings data

## given in Belsley, Kuh and Welsch.

lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)

plot(lm.SR)

## 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

## Was default in R <= 2.1.x:

## Cook's distances instead of Residual-Leverage plot

plot(lm.SR, which = 1:4)

## 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")

\dontshow{

## An example with *long* formula that needs abbreviation:

for(i in 1:5) assign(paste("long.var.name", i, sep = "."), runif(10))

plot(lm(long.var.name.1 ~

        long.var.name.2 + long.var.name.3 + long.var.name.4 + long.var.name.5))

}

}

\keyword{hplot}

\keyword{regression}