\Header{influence.measures}{Regression Diagnostics}
\alias{cooks.distance}{influence.measures}
\alias{covratio}{influence.measures}
\alias{dfbetas}{influence.measures}
\alias{dffits}{influence.measures}
\alias{hat}{influence.measures}
\alias{print.infl}{influence.measures}
\alias{rstandard}{influence.measures}
\alias{rstudent}{influence.measures}
\alias{summary.infl}{influence.measures}
\keyword{regression}{influence.measures}
\begin{Description}\relax
This suite of functions can be used to compute some of the regression
diagnostics discussed in Belsley, Kuh and Welsch (1980), and in Cook
and Weisberg (1982).\end{Description}
\begin{Usage}
\begin{verbatim}
influence.measures(lm.obj)

rstandard(lm.obj,
          infl = lm.influence(lm.obj),
          res = weighted.residuals(lm.obj),
          sd = sqrt(deviance(lm.obj)/df.residual(lm.obj)))
rstudent (lm.obj, infl = ..., res = ...)
dffits   (lm.obj, infl = ..., res = ...)
dfbetas  (lm.obj, infl = ...)
covratio (lm.obj, infl = ..., res = ...)
cooks.distance(lm.obj, infl = ..., res = ..., sd = ...)

hat(x, intercept = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{lm.obj}] the resulting object returned by \code{\Link{lm}}.
\item[\code{infl}] influence structure as returned by \code{\Link{lm.influence}}.
\item[\code{res}] (possibly weighted) residuals, with proper default.
\item[\code{sd}] standard deviation to use, see default.
\item[\code{x}] the \eqn{X}{} or design matrix.
\item[\code{intercept}] should an intercept column be pre-prended to \code{x}?
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
The primary function is \code{influence.measures} which produces a
class \code{"infl"} object tabular display showing the DFBETAS for
each model variable, DFFITS, covariance ratios, Cook's distances and
the diagonal elements of the hat matrix.  Cases which are influential
with respect to any of these measures are marked with an asterisk.

The functions \code{dfbetas}, \code{dffits},
\code{covratio} and \code{cooks.distance} provide direct access to the
corresponding diagnostic quantities.  Functions \code{rstandard} and
\code{rstudent} give the standardized and Studentized residuals
respectively. (These re-normalize the residuals to have unit variance,
using an overall and leave-one-out measure of the error variance
respectively.)

The optional \code{infl}, \code{res} and \code{sd} arguments are there
to encourage the use of these direct access functions, in situations
where, e.g., the underlying basic influence measures (from
\code{\Link{lm.influence}}) are already available.

Note that cases with \code{weights == 0} are \emph{dropped} from all
these functions, but that if a linear model has been fitted with
\code{na.action = na.exclude}, suitable values are filled it for the
cases excluded during fitting.

The function \code{hat()} exists mainly for S (version 2) compatibility.\end{Details}
\begin{References}\relax
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.\end{References}
\begin{SeeAlso}\relax
\code{\Link{lm.influence}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## Analysis of the life-cycle savings data
## given in Belsley, Kuh and Welsch.
data(LifeCycleSavings)
lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
summary(inflm.SR <- influence.measures(lm.SR))
inflm.SR
which(apply(inflm.SR$is.inf, 1, any)) # which observations `are' influential
dim(dfb <- dfbetas(lm.SR))            # the 1st columns of influence.measures
all(dfb == inflm.SR$infmat[, 1:5])
rstandard(lm.SR)
rstudent(lm.SR)
dffits(lm.SR)
covratio(lm.SR)

## Huber's data [Atkinson 1985]
xh <- c(-4:0, 10)
yh <- c(2.48, .73, -.04, -1.44, -1.32, 0)
summary(lmH <- lm(yh ~ xh))
influence.measures(lmH)
\end{ExampleCode}
\end{Examples}

