### Name: influence.measures
### Title: Regression Deletion Diagnostics
### Aliases: influence.measures print.infl summary.infl hat hatvalues
###   hatvalues.lm rstandard rstandard.lm rstandard.glm rstudent
###   rstudent.lm rstudent.glm dfbeta dfbeta.lm dfbetas dfbetas.lm dffits
###   covratio cooks.distance cooks.distance.lm cooks.distance.glm
### Keywords: regression

### ** 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)

inflm.SR <- influence.measures(lm.SR)
which(apply(inflm.SR$is.inf, 1, any))
# which observations 'are' influential
summary(inflm.SR) # only these
inflm.SR          # all
plot(rstudent(lm.SR) ~ hatvalues(lm.SR)) # recommended by some

## The 'infl' argument is not needed, but avoids recomputation:
rs <- rstandard(lm.SR)
iflSR <- influence(lm.SR)
identical(rs, rstandard(lm.SR, infl = iflSR))
## to "see" the larger values:
1000 * round(dfbetas(lm.SR, infl = iflSR), 3)

## 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))
(im <- influence.measures(lmH))
plot(xh,yh, main = "Huber's data: L.S. line and influential obs.")
abline(lmH); points(xh[im$is.inf], yh[im$is.inf], pch=20, col=2)

## Irwin's data [Williams 1987]
xi <- 1:5
yi <- c(0,2,14,19,30) # number of mice responding to does xi
mi <- rep(40, 5)      # number of mice exposed
summary(lmI <- glm(cbind(yi, mi -yi) ~ xi, family = binomial))
signif(cooks.distance(lmI), 3)# ~= Ci in Table 3, p.184
(imI <- influence.measures(lmI))
stopifnot(all.equal(imI$infmat[,"cook.d"],
          cooks.distance(lmI)))