| influence.measures {stats} | R Documentation |
This suite of functions can be used to compute some of the regression (leave-one-out deletion) diagnostics for linear and generalized linear models discussed in Belsley, Kuh and Welsch (1980), Cook and Weisberg (1982), etc.
influence.measures(model)
rstandard(model, ...)
## S3 method for class 'lm'
rstandard(model, infl = lm.influence(model, do.coef = FALSE),
sd = sqrt(deviance(model)/df.residual(model)), ...)
## S3 method for class 'glm'
rstandard(model, infl = lm.influence(model, do.coef = FALSE),
...)
rstudent(model, ...)
## S3 method for class 'lm'
rstudent(model, infl = lm.influence(model, do.coef = FALSE),
res = infl$wt.res, ...)
## S3 method for class 'glm'
rstudent(model, infl = influence(model, do.coef = FALSE), ...)
dffits(model, infl = , res = )
dfbeta(model, ...)
## S3 method for class 'lm'
dfbeta(model, infl = lm.influence(model, do.coef = TRUE), ...)
dfbetas(model, ...)
## S3 method for class 'lm'
dfbetas(model, infl = lm.influence(model, do.coef = TRUE), ...)
covratio(model, infl = lm.influence(model, do.coef = FALSE),
res = weighted.residuals(model))
cooks.distance(model, ...)
## S3 method for class 'lm'
cooks.distance(model, infl = lm.influence(model, do.coef = FALSE),
res = weighted.residuals(model),
sd = sqrt(deviance(model)/df.residual(model)),
hat = infl$hat, ...)
## S3 method for class 'glm'
cooks.distance(model, infl = influence(model, do.coef = FALSE),
res = infl$pear.res,
dispersion = summary(model)$dispersion,
hat = infl$hat, ...)
hatvalues(model, ...)
## S3 method for class 'lm'
hatvalues(model, infl = lm.influence(model, do.coef = FALSE), ...)
hat(x, intercept = TRUE)
model |
an R object, typically returned by |
infl |
influence structure as returned by
|
res |
(possibly weighted) residuals, with proper default. |
sd |
standard deviation to use, see default. |
dispersion |
dispersion (for |
hat |
hat values |
x |
the |
intercept |
should an intercept column be prepended to |
... |
further arguments passed to or from other methods. |
The primary high-level function is influence.measures which produces a
class "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 dfbetas, dffits,
covratio and cooks.distance provide direct access to the
corresponding diagnostic quantities. Functions rstandard and
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.)
Values for generalized linear models are approximations, as described
in Williams (1987) (except that Cook's distances are scaled as
F rather than as chi-square values). The approximations can be
poor when some cases have large influence.
The optional infl, res and sd arguments are there
to encourage the use of these direct access functions, in situations
where, e.g., the underlying basic influence measures (from
lm.influence or the generic influence) are
already available.
Note that cases with weights == 0 are dropped from all
these functions, but that if a linear model has been fitted with
na.action = na.exclude, suitable values are filled in for the
cases excluded during fitting.
The function hat() exists mainly for S (version 2)
compatibility; we recommend using hatvalues() instead.
For hatvalues, dfbeta, and dfbetas, the method
for linear models also works for generalized linear models.
Several R core team members and John Fox, originally in his ‘car’ package.
Belsley, D. A., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics. New York: Wiley.
Cook, R. D. and Weisberg, S. (1982) Residuals and Influence in Regression. London: Chapman and Hall.
Williams, D. A. (1987) Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics 36, 181–191.
Fox, J. (1997) Applied Regression, Linear Models, and Related Methods. Sage.
Fox, J. (2002) An R and S-Plus Companion to Applied Regression. Sage Publ.; http://www.socsci.mcmaster.ca/jfox/Books/Companion/.
influence (containing lm.influence).
‘plotmath’ for the use of hat in plot annotation.
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)))