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 lm or
glm . |
infl |
influence structure as returned by
lm.influence or influence (the latter
only for the glm method of rstudent and
cooks.distance ). |
res |
(possibly weighted) residuals, with proper default. |
sd |
standard deviation to use, see default. |
dispersion |
dispersion (for glm objects) to use,
see default. |
hat |
hat values H[i,i], see default. |
x |
the X or design matrix. |
intercept |
should an intercept column be pre-prended to x ? |
... |
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 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
).
## 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) 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)