influence.measures
Regression Deletion Diagnostics
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.
- Keywords
- regression
Usage
influence.measures(model)
rstandard(model, ...)
"rstandard"(model, infl = lm.influence(model, do.coef = FALSE), sd = sqrt(deviance(model)/df.residual(model)), ...)
"rstandard"(model, infl = influence(model, do.coef = FALSE), type = c("deviance", "pearson"), ...)
rstudent(model, ...)
"rstudent"(model, infl = lm.influence(model, do.coef = FALSE), res = infl$wt.res, ...)
"rstudent"(model, infl = influence(model, do.coef = FALSE), ...)
dffits(model, infl = , res = )
dfbeta(model, ...)
"dfbeta"(model, infl = lm.influence(model, do.coef = TRUE), ...)
dfbetas(model, ...)
"dfbetas"(model, infl = lm.influence(model, do.coef = TRUE), ...)
covratio(model, infl = lm.influence(model, do.coef = FALSE), res = weighted.residuals(model))
cooks.distance(model, ...)
"cooks.distance"(model, infl = lm.influence(model, do.coef = FALSE), res = weighted.residuals(model), sd = sqrt(deviance(model)/df.residual(model)), hat = infl$hat, ...)
"cooks.distance"(model, infl = influence(model, do.coef = FALSE), res = infl$pear.res, dispersion = summary(model)$dispersion, hat = infl$hat, ...)
hatvalues(model, ...)
"hatvalues"(model, infl = lm.influence(model, do.coef = FALSE), ...)
hat(x, intercept = TRUE)
Arguments
- model
- an R object, typically returned by
lm
orglm
. - infl
- influence structure as returned by
lm.influence
orinfluence
(the latter only for theglm
method ofrstudent
andcooks.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.
- type
- type of residuals for
glm
method forrstandard
. Can be abbreviated. - x
- the $X$ or design matrix.
- intercept
- should an intercept column be prepended to
x
? - ...
- further arguments passed to or from other methods.
Details
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.
Note
For hatvalues
, dfbeta
, and dfbetas
, the method
for linear models also works for generalized linear models.
References
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.
Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, second edition. Sage Publ; https://socserv.mcmaster.ca/jfox/Books/Companion/index.html.
See Also
influence
(containing lm.influence
).
plotmath for the use of hat
in plot annotation.