Regression Diagnostics

Description

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).

Usage

influence.measures(lm.obj)
summary.infl (object, digits = max(2, getOption("digits") - 5), ...)
  print.infl (x, digits = max(3, getOption("digits") - 4), ...)

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(xmat)

Arguments

Details

The primary 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.)

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) are already available.

Note that cases with weights == 0 are dropped from all these functions.

References

Belsley, D. A., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics. New York: Wiley.

Cook, R. D. and Weisber,g S. (1982) Residuals and Influence in Regression. London: Chapman and Hall.

See Also

lm.influence.

Examples

## 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)