influence.measures           package:base           R Documentation

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)

     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(x, intercept = TRUE)

Arguments:

  lm.obj: the resulting object returned by `lm'.

    infl: influence structure as returned by `lm.influence'.

     res: (possibly weighted) residuals, with proper default.

      sd: standard deviation to use, see default.

       x: the X or design matrix.

intercept: should an intercept column be pre-prended to `x'?

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, but that if a linear model has been fitted with
     `na.action = na.exclude', suitable values are filled it for the
     cases excluded during fitting.

     The function `hat()' exists mainly for S (version 2)
     compatibility.

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.

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)

