influence.measures           package:base           R Documentation

_R_e_g_r_e_s_s_i_o_n _D_i_a_g_n_o_s_t_i_c_s

_D_e_s_c_r_i_p_t_i_o_n:

     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).

_U_s_a_g_e:

     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)

_A_r_g_u_m_e_n_t_s:

  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.

    xmat: the `X' or design matrix.

_D_e_t_a_i_l_s:

     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.

_R_e_f_e_r_e_n_c_e_s:

     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.

_S_e_e _A_l_s_o:

     `lm.influence'.

_E_x_a_m_p_l_e_s:

     ## 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)

