influence.measures package:stats R Documentation _R_e_g_r_e_s_s_i_o_n _D_e_l_e_t_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 (leave-one-out deletion) diagnostics for linear and generalized linear models discussed in Belsley, Kuh and Welsch (1980), Cook and Weisberg (1982), etc. _U_s_a_g_e: 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) _A_r_g_u_m_e_n_t_s: 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 prepended to 'x'? ...: further arguments passed to or from other methods. _D_e_t_a_i_l_s: 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. _N_o_t_e: For 'hatvalues', 'dfbeta', and 'dfbetas', the method for linear models also works for generalized linear models. _A_u_t_h_o_r(_s): Several R core team members and John Fox, originally in his 'car' package. _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 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.; . _S_e_e _A_l_s_o: 'influence' (containing 'lm.influence'). 'plotmath' for the use of 'hat' in plot annotation. _E_x_a_m_p_l_e_s: require(graphics) ## Analysis of the life-cycle savings data ## given in Belsley, Kuh and Welsch. 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) ## Irwin's data [Williams 1987] xi <- 1:5 yi <- c(0,2,14,19,30) # number of mice responding to does xi mi <- rep(40, 5) # number of mice exposed summary(lmI <- glm(cbind(yi, mi -yi) ~ xi, family = binomial)) signif(cooks.distance(lmI), 3)# ~= Ci in Table 3, p.184 (imI <- influence.measures(lmI)) stopifnot(all.equal(imI$infmat[,"cook.d"], cooks.distance(lmI)))