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.

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)

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.

Aliases

• influence.measures
• hat
• hatvalues
• hatvalues.lm
• rstandard
• rstandard.lm
• rstandard.glm
• rstudent
• rstudent.lm
• rstudent.glm
• dfbeta
• dfbeta.lm
• dfbetas
• dfbetas.lm
• dffits
• covratio
• cooks.distance
• cooks.distance.lm
• cooks.distance.glm