Deletion Diagnostics



Deletion Diagnostics for Linear and Generalized Linear Models

These functions calculate a variety of leave-one-out deletion diagnostics for linear and generalized linear models, including studentized residuals (for outlier detection), hatvalues (for detecting high-leverage observations), and Cook's distances, dfbeta, and dfbetas (for detecting influential observations).

rstudent(model, ...)

rstudent.lm(model, infl=influence(model))

rstudent.glm(model, infl=influence(model))

hatvalues(model, ...)

hatvalues.lm(model, infl=influence(model))

cookd(model, ...)

cookd.lm(model, infl=influence(model), sumry=summary(model))

cookd.glm(model, infl=influence(model), sumry=summary(model))

dfbeta(model, ...)

dfbeta.lm(model, infl=influence(model))

dfbetas(model, ...)

dfbetas.lm(model, infl=influence(model), sumry=summary(model))

influence(model, ...)


lm or glm model object.
optionally, an influence-object precomputed for the model by influence.
optionally, a summary-object precomputed for the model by summary.
arguments to be passed down from generic functions to method functions.

Basic quantities are computed by influence.lm or influence.glm, which are slightly modified versions of lm.influence from the base package. 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). Normally, the generic versions of these functions are the ones to be used directly. For hatvalues, dfbeta, and dfbetas, the method for linear models also works for generalized linear models. The following diagnostics are provided: [object Object],{studentized residuals.},[object Object],{observation leverages.},[object Object],{Cook's distance influence measure for observations.},[object Object],{change in each coefficient upon deleting observations.},[object Object],{standardized change in each coefficient for deleting observations.}


  • rstudent, hatvalues, and cookd return vectors with one entry for each observation; dfbeta and dfbetas return matrices with rows for observations and columns for coefficients. influence returns a list with entries:
  • hathat-values.
  • sigmaleave-one-out estimates of linear-model standard error or generalized-linear-model scale.
  • coefficientsdfbeta values.
  • wt.resweighted residuals (for a linear model).
  • dev.resdeviance residuals (for a generalized linear model).
  • pear.resPearson residuals (for a generalized linear model).


Belsley, D. A. and Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics. Wiley. Cook, R. D. and Weisberg, S. (1984) Residuals and Influence in Regression.) Wiley. Fox, J. (1997) Applied Regression, Linear Models, and Related Methods. Sage. Williams, D. A. (1987) Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics 36, 181--191. [object Object] influence.measures data(Duncan) attach(Duncan) mod <- lm(prestige ~ income + education) qq.plot(rstudent(mod), distribution="t", df=41) plot(hatvalues(mod)) plot(cookd(mod)) plot(dfbeta(mod)[,2]) plot(dfbetas(mod)[,2]) regression models

  • rstudent
  • rstudent.lm
  • rstudent.glm
  • hatvalues
  • hatvalues.lm
  • cookd
  • cookd.lm
  • cookd.glm
  • dfbeta
  • dfbeta.lm
  • dfbetas
  • dfbetas.lm
  • influence
  • influence.lm
  • influence.glm
Documentation reproduced from package car, version 0.8-1, License: GPL version 2 or newer

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