Functions For Constructing Effect Plots

effect constructs an "eff" object for a term (usually a high-order term) in a linear or generalized linear model, or an "effpoly" object for a term in a multinomial or proportional-odds logit model, absorbing the lower-order terms marginal to the term in question, and averaging over other terms in the model. allEffects identifies all of the high-order terms in a model and returns a list of "eff" or "effpoly" objects (i.e., an object of type "efflist").

models, hplot
effect(term, mod, ...)

## S3 method for class 'lm':
effect(term, mod, xlevels=list(), default.levels=10, given.values, 
	se=TRUE, confidence.level=.95, 
    transformation=list(link=family(mod)$linkfun, inverse=family(mod)$linkinv), 
    typical=mean, ...)
## S3 method for class 'multinom':
effect(term, mod, confidence.level=.95, xlevels=list(), default.levels=10, 
	given.values, se=TRUE, typical=mean, ...)
## S3 method for class 'polr':
effect(term, mod, confidence.level=.95, xlevels=list(), default.levels=10, 
	given.values, se=TRUE, typical=mean, latent=FALSE, ...)
allEffects(mod, ...)

## S3 method for class 'eff':
as.data.frame(x, row.names=NULL, optional=TRUE, ...)

## S3 method for class 'effpoly':
as.data.frame(x, row.names=NULL, optional=TRUE, ...)

## S3 method for class 'efflatent':
as.data.frame(x, row.names=NULL, optional=TRUE, ...)
the quoted name of a term, usually, but not necessarily, a high-order term in the model. The term must be given exactly as it appears in the printed model, although either colons (:) or asterisks (*) may be used f
an object of class "lm", "glm", "multinom", or "polr".
an optional list of values at which to set covariates, with components of the form covariate.name = vector.of.values.
number of values for covariates that are not specified explicitly via xlevels; covariate values set by default are evenly spaced between the minimum and maximum values in the data.
a numeric vector of named elements, setting particular columns of the model matrix to specific values for terms not appearing in an effect; if specified, takes precedence over the application of the function given in the typical
if TRUE, the default, calculate standard errors and confidence limits for the effects.
level at which to compute confidence limits based on the standard-normal distribution; the default is 0.95.
a two-element list with elements link and inverse. For a generalized linear model, these are by default the link function and inverse-link (mean) function. For a linear model, these default to NULL. If
a function to be applied to the columns of the model matrix over which the effect is "averaged"; the default is mean.
if TRUE, effects in a proportional-odds logit model are computed on the scale of the latent response; if FALSE (the default) effects are computed as individual-level probabilities and logits.
an object of class "eff" or "effpoly".
row.names, optional
not used.
arguments to be passed down.

Normally, the functions to be used directly are allEffects, to return a list of high-order effects, and the generic plot function to plot the effects. (see plot.efflist, plot.eff, and plot.effpoly). Plots are drawn using the xyplot (or in some cases, the densityplot) function in the lattice package. Effects may also be printed (implicitly or explicitly via print) or summarized (using summary) (see print.efflist, summary.efflist, print.eff, summary.eff, print.effpoly, and summary.effpoly). If asked, the effect function will compute effects for terms that have higher-order relatives in the model, averaging over those terms (which rarely makes sense), or for terms that do not appear in the model but are higher-order relatives of terms that do. For example, for the model Y ~ A*B + A*C + B*C, one could compute the effect corresponding to the absent term A:B:C, which absorbs the constant, the A, B, and C main effects, and the three two-way interactions. In either of these cases, a warning is printed. In calculating effects, the strategy for `safe' prediction described in Hastie (1992: Sec. 7.3.3) is employed.


  • For lm and glm, effect returns an "eff" object, and for multinom and polr, an "effpoly" object, with the following components:
  • termthe term to which the effect pertains.
  • formulathe complete model formula.
  • responsea character string giving the name of the response variable.
  • y.levels(for "effpoly" objects) levels of the polytomous response variable.
  • variablesa list with information about each predictor, including its name, whether it is a factor, and its levels or values.
  • fit(for "eff" objects) a one-column matrix of fitted values, representing the effect on the scale of the linear predictor; this is a ravelled table, representing all combinations of predictor values.
  • prob(for "effpoly" objects) a matrix giving fitted probabilities for the effect for the various levels of the the response (columns) and combinations of the focal predictors (rows).
  • logit(for "effpoly" objects) a matrix giving fitted logits for the effect for the various levels of the the response (columns) and combinations of the focal predictors (rows).
  • xa data frame, the columns of which are the predictors in the effect, and the rows of which give all combinations of values of these predictors.
  • model.matrixthe model matrix from which the effect was calculated.
  • dataa data frame with the data on which the fitted model was based.
  • discrepancythe percentage discrepancy for the `safe' predictions of the original fit; should be very close to 0.
  • se(for "eff" objects) a vector of standard errors for the effect, on the scale of the linear predictor.
  • se.prob, se.logit(for "effpoly" objects) matrices of standard errors for the effect, on the probability and logit scales.
  • lower, upper(for "eff" objects) one-column matrices of confidence limits, on the scale of the linear predictor.
  • lower.prob, upper.prob, lower.logit, upper.logit(for "effpoly" objects) matrices of confidence limits for the fitted logits and probabilities; the latter are computed by transforming the former.
  • confidence.levelfor the confidence limits.
  • transformation(for "eff" objects) a two-element list, with element link giving the link function, and element inverse giving the inverse-link (mean) function.
  • effectList returns a list of "eff" or "effpoly" objects corresponding to the high-order terms of the model.


Fox, J. (1987) Effect displays for generalized linear models. Sociological Methodology 17, 347--361. Fox, J. (2003) Effect displays in R for generalised linear models. Journal of Statistical Software 8:15, 1--27, <http://www.jstatsoft.org/counter.php?id=75&url=v08/i15/effect-displays-revised.pdf&ct=1>. Fox, J. and R. Andersen (2006) Effect displays for multinomial and proportional-odds logit models. Sociological Methodology 36, 225--255. Hastie, T. J. (1992) Generalized additive models. In Chambers, J. M., and Hastie, T. J. (eds.) Statistical Models in S, Wadsworth.

See Also

print.eff, summary.eff, plot.eff, print.summary.eff, print.effpoly, summary.effpoly, plot.effpoly, print.efflist, summary.efflist, plot.efflist, xyplot, densityplot

  • effect
  • effect.lm
  • effect.multinom
  • effect.polr
  • allEffects
  • as.data.frame.eff
  • as.data.frame.effpoly
  • as.data.frame.efflatent
mod.cowles <- glm(volunteer ~ sex + neuroticism*extraversion, 
    data=Cowles, family=binomial)
eff.cowles <- allEffects(mod.cowles, xlevels=list(neuroticism=0:24, 
    extraversion=seq(0, 24, 6)), given.values=c(sexmale=0.5))

plot(eff.cowles, 'sex', ylab="Prob(Volunteer)")

plot(eff.cowles, 'neuroticism:extraversion', ylab="Prob(Volunteer)",

plot(eff.cowles, 'neuroticism:extraversion', multiline=TRUE, 
plot(effect('sex:neuroticism:extraversion', mod.cowles,
    xlevels=list(neuroticism=0:24, extraversion=seq(0, 24, 6))), multiline=TRUE)

mod.beps <- multinom(vote ~ age + gender + economic.cond.national +
				economic.cond.household + Blair + Hague + Kennedy +
				Europe*political.knowledge, data=BEPS)
plot(effect("Europe*political.knowledge", mod.beps, 
	xlevels=list(Europe=1:11, political.knowledge=0:3)))
plot(effect("Europe*political.knowledge", mod.beps, 
		xlevels=list(Europe=1:11, political.knowledge=0:3),
	style="stacked", colors=c("blue", "red", "orange"), rug=FALSE)
mod.wvs <- polr(poverty ~ gender + religion + degree + country*poly(age,3),
plot(effect("country*poly(age, 3)", mod.wvs))

plot(effect("country*poly(age, 3)", mod.wvs), style="stacked", 
	colors=c("gray75", "gray50", "gray25"))
plot(effect("country*poly(age, 3)", latent=TRUE, mod.wvs))

mod.pres <- lm(prestige ~ log(income, 10) + poly(education, 3) + poly(women, 2), 
eff.pres <- allEffects(mod.pres, default.levels=50)
plot(eff.pres, ask=FALSE)
Documentation reproduced from package effects, version 2.0-0, License: GPL (>= 2)

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