Functions For Constructing Effect Plots

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

models, hplot
effect(term, mod, xlevels=list(), default.levels=10, se=TRUE, 
    transformation=list(link=family(mod)$linkfun, inverse=family(mod)$linkinv), 
all.effects(mod, ...)

## S3 method for class 'effect':
print(x, type=c("response", "link"), ...)
## S3 method for class 'effect.list':
print(x, ...)
## S3 method for class 'effect':
summary(object, type=c("response", "link"), ...)
## S3 method for class 'effect.list':
summary(object, ...)
## S3 method for class 'effect':
plot(x, x.var=which.max(levels),
    z.var=which.min(levels), multiline=is.null(x$se), rug=TRUE, xlab,
    ylab=x$response, main=paste(effect, "effect plot"),
    colors=palette(), symbols=1:10, lines=1:10, cex=1.5, ylim,
    factor.names=TRUE, type=c("response", "link"), ticks=list(at=NULL, n=5), 
    alternating=TRUE, rescale.axis=TRUE, ...)
## S3 method for class 'effect.list':
plot(x, selection, ...)
## S3 method for class 'effect':
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.
an object of class "lm" or "glm".
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.
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.
x, object
an object of type "effect" or "effect.list", as appropriate.
if "response" (the default), effects are printed or the vertical axis is labelled on the scale of the response variable; if "link", effects are printed or the vertical axis labelled on the scale of the linear pre
the index (number) of the covariate or factor to place on the horizontal axis of each panel of the effect plot. The default is the predictor with the largest number of levels or values.
the index (number) of the covariate or factor for which individual lines are to be drawn in each panel of the effect plot. The default is the predictor with the smallest number of levels or values. This argument is only used if multi
if TRUE, each panel of the display represents combinations of values of two predictors, with one predictor (corresponding to x.var) on the horzontal axis, and the other (corresponding to z.var) used to defi
if TRUE, the default, a rug plot is shown giving the marginal distribution of the predictor on the horizontal axis, if this predictor is a covariate.
the label for the horizontal axis of the effect plot; if missing, the function will use the name of the predictor on the horizontal axis.
the label for the vertical axis of the effect plot; the default is the response variable for the model from which the effect was computed.
the title for the plot, printed at the top; the default title is constructed from the name of the effect.
colors[1] is used to plot effects, colors[2] to plot confidence bands. In a mulitline plot, the successive colors correspond to the levels of the z.var covariate or factor.
symbols, lines
corresponding to the levels of the z.var covariate or factor on a multiline plot. These arguments are used only if multiline = TRUE; in this case a legend is drawn at the top of the display.
character expansion for plotted symbols; default is 1.
2-element vector containing the lower and upper limits of the vertical axes; if NULL, the default, then the vertical axes are scaled from the data.
a logical value, default TRUE, that controls the inclusion of factor names in conditioning-variable labels.
a two-item list controlling the placement of tick marks on the vertical axis, with elements at and n. If at=NULL (the default), the program attempts to find `nice' locations for the ticks, and the value of
if TRUE (the default), the axis labels alternate by panels in multi-panel displays from left to right and top to bottom; if FALSE, axis labels appear at the bottom and on the left.
if TRUE (the default), the tick marks on the vertical axis are labelled on the response scale (e.g., the probability scale for effects computed on the logit scale for a binomial GLM).
the optional index (number) or quoted name of the effect in an effect list to be plotted; if not supplied, a menu of high-order terms is presented.
arguments to be passed down.
row.names, optional
not used.

Normally, the functions to be used directly are all.effects, to return a list of high-order effects, and the generic plot function to plot the effects. Plots are drawn using the xyplot function in the lattice package. Effects may also be printed (implicitly or explicitly via print) or summarized (using summary). 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 a generalized linear model, by default, effect prints the computed effect on the scale of the response variable using the inverse of the link function. In a logit model, for example, this means that the effects are expressed on the probability scale. By default, effects in a GLM are plotted on the scale of the linear predictor, but the vertical axis is labelled on the response scale. This preserves the linear structure of the model while permitting interpretation on what is usually a more familiar scale. This approach may also be used with linear models, for example to display effects on the scale of the response even if the data are analyzed on a transformed scale, such as log or square-root. In calculating effects, the strategy for `safe' prediction described in Hastie (1992: Sec. 7.3.3) is employed.


  • effect returns a list with the following components:
  • termthe term to which the effect pertains.
  • formulathe complete model formula.
  • responsea character string giving the response variable.
  • variablesa list with information about each predictor, including its name, whether it is a factor, and its levels or values.
  • fita 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.
  • xa data frame, the columns of which are the predictors, and the rows of which give all combinations of values of the 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.
  • sea vector of standard errors for the effect, on the scale of the linear predictor.
  • lower, upperone-column matrices of confidence limits, on the scale of the linear predictor.
  • confidence.levelcorresponding to the confidence limits.
  • transformationa two-element list, with element link giving the link function, and element inverse giving the inverse-link (mean) function.


Fox, J. (1987) Effect displays for generalized linear models. Sociological Methodology 17, 347--361. Hastie, T. J. (1992) Generalized additive models. In Chambers, J. M., and Hastie, T. J. (eds.) Statistical Models in S, Wadsworth.

See Also


  • effect
  • all.effects
  • print.effect
  • print.effect.list
  • summary.effect
  • summary.effect.list
  • plot.effect
  • plot.effect.list
  • as.data.frame.effect
mod.cowles <- glm(volunteer ~ sex + neuroticism*extraversion, 
    data=Cowles, family=binomial)
eff.cowles <- all.effects(mod.cowles, xlevels=list(neuroticism=0:24, 
    extraversion=seq(0, 24, 6)))
    model: volunteer ~ sex + neuroticism * extraversion
    sex effect
    female      male 
    0.4409441 0.3811941 
    neuroticism*extraversion effect
    neuroticism          0         6        12        18        24
            0  0.07801066 0.1871263 0.3851143 0.6301824 0.8225756
            1  0.08636001 0.1963396 0.3870453 0.6200668 0.8083638
            2  0.09551039 0.2058918 0.3889798 0.6098458 0.7932997
            3  0.10551835 0.2157839 0.3909179 0.5995275 0.7773775
           . . .
            23 0.51953129 0.4747277 0.4303273 0.3870199 0.3454282
            24 0.54709527 0.4895731 0.4323256 0.3768303 0.3243880
plot(eff.cowles, 'sex', ylab="Prob(Volunteer)")
    Loading required package: lattice

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)
Warning message: 
    sex:neuroticism:extraversion does not appear in the model in: 
      effect("sex:neuroticism:extraversion", mod.cowles, 
      xlevels = list(neuroticism = 0:24,  

mod.pres <- lm(prestige ~ log(income, 10) + poly(education, 3) + poly(women, 2), 
eff.pres <- all.effects(mod.pres, default.levels=50)
Documentation reproduced from package effects, version 0.9-0, License: GPL version 2 or newer

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