| effect {effects} | R Documentation |
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").
effect(term, mod, ...)
## S3 method for class 'lm':
effect(term, mod, xlevels=list(), default.levels=10, se=TRUE,
confidence.level=.95,
transformation=list(link=family(mod)$linkfun, inverse=family(mod)$linkinv),
typical=mean, ...)
all.effects(mod, ...)
## S3 method for class 'effect':
as.data.frame(x, row.names=NULL, optional=TRUE)
term |
the quoted name of a term, usually, but not necessarily, a high-order term in the model. |
mod |
an object of class "lm" or "glm". |
xlevels |
an optional list of values at which to set covariates,
with components of the form covariate.name = vector.of.values. |
default.levels |
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. |
se |
if TRUE, the default, calculate standard errors and
confidence limits for the effects. |
confidence.level |
level at which to compute confidence limits
based on the standard-normal distribution; the default is 0.95. |
transformation |
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 NULL, the identify function,
I, is used; this effect can also be achieved by setting the
argument to NULL. The inverse-link may be used to transform effects
when they are printed or plotted; the link may be used in positioning
axis labels (see below). If the link is not given, an attempt will be
made to approximate it from the inverse-link. |
typical |
a function to be applied to the columns of the model matrix
over which the effect is "averaged"; the default is mean. |
... |
arguments to be passed down. |
x |
an object of type "effect". |
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.
(see plot.effect.list and plot.effect).
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)
(see print.effect.list, summary.effect.list,
print.effect, and summary.effect).
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.
effect returns an "effect" object with the following components:
term |
the term to which the effect pertains. |
formula |
the complete model formula. |
response |
a character string giving the response variable. |
variables |
a list with information about each predictor, including its name, whether it is a factor, and its levels or values. |
fit |
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. |
x |
a data frame, the columns of which are the predictors, and the rows of which give all combinations of values of the predictors. |
model.matrix |
the model matrix from which the effect was calculated. |
data |
a data frame with the data on which the fitted model was based. |
discrepancy |
the percentage discrepancy for the `safe' predictions of the original fit; should be very close to 0. |
se |
a vector of standard errors for the effect, on the scale of the linear predictor. |
lower, upper |
one-column matrices of confidence limits, on the scale of the linear predictor. |
confidence.level |
corresponding to the confidence limits. |
transformation |
a two-element list, with element link giving the
link function, and element inverse giving the inverse-link (mean) function. |
John Fox jfox@mcmaster.ca.
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>.
Hastie, T. J. (1992) Generalized additive models. In Chambers, J. M., and Hastie, T. J. (eds.) Statistical Models in S, Wadsworth.
print.effect, summary.effect, plot.effect,
print.summary.effect, print.effect.list, summary.effect.list,
plot.effect.list, xyplot
data(Cowles)
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)))
eff.cowles
## Not run:
model: volunteer ~ sex + neuroticism * extraversion
sex effect
sex
female male
0.4409441 0.3811941
neuroticism*extraversion effect
extraversion
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
## End(Not run)
plot(eff.cowles, 'sex', ylab="Prob(Volunteer)")
## Not run:
Loading required package: lattice
## End(Not run)
plot(eff.cowles, 'neuroticism:extraversion', ylab="Prob(Volunteer)",
ticks=list(at=c(.1,.25,.5,.75,.9)))
plot(eff.cowles, 'neuroticism:extraversion', multiline=TRUE,
ylab="Prob(Volunteer)")
plot(effect('sex:neuroticism:extraversion', mod.cowles,
xlevels=list(neuroticism=0:24, extraversion=seq(0, 24, 6))), multiline=TRUE)
## Not run:
Warning message:
sex:neuroticism:extraversion does not appear in the model in:
effect("sex:neuroticism:extraversion", mod.cowles,
xlevels = list(neuroticism = 0:24,
## End(Not run)
data(Prestige)
mod.pres <- lm(prestige ~ log(income, 10) + poly(education, 3) + poly(women, 2),
data=Prestige)
eff.pres <- all.effects(mod.pres, default.levels=50)
plot(eff.pres, ask=FALSE)