# effect

##### 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"`

).

##### Usage

```
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, ...)
```

##### Arguments

- term
- 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 - mod
- an object of class
`"lm"`

,`"glm"`

,`"multinom"`

, or`"polr"`

. - 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. - given.values
- 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`

- 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 - typical
- a function to be applied to the columns of the model matrix
over which the effect is "averaged"; the default is
`mean`

. - latent
- 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. - x
- an object of class
`"eff"`

or`"effpoly"`

. - row.names, optional
- not used.
- ...
- arguments to be passed down.

##### Details

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.

##### Value

- For
`lm`

and`glm`

,`effect`

returns an`"eff"`

object, and for`multinom`

and`polr`

, an`"effpoly"`

object, with the following components: term the term to which the effect pertains. formula the complete model formula. response a character string giving the name of the response variable. y.levels (for `"effpoly"`

objects) levels of the polytomous response variable.variables a 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).x a 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.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 (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.level for 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.

##### References

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, <*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`

##### Examples

```
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))
eff.cowles
plot(eff.cowles, 'sex', ylab="Prob(Volunteer)")
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)
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),
given.values=c(gendermale=0.5)),
style="stacked", colors=c("blue", "red", "orange"), rug=FALSE)
mod.wvs <- polr(poverty ~ gender + religion + degree + country*poly(age,3),
data=WVS)
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),
data=Prestige)
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)*