effects (version 1.0-1)

effect: Functions For Constructing Effect Plots

Description

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").

Usage

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)

Arguments

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

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.

Value

• 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.

Details

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.

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, <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.

See Also

print.effect, summary.effect, plot.effect, print.summary.effect, print.effect.list, summary.effect.list, plot.effect.list, xyplot

Examples

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
    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
plot(eff.cowles, 'sex', ylab="Prob(Volunteer)")
    Loading required package: lattice

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

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)