car (version 1.0-3)

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=family(mod)$linkinv, typical=mean)
    
all.effects(mod, ...)

## S3 method for class 'effect':
print(x, ...)## S3 method for class 'effect':
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, colors=palette(), symbols=1:10, lines=1:10, cex=1.5, ylim=NULL,
    factor.names=TRUE, transform=list(link=I, inverse=I, at=NULL, n=5), ...)
## S3 method for class 'effect.list':
plot(x, selection, ...)
## 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 function to be applied to the calculated effects and confidence limits; the default is the inverse-link function for the model, which is the identity function for a linear model (i.e., no transformation.)

typical

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.

x.var

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.

multiline

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

rug

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.

z.var

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

colors

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.

cex

character expansion for plotted symbols; default is 1.

ylim

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.

factor.names

a logical value, default TRUE, that controls the inclusion of factor names in conditioning-variable labels.

xlab

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.

ylab

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.

selection

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.

transform

see details.

...

arguments to be passed down.

row.names, optional

not used.

Value

• effect returns a list with the following components:
• term
  the high-order 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.
• effect
  a one-column matrix of fitted values, representing the effect on the original scale; this is a ravelled table, representing all combinations of predictor values.
• fit
  a one-column matrix of fitted values, representing the effect on the transformed scale.
• 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 or standard errors for the effect, on the original scale.
• lower, upper
  one-column matrices of confidence limits, on the transformed scale.
• confidence.level
  corresponding to the confidence limits.

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. 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 transforms the computed effect to 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. This approach may also be used with linear models, for example to plot effects on the scale of the response even if the data are analyzed on a transformed scale, such as log or square-root. An alternative approach is to compute the effects on the scale of the link function --- e.g., the logit scale --- by specifying the argument transformation=I to effect, and instead transforming the response axis (in the manner of plotting a log axis) using the transform argument to the plot method for effect objects. This argument takes a list indicating how the response axis is to be transformed, with the following elements: [object Object],[object Object],[object Object],[object Object] 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. Hastie, T. J. (1992) Generalized additive models. In Chambers, J. M., and Hastie, T. J. (eds.) Statistical Models in S, Wadsworth.

See Also

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 
    Loading required package: grid
plot(eff.cowles, 'neuroticism:extraversion', ylab="Prob(Volunteer)")
plot(eff.cowles, 'neuroticism:extraversion', multiline=TRUE, 
    ylab="Prob(Volunteer)")
    
plot(effect('sex:neuroticism:extraversion',
    glm(volunteer ~ sex*neuroticism*extraversion, data=Cowles, family=binomial),
    xlevels=list(neuroticism=0:24, extraversion=seq(0, 24, 6))), multiline=TRUE)

logit <- function(p) log(p/(1-p))
prob <- function(logit) 1/(1 + exp(-logit))
eff.cowles.2 <- all.effects(mod.cowles, xlevels=list(neuroticism=0:24, 
    extraversion=seq(0, 24, 6)), transformation=I)    
plot(eff.cowles.2, transform=list(inverse=prob))
plot(eff.cowles.2, transform=list(link=logit, inverse=prob, at=c(.1,.25,.5,.75,.9)))
    
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)