plot.gam: Default GAM plotting

Description

Takes a fitted gam object produced by gam() and plots the component smooth functions that make it up, on the scale of the linear predictor. Optionally produces term plots for parametric model components as well.

Usage

## S3 method for class 'gam':
plot(x,residuals=FALSE,rug=TRUE,se=TRUE,pages=0,select=NULL,scale=-1,
         n=100,n2=40,pers=FALSE,theta=30,phi=30,jit=FALSE,xlab=NULL,
         ylab=NULL,main=NULL,ylim=NULL,xlim=NULL,too.far=0.1,
         all.terms=FALSE,shade=FALSE,shade.col="gray80",shift=0,
         trans=I,seWithMean=FALSE,unconditional=FALSE,by.resids=FALSE,
         scheme=0,...)

Arguments

a fitted gam object as produced by gam().

residuals

If TRUE then partial residuals are added to plots of 1-D smooths. If FALSE then no residuals are added. If this is an array of the correct length then it is used as the array of residuals to be used for producing partial residu

rug

when TRUE (default) then the covariate to which the plot applies is displayed as a rug plot at the foot of each plot of a 1-d smooth, and the locations of the covariates are plotted as points on the contour plot representing a 2-d smooth. Setting to

when TRUE (default) upper and lower lines are added to the 1-d plots at 2 standard errors above and below the estimate of the smooth being plotted while for 2-d plots, surfaces at +1 and -1 standard errors are contoured and overlayed on the co

pages

(default 0) the number of pages over which to spread the output. For example, if pages=1 then all terms will be plotted on one page with the layout performed automatically. Set to 0 to have the routine leave all graphics settings as they ar

select

Allows the plot for a single model term to be selected for printing. e.g. if you just want the plot for the second smooth term set select=2.

scale

set to -1 (default) to have the same y-axis scale for each plot, and to 0 for a different y axis for each plot. Ignored if ylim supplied.

number of points used for each 1-d plot - for a nice smooth plot this needs to be several times the estimated degrees of freedom for the smooth. Default value 100.

Square root of number of points used to grid estimates of 2-d functions for contouring.

pers

Set to TRUE if you want perspective plots for 2-d terms.

theta

One of the perspective plot angles.

phi

The other perspective plot angle.

jit

Set to TRUE if you want rug plots for 1-d terms to be jittered.

xlab

If supplied then this will be used as the x label for all plots.

ylab

If supplied then this will be used as the y label for all plots.

main

Used as title (or z axis label) for plots if supplied.

ylim

If supplied then this pair of numbers are used as the y limits for each plot.

xlim

If supplied then this pair of numbers are used as the x limits for each plot.

too.far

If greater than 0 then this is used to determine when a location is too far from data to be plotted when plotting 2-D smooths. This is useful since smooths tend to go wild away from data. The data are scaled into the unit square before deciding what to ex

all.terms

if set to TRUE then the partial effects of parametric model components are also plotted, via a call to termplot. Only terms of order 1 can be plotted in this way.

shade

Set to TRUE to produce shaded regions as confidence bands for smooths (not avaliable for parametric terms, which are plotted using termplot).

shade.col

define the color used for shading confidence bands.

shift

constant to add to each smooth (on the scale of the linear predictor) before plotting. Can be useful for some diagnostics, or with trans.

trans

function to apply to each smooth (after any shift), before plotting. shift and trans are occasionally useful as a means for getting plots on the response scale, when the model consists only of a single smooth.

seWithMean

if TRUE the component smooths are shown with confidence intervals that include the uncertainty about the overall mean. If FALSE then the uncertainty relates purely to the centred smooth itself. Marra and Wood (2012) suggests t

unconditional

if TRUE then the smoothing parameter uncertainty corrected covariance matrix is used to compute uncertainty bands, if available. Otherwise the bands treat the smoothing parameters as fixed.

by.resids

Should partial residuals be plotted for terms with by variables? Usually the answer is no, they would be meaningless.

scheme

Integer or integer vector selecting a plotting scheme for each plot. See details.

...

other graphics parameters to pass on to plotting commands.

Value

The function simply generates plots.

WARNING

Note that the behaviour of this function is not identical to plot.gam() in S-PLUS.

Plotting can be slow for models fitted to large datasets. Set rug=FALSE to improve matters. If it's still too slow set too.far=0, but then take care not to overinterpret smooths away from supporting data.

Plots of 2-D smooths with standard error contours shown can not easily be customized.

The function can not deal with smooths of more than 2 variables!

Details

Produces default plot showing the smooth components of a fitted GAM, and optionally parametric terms as well, when these can be handled by termplot.

For smooth terms plot.gam actually calls plot method functions depending on the class of the smooth. Currently random.effects, Markov random fields (mrf), Spherical.Spline and factor.smooth.interaction terms have special methods (documented in their help files), the rest use the defaults described below.

For plots of 1-d smooths, the x axis of each plot is labelled with the covariate name, while the y axis is labelled s(cov,edf) where cov is the covariate name, and edf the estimated (or user defined for regression splines) degrees of freedom of the smooth. scheme == 0 produces a smooth curve with dashed curves indicating 2 standard error bounds. scheme == 1 illustrates the error bounds using a shaded region.

For scheme==0, contour plots are produced for 2-d smooths with the x-axes labelled with the first covariate name and the y axis with the second covariate name. The main title of the plot is something like s(var1,var2,edf), indicating the variables of which the term is a function, and the estimated degrees of freedom for the term. When se=TRUE, estimator variability is shown by overlaying contour plots at plus and minus 1 s.e. relative to the main estimate. If se is a positive number then contour plots are at plus or minus se multiplied by the s.e. Contour levels are chosen to try and ensure reasonable separation of the contours of the different plots, but this is not always easy to achieve. Note that these plots can not be modified to the same extent as the other plot. For 2-d smooths scheme==1 produces a perspective plot, while scheme==2 produces a heatmap, with overlaid contours.

Smooths of more than 2 variables are not plotted, but see vis.gam.

Fine control of plots for parametric terms can be obtained by calling termplot directly, taking care to use its terms argument.

Note that, if seWithMean=TRUE, the confidence bands include the uncertainty about the overall mean. In other words although each smooth is shown centred, the confidence bands are obtained as if every other term in the model was constrained to have average 0, (average taken over the covariate values), except for the smooth concerned. This seems to correspond more closely to how most users interpret componentwise intervals in practice, and also results in intervals with close to nominal (frequentist) coverage probabilities by an extension of Nychka's (1988) results presented in Marra and Wood (2012).

Sometimes you may want a small change to a default plot, and the arguments to plot.gam just won't let you do it. In this case, the quickest option is sometimes to clone the smooth.construct and Predict.matrix methods for the smooth concerned, modifying only the returned smoother class (e.g. to foo.smooth). Then copy the plot method function for the original class (e.g. mgcv:::plot.mgcv.smooth), modify the source code to plot exactly as you want and rename the plot method function (e.g. plot.foo.smooth). You can then use the cloned smooth in models (e.g. s(x,bs="foo")), and it will automatically plot using the modified plotting function.

References

Chambers and Hastie (1993) Statistical Models in S. Chapman & Hall.

Marra, G and S.N. Wood (2012) Coverage Properties of Confidence Intervals for Generalized Additive Model Components. Scandinavian Journal of Statistics.

Nychka (1988) Bayesian Confidence Intervals for Smoothing Splines. Journal of the American Statistical Association 83:1134-1143.

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Examples

Run this code

library(mgcv)
set.seed(0)
## fake some data...
f1 <- function(x) {exp(2 * x)}
f2 <- function(x) { 
  0.2*x^11*(10*(1-x))^6+10*(10*x)^3*(1-x)^10 
}
f3 <- function(x) {x*0}

n<-200
sig2<-4
x0 <- rep(1:4,50)
x1 <- runif(n, 0, 1)
x2 <- runif(n, 0, 1)
x3 <- runif(n, 0, 1)
e <- rnorm(n, 0, sqrt(sig2))
y <- 2*x0 + f1(x1) + f2(x2) + f3(x3) + e
x0 <- factor(x0)

## fit and plot...
b<-gam(y~x0+s(x1)+s(x2)+s(x3))
plot(b,pages=1,residuals=TRUE,all.terms=TRUE,shade=TRUE,shade.col=2)
plot(b,pages=1,seWithMean=TRUE) ## better coverage intervals

## just parametric term alone...
termplot(b,terms="x0",se=TRUE)

## more use of color...
op <- par(mfrow=c(2,2),bg="blue")
x <- 0:1000/1000
for (i in 1:3) {
  plot(b,select=i,rug=FALSE,col="green",
    col.axis="white",col.lab="white",all.terms=TRUE)
  for (j in 1:2) axis(j,col="white",labels=FALSE)
  box(col="white")
  eval(parse(text=paste("fx <- f",i,"(x)",sep="")))
  fx <- fx-mean(fx)
  lines(x,fx,col=2) ## overlay `truth' in red
}
par(op)

## example with 2-d plots, and use of schemes...
b1 <- gam(y~x0+s(x1,x2)+s(x3))
op <- par(mfrow=c(2,2))
plot(b1,all.terms=TRUE)
par(op) 
op <- par(mfrow=c(2,2))
plot(b1,all.terms=TRUE,scheme=1)
par(op)
op <- par(mfrow=c(2,2))
plot(b1,all.terms=TRUE,scheme=c(2,1))
par(op)

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