Takes a fitted rqss object produced by rqss() and plots
the component smooth functions that make up the ANOVA decomposition.
Since the components "omit the intercept" the estimated intercept is added back
in – this facilitates the comparison of quantile fits particularly.
For models with a partial linear component or several qss components
it may be preferable to plot the output of predict.rqss.
Note that these functions are intended to plot rqss objects only, attempting
to plot summary.rqss objects just generates a warning message.
Usage
## S3 method for class 'rqss'
plot(x, rug = TRUE, jit = TRUE, bands = NULL, coverage = 0.95,
add = FALSE, shade = TRUE, select = NULL, pages = 0, titles = NULL,
bcol = NULL, ...)
## S3 method for class 'qss1'
plot(x, rug = TRUE, jit = TRUE, add = FALSE, ...)
## S3 method for class 'qss2'
plot(x, render = "contour", ncol = 100, zcol = NULL, ...)
## S3 method for class 'summary.rqss'
plot(x, ...)
Arguments
x
a fitted rqss object produced by rqss().
...
additional arguments for the plotting algorithm
rug
if TRUE, a rugplot for the x-coordinate is plotted
jit
if TRUE, the x-values of the rug plot are jittered
bands
if TRUE, confidence bands for the smoothed effects are plotted, if
"uniform" then uniform bands are plotted, if "both" then both the uniform
and the pointwise bands are plotted.
coverage
desired coverage probability of confidence bands, if requested
select
vector of indices of qss objects to be plotted, by default all
pages
number of pages desired for the plots
render
a character specifying the rendering for bivariate fits;
either "contour" (default) or "rgl". The latter
requires package rgl.
add
if TRUE then add qss curve to existing (usually) scatterplot,
otherwise initiate a new plot
shade
if TRUE then shade the confidence band
titles
title(s) as vector of character strings, by default titles are chosen for
each plot as "Effect of CovariateName"
bcol
vector of two colors for confidence bands
ncol, zcol
Only for render = "rgl": number of colors and
z values for color construction.
Details
If bands == "uniform" then the bands are uniform bands based on the
Hotelling (1939) tube approach. See also Naiman (1986),
Johansen and Johnstone (1990), Sun and Loader (1994),
and Krivobokova, Kneib, and Claeskens (2009), in particular the computation of
the "tube length" is based on the last of these references. If bands
is non null, and not "uniform" then pointwise bands are returned.
Since bands for bivariate components are not (yet) supported, if requested
such components will be returned as NULL.
Value
The function produces plots for the ANOVA components as a side effect. For
"qss1" the "add = TRUE" can be used to overplot the fit on a
scatterplot. When there are multiple pages required "par(ask = TRUE)"
is turned on so that the plots may be examined sequentially. If bands != NULL
then a list with three components for each qss component is returned (invisibly):
x
The x coordinates of the confidence bands
blo
The y coordinates of the lower confidence curve, if
bands = "both" then this is a matrix with two columns
bhi
The y coordinates of the upper confidence curve, if
bands = "both" then this is a matrix with two columns
Author(s)
Roger Koenker
References
[1] Hotelling, H. (1939): “Tubes and Spheres in $n$-spaces, and a class
of statistical problems,” Am J. Math, 61, 440–460.
[2] Johansen, S., and I.M. Johnstone (1990): “Hotelling's
Theorem on the Volume of Tubes: Some Illustrations in Simultaneous
Inference and Data Analysis,” The Annals of Statistics, 18, 652–684.
[3] Naiman, D. (1986) Conservative confidence bands in curvilinear regression,
The Annals of Statistics, 14, 896–906.
[4] Sun, J. and C.R. Loader, (1994) Simultaneous confidence bands for linear
regression and smoothing, The Annals of Statistics, 22, 1328–1345.
[5] Krivobokova, T., T. Kneib, and G. Claeskens (2009) Simultaneous Confidence
Bands for Penalized Spline Estimators, preprint.
[6] Koenker, R. (2010) Additive Models for Quantile Regression: Model Selection
and Confidence Bandaids, preprint.
See Also
rqss
Examples
n <- 200
x <- sort(rchisq(n,4))
z <- x + rnorm(n)
y <- log(x)+ .1*(log(x))^2 + log(x)*rnorm(n)/4 + z
plot(x,y-z)
fN <- rqss(y~qss(x,constraint="N")+z)
plot(fN)
fI <- rqss(y~qss(x,constraint="I")+z)
plot(fI, col="blue")
fCI <- rqss(y~qss(x,constraint="CI")+z)
plot(fCI, col="red")
## A bivariate example
data(CobarOre)
fCO <- rqss(z~qss(cbind(x,y),lambda=.08), data = CobarOre)
plot(fCO)