predict.rqss: Predict from fitted nonparametric quantile regression smoothing spline models

Description

Additive models for nonparametric quantile regression using total variation penalty methods can be fit with the rqss function. Univarariate and bivariate components can be predicted using these functions.

Usage

# S3 method for rqss
predict(object, newdata, interval = "none", level = 0.95, ...)
# S3 method for qss1
predict(object, newdata, ...)
# S3 method for qss2
predict(object, newdata, ...)

Arguments

object

is a fitted object produced by rqss

newdata

a data frame describing the observations at which prediction is to be made. For qss components, newdata should lie in strictly within the convex hull of the fitting data. Newdata corresponding to the partially linear component of the model may require caution concerning the treatment of factor levels, if any.

interval

If set to confidence then a level confidence interval for the predictions is returned.

level

intended coverage probability for the confidence intervals

…

optional arguments

Value

A vector of predictions, or in the case that interval = "confidence") a matrix whose first column is the vector of predictions and whose second and third columns are the lower and upper confidence limits for each prediction.

Details

For both univariate and bivariate prediction linear interpolation is done. In the bivariate case, this involves computing barycentric coordinates of the new points relative to their enclosing triangles. It may be of interest to plot individual components of fitted rqss models: this is usually best done by fixing the values of other covariates at reference values typical of the sample data and predicting the response at varying values of one qss term at a time. Direct use of the predict.qss1 and predict.qss2 functions is discouraged since it usually corresponds to predicted values at absurd reference values of the other covariates, i.e. zero.

Examples

Run this code

# NOT RUN {
n <- 200
lam <- 2
x <- sort(rchisq(n,4))
z <- exp(rnorm(n)) + x
y <- log(x)+ .1*(log(x))^2 + z/4 +  log(x)*rnorm(n)/4
plot(x,y - z/4 + mean(z)/4)
Ifit <- rqss(y ~ qss(x,constraint="I") + z)
sfit <- rqss(y ~ qss(x,lambda = lam) + z)
xz <- data.frame(z = mean(z),
                 x = seq(min(x)+.01,max(x)-.01,by=.25))
lines(xz[["x"]], predict(Ifit, xz), col=2)
lines(xz[["x"]], predict(sfit, xz), col=3)
legend(10,2,c("Increasing","Smooth"),lty = 1, col = c(2,3))
title("Predicted Median Response at Mean Value of z")
# }
# NOT RUN {
<!-- %%keep objects for inspection : do not rm(x,y,z,xz,fit) -->
# }
# NOT RUN {
## Bivariate example -- loads pkg "tripack"
require(tripack)
require(akima)
data(CobarOre)
fit <- rqss(z ~ qss(cbind(x,y), lambda=.08),
            data= CobarOre)
plot(fit, col="grey",
     main = "CobarOre data -- rqss(z ~ qss(cbind(x,y)))")
T <- with(CobarOre, tri.mesh(x, y))
set.seed(77)
ndum <- 100
xd <- with(CobarOre, runif(ndum, min(x), max(x)))
yd <- with(CobarOre, runif(ndum, min(y), max(y)))
table(s <- in.convex.hull(T, xd, yd))
pred <- predict(fit, data.frame(x = xd[s], y = yd[s]))
contour(interp(xd[s],yd[s], pred),
        col="red", add = TRUE)
# }