# predict.rqss

##### Predict from fitted nonparametric quantile regression smoothing spline models

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.

- Keywords
- robust, regression, smooth

##### 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

##### 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.

##### 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.

##### See Also

##### Examples

```
# 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)
# }
```

*Documentation reproduced from package quantreg, version 5.54, License: GPL (>= 2)*