# predict.rq

##### Quantile Regression Prediction

Prediction based on fitted quantile regression model

- Keywords
- regression

##### Usage

```
# S3 method for rq
predict(object, newdata, type = "none", interval = c("none", "confidence"),
level = .95, na.action = na.pass, ...)
# S3 method for rqs
predict(object, newdata, type = "Qhat", stepfun = FALSE, na.action = na.pass, ...)
# S3 method for rq.process
predict(object, newdata, type = "Qhat", stepfun = FALSE, na.action = na.pass, ...)
```

##### Arguments

- object
object of class rq or rqs or rq.process produced by

`rq`

- newdata
An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

- interval
type of interval desired: default is 'none', when set to 'confidence' the function returns a matrix predictions with point predictions for each of the 'newdata' points as well as lower and upper confidence limits.

- level
converage probability for the 'confidence' intervals.

- type
For

`predict.rq`

, the method for 'confidence' intervals, if desired. If 'percentile' then one of the bootstrap methods is used to generate percentile intervals for each prediction, if 'direct' then a version of the Portnoy and Zhou (1998) method is used, and otherwise an estimated covariance matrix for the parameter estimates is used. Further arguments to determine the choice of bootstrap method or covariance matrix estimate can be passed via the … argument. For`predict.rqs`

and`predict.rq.process`

when`stepfun = TRUE`

,`type`

is "Qhat", "Fhat" or "fhat" depending on whether the user would like to have estimates of the conditional quantile, distribution or density functions respectively. As noted below the two former estimates can be monotonized with the function`rearrange`

. When the "fhat" option is invoked, a list of conditional density functions is returned based on Silverman's adaptive kernel method as implemented in`akj`

and`approxfun`

.- stepfun
If 'TRUE' return stepfunctions otherwise return matrix of predictions. these functions can be estimates of either the conditional quantile or distribution functions depending upon the

`type`

argument. When`stepfun = FALSE`

a matrix of point estimates of the conditional quantile function at the points specified by the`newdata`

argument.- na.action
function determining what should be done with missing values in 'newdata'. The default is to predict 'NA'.

- …
Further arguments passed to or from other methods.

##### Details

Produces predicted values, obtained by evaluating the quantile regression function in the frame 'newdata' (which defaults to 'model.frame(object)'. These predictions purport to estimate the conditional quantile function of the response variable of the fitted model evaluated at the covariate values specified in "newdata" and the quantile(s) specified by the "tau" argument. Several methods are provided to compute confidence intervals for these predictions.

##### Value

A vector or matrix of predictions, depending upon the setting of
'interval'. In the case that there are multiple taus in `object`

when object is of class 'rqs' setting 'stepfun = TRUE' will produce a
`stepfun`

object or a list of `stepfun`

objects.
The function `rearrange`

can be used to monotonize these
step-functions, if desired.

##### References

Zhou, Kenneth Q. and Portnoy, Stephen L. (1998) Statistical inference on heteroscedastic models based on regression quantiles Journal of Nonparametric Statistics, 9, 239-260

##### See Also

##### Examples

```
# NOT RUN {
data(airquality)
airq <- airquality[143:145,]
f <- rq(Ozone ~ ., data=airquality)
predict(f,newdata=airq)
f <- rq(Ozone ~ ., data=airquality, tau=1:19/20)
fp <- predict(f, newdata=airq, stepfun = TRUE)
fpr <- rearrange(fp)
plot(fp[[2]],main = "Conditional Ozone Quantile Prediction")
lines(fpr[[2]], col="red")
legend(.2,20,c("raw","cooked"),lty = c(1,1),col=c("black","red"))
fp <- predict(f, newdata=airq, type = "Fhat", stepfun = TRUE)
fpr <- rearrange(fp)
plot(fp[[2]],main = "Conditional Ozone Distribution Prediction")
lines(fpr[[2]], col="red")
legend(20,.4,c("raw","cooked"),lty = c(1,1),col=c("black","red"))
# }
```

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