# Restricted Regression Quantiles

### Description

This function fits a restricted quantile regression model to avoid crossing of quantile curves.

### Usage

1 2 3 4 |

### Arguments

`formula` |
a formula object, with the response on the left of a |

`x` |
the design matrix. |

`y` |
the response variable. |

`tau` |
the quantile(s) to be estimated. |

`data` |
a data frame in which to interpret the variables named in the formula. |

`subset` |
an optional vector specifying a subset of observations to be used in the fitting process. |

`weights` |
an optional vector of weights to be used in the fitting process. Should be NULL or a numeric vector. |

`na.action` |
a function which indicates what should happen when the data contain |

`method` |
the algorithm used to compute the fit (see |

`model` |
if |

`contrasts` |
a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels. |

`...` |
optional arguments passed to |

### Author(s)

Marco Geraci

### References

He X. Quantile curves without crossing. The American Statistician 1997;51(2):186-192.

Koenker R (2013). quantreg: Quantile Regression. R package version 5.05. URL http://CRAN.R-project.org/package=quantreg.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
data(esterase)
# Fit standard quantile regression
fit <- quantreg::rq(Count ~ Esterase, data = esterase, tau = c(.1,.25,.5,.75,.9))
yhat <- fit$fitted.values
# Fit restricted quantile regression
fitr <- rrq(Count ~ Esterase, data = esterase, tau = c(.1,.25,.5,.75,.9))
yhat2 <- predict(fitr)
# Plot results
par(mfrow = c(1, 2))
# Plot regression quantiles
with(esterase, plot(Count ~ Esterase, pch = 16, cex = .8))
apply(yhat, 2, function(y,x) lines(x,y,lwd = 1.5), x = esterase$Esterase)
# Plot restricted regression quantiles
with(esterase, plot(Count ~ Esterase, pch = 16, cex = .8))
apply(yhat2, 2, function(y,x) lines(x,y,lwd = 1.5), x = esterase$Esterase)
``` |