Restricted Regression Quantiles

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Description

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

Usage

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rrq(formula, tau, data, subset, weights, na.action, method = "fn",
model = TRUE, contrasts = NULL, ...)
rrq.fit(x, y, tau, method = "fn", ...)
rrq.wfit(x, y, tau, weights, method = "fn", ...)

Arguments

formula

a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right.

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 NAs.

method

the algorithm used to compute the fit (see rq).

model

if TRUE then the model frame is returned. This is essential if one wants to call summary subsequently.

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 rq.fit or rq.wfit.

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

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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)

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