Quantile Regression for Counts

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Description

This function is used to fit a quantile regression model when the response is a count variable.

Usage

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lqm.counts(formula, data, weights = NULL, offset = NULL, contrasts = NULL,
	tau = 0.5, M = 50, zeta = 1e-05, B = 0.999, cn = NULL, alpha = 0.05,
	control = list())

Arguments

formula

an object of class formula: a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which lqm is called.

weights

an optional vector of weights to be used in the fitting process.

offset

an optional offset to be included in the model frame.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

tau

quantile to be estimated.

M

number of dithered samples.

zeta

small constant (see References).

B

right boundary for uniform random noise U[0,B] to be added to the response variable (see References).

cn

small constant to be passed to F.lqm (see References).

alpha

significance level.

control

list of control parameters of the fitting process. See lqmControl.

Details

A linear quantile regression model if fitted to the log–transformed response. Additional tranformation functions will be implemented. The notation used here follows closely that of Machado and Santos Silva (2005).

Value

an object of class "lqm.counts" containing the following components

tau

the estimated quantile.

theta

regression quantile (on the log–scale).

fitted

predicted quantile (on the response scale).

tTable

coefficients, standard errors, etc.

x

the model matrix.

y

the model response.

offset

offset.

nobs

the number of observations.

M

specified number of dithered samples for standard error estimation.

Mn

actual number of dithered samples used for standard error estimation that gave an invertible D matrix (Machado and Santos Silva, 2005).

term.labels

names for theta.

terms

the terms object used.

rdf

the number of residual degrees of freedom.

InitialPar

starting values for theta.

control

list of control parameters used for optimization (see lqmControl).

Author(s)

Marco Geraci

References

Machado JAF and Santos Silva JMC (2005). Quantiles for counts. Journal of the American Statistical Association, 100(472), 1226–1237.

Examples

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n <- 100
x <- runif(n)
test <- data.frame(x = x, y = rpois(n, 2*x))
lqm.counts(y ~ x, data = test, M = 50)

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