lqmm (version 1.01)

lqm: Fitting Linear Quantile Models

Description

lqm is used to fit linear quantile models based on the asymmetric Laplace distribution.

Usage

lqm(formula, data, subset, na.action, weights = NULL, iota = 0.5,
	contrasts = NULL, control = list(), fit = TRUE)

Arguments

formula

an object of class formula for fixed effects: 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 envir

subset

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

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options.

weights

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

iota

the quantile(s) to be estimated. This must be a number between 0 and 1, otherwise the execution is stopped. If more than one quantile is specified, rounding off to the 4th decimal must give non--duplicated values of iota, otherwise the execut

contrasts

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

control

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

fit

logical flag. If FALSE the function returns a list of arguments to be passed to lqm.fit.gs.

Value

• lqm returns an object of class lqm. The function summary is used to obtain and print a summary of the results. The generic accessor functions coefficients, predict and residuals extract various useful features of the value returned by lqm. An object of class lqm is a list containing the following components:
• theta
  a vector of coefficients. theta is a named matrix of coefficients when iota is a vector of values.
• scale
  the scale parameter.
• logLik
  the log--likelihood.
• opt
  details on optimization (see lqm.fit.gs).
• call
  the matched call.
• term.labels
  names for theta.
• terms
  the terms object used.
• nobs
  the number of observations.
• edf,dim_theta
  the length of theta.
• rdf
  the number of residual degrees of freedom.
• iota
  the estimated quantile(s).
• x
  the model matrix.
• y
  the model response.
• weights
  the weights used in the fitting process (a vector of 1's if weights = NULL).
• InitialPar
  starting values for theta.
• control
  list of control parameters used for optimization (see lqmControl).

Details

The function computes an estimate on the iota-th quantile function of the response, conditional on the covariates, as specified by the formula argument. The quantile predictor is assumed to be linear. The function maximizes the (log)likelihood of a Laplace regression which is equivalent to the minimization of the weighted sum of absolute residuals (Koenker and Bassett, 1978). The optimization algorithm is based on the gradient of the Laplace log--likelihood (Bottai, Orsini and Geraci, 2011).

References

Bottai M, Orsini N and Geraci M (2011). A Gradient Search Maximization Algorithm for Laplace Likelihood. Unpublished manuscript. Koenker R and Bassett G (1978). Regression Quantiles. Econometrica 46(1), 33--50.

See Also

summary.lqm

Examples

set.seed(12356)
n <- 200
p <- 1:3/4
test <- data.frame(x = runif(n,0,1))
test$y <- 30 + test$x + rnorm(n)
fit.lqm <- lqm(y ~ x, data = test, iota = p,
	control = list(verbose = FALSE, loop_tol = 0.001), fit = TRUE)
fit.lqm