Binary Quantile Regression

Description

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

Usage

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rq.bin(formula, tau = 0.5, data, weights = NULL, contrasts = NULL,
	normalize = "last", control = NULL, fit = TRUE)
rqbin.fit(x, y, tau = 0.5, weights, control)

Arguments

formula

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

x

the design matrix.

y

the response variable.

tau

quantile to be estimated.

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. Should be NULL or a numeric vector - not yet implemented.

contrasts

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

normalize

character specifying the type of normalization of the coefficients: if "last" (default), the last coefficient is set equal to 1; if "all", the vector of all coefficients except the intercept has norm equal to 1.

control

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

fit

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

Details

A binary quantile regression model is fitted as linear specification of the quantile function of a latent response variable (Manski 1975, 1985). The function rqbin.fit calls the Fortran routine simann.f implementing the simulated annealing algorithm of Goffe et al (1994) – original code by William Goffe, modified by Gregory Kordas. Normalization is necessary for estimation to be possible. The normalization proposed by Horowitz (1992) assumes that there is a continuous regressor independent of the (latent) error and the corresponding regression coefficient is constrained to be equal to 1. Therefore, the user must ensure that the last term in formula or the last column in the matrix x corresponds to such regressor. If the argument normalize = "all", then the normalization proposed by Manski (1975) is applied so that the norm of the vector with all the 'slopes' (i.e., excluding the intercept), is equal to 1.

Value

a list of class rq.bin containing the following components

coefficients

a vector of coefficients. coefficients is a named matrix of coefficients when tau is a vector of values.

logLik

the log–likelihood.

opt

details on optimization.

call

the matched call.

term.labels

names for theta.

terms

the terms object used.

nobs

the number of observations.

edf

the numer of parameters (minus 1 if normalize is last).

rdf

the number of residual degrees of freedom.

tau

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).

levels

factors levels.

control

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

normalize

type of normalization.

Author(s)

Marco Geraci

References

Goffe WL, Ferrier GD, Rogers J. Global optimization of statistical functions with simulated annealing. Journal of Econometrics 1994;60(1):65-99. Code retrieved from http://econpapers.repec.org/software/wpawuwppr/9406001.htm.

Kordas G. Smoothed binary regression quantiles. Journal of Applied Econometrics 2006;21(3):387-407. Code retrieved from http://qed.econ.queensu.ca/jae/2006-v21.3/kordas/.

Horowitz JL. A Smoothed Maximum Score Estimator for the Binary Response Model. Econometrica 1992;60(3):505-531.

Manski CF. Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 1975;3(3):205-228.

Manski, CF. Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator. Journal of Econometrics 1985;27(3):313-333.

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