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Qtools (version 1.0)

rq.bin: Binary Quantile Regression

Description

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

Usage

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

Value

a list of class rq.bin containing the following componentscoefficientsa vector of coefficients. coefficients is a named matrix of coefficients when tau is a vector of values.logLikthe log--likelihood.optdetails on optimization.callthe matched call.term.labelsnames for theta.termsthe terms object used.nobsthe number of observations.edfthe numer of parameters (minus 1 if normalize is last).rdfthe number of residual degrees of freedom.tauthe estimated quantile(s).xthe model matrix.ythe model response.weightsthe weights used in the fitting process (a vector of 1's if weights = NULL).levelsfactors levels.controllist of control parameters used for optimization (see rqbinControl).normalizetype of normalization.

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.

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/RePEc:wpa:wuwppr:9406001. 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.