% Generated by roxygen2: do not edit by hand % Please edit documentation in R/rcbr.R name{rcbr} alias{rcbr} title{Estimation of Random Coefficient Binary Response Models} usage{ rcbr(formula, data, subset, offset, method = “GK”, …) } description{ Two methods are implemented for estimating binary response models

with random coefficients:  A nonparametric maximum likelihood method
proposed by Cosslett (1986) and extended by Ichimura and Thompson (1998),
and a (hemispherical) deconvolution method proposed by Gautier and
and Kitamura (2013).  The former is closely related to the NPMLE
for mixture models of Kiefer and Wolfowitz (1956).  The latter is an
R translation of the matlab implementation of Gautier and Kitamura.

} details{ The code{predict} method produces estimates of the probability of a “success”

(y = 1) for a particular vector, \code{(z,v)},  when aggregated over the estimated
distribution of random coefficients.

The code{logLik} produces an evaluation of the log likelihood value

associated with a fitted model.

@param formula an expression of the generic form code{y ~ z + v} where

\code{y} is the observed binary response, \code{z} is an observed covariate
with a random coefficient, and \code{v} is an observed covariate with
coefficient normalize to be one.  If \code{z} is not present then the
model has only a random "intercept" coefficient  and thus corresponds
to the basic model of Cosslett (1983);  this model is also referred to
as the current status model in the biostatistics literature, see Groeneboom
and Hendrikx (2016).  When \code{z} is present there are random coefficients
associated with both the intercept and \code{z}. 
@param data is a \code{data.frame} containing the data referenced in the
formula.
@param  subset specifies a subsample of the data used for fitting the model
@param  offset specifies a fixed shift in \code{v} representing the
potential effect of other covariates having fixed coefficients that may be
useful for profile likelihood computations.  (Should be vector of the same
length as \code{v}.
@param method controls whether the Gautier and Kitamura, "GK", or Kiefer and
Wolfowitz, "KW" methods are used.
@param ...  miscellaneous other arguments to control fitting.  
See \code{GK.control} and \code{KW.control} for further details.

@return of object of class code{GK}, code{KW1}, with components described in

further detail in the respective fitting functions.

@author Jiaying Gu and Roger Koenker

@references Kiefer, J. and J. Wolfowitz (1956) Consistency of the Maximum

Likelihood Estimator in the Presence of Infinitely Many Incidental
Parameters, \emph{Ann. Math. Statist}, 27, 887-906.

Cosslett, S. (1983) Distribution Free Maximum Likelihood Estimator of the

Binary Choice Model, \emph{Econometrica}, 51, 765-782.

Gautier, E. and Y. Kitamura (2013) Nonparametric estimation in random coefficients

binary choice models, \emph{Ecoonmetrica}, 81, 581-607.

Groeneboom, P. and K. Hendrickx (2016) Current Status Linear Regression,

preprint available from \url{https://arxiv.org/abs/1601.00202}.

Ichimuma, H. and T. S. Thompson, (1998) Maximum likelihood estimation of a binary

choice model with random coefficients of unknown distribution," 
\emph{Journal of Econometrics},  86, 269-295.

} keyword{nonparametric}