A binary response model of choice between automobile and transit for t
ravel to work is estimated using fixed- and random-coefficients probit
specifications, a semiparametric single-index specification, and a se
miparametric specification that permits arbitrary heteroskedasticity o
f unknown form. The estimation methods are maximum likelihood for the
probit models, semiparametric quasi-maximum-likelihood for the single-
index model, and maximum score and smoothed maximum score for the arbi
trarily heteroskedastic model. Specification tests result in rejection
of the fixed-coefficients probit and single-index models but not of t
he random-coefficients probit model and the semiparametric model with
arbitrary heteroskedasticity.