Estimation in choice-based sampling with measurement error and bootstrap analysis

In this paper we discuss the estimation of a logit binary response model. The sampling is choice-based and is done in two stages. We investigate a likelihood-based estimator which reduces to the usual logistic estimator when there is no measurement error and which takes into account the constraints imposed by the structure of the problem. Estimated standard errors obtained by formulae for prospective analysis are asymptotically correct. A robust estimation procedures is proposed and an asymptotic covariance matrix obtained. Several bootstrap methods are applied to this retrospective problem. Numerical results are presented to illustrate useful properties of the methods.