Showing papers by "Yu Xie published in 1988"

The logit model the probit model and response-based samples.

Abstract: It is well known that the choice of the probit versus the logit model is usually inconsequential for analyzing binary response from random samples and samples stratified on exogenous variables There is reason to suspect however that the choice between these 2 types of models has serious consequences when the sample is response-based A response-based sample is 1 that is stratified on the discrete variable of outcome This paper shows that in the context of response-based samples the conventional wisdom is incorrect The paper 1st discusses the problem of model specification Secondly it formally states the estimation problem from response-based samples and briefly introduces the Manski-Lerman weighted maximum likelihood estimations solution It then reports the asymptotic bias of alternative estimators under response-based sampling Finally it presents a Monte Carlo experiment that provides evidence on small sample bias and precision The choice between the probit and logit models is shown to be a real concern for estimation from response-based samples If the true model is logit the ordinary maximum likelihood procedure yields the best asymptotic unbiased estimator But even a small misspecification of the model say approximating the probit by the logit renders the maximum likelihood estimator biased Therefore care must be taken when the researcher analyzes response-based samples A conservative approach is always to use a weighted maximum likelihood procedure even for the logit model