Bayesian analysis of errors-in-variables in binary regression models

Abstract

There has been considerable research done on the problems of errors-in-variables for linear regression. including a Bayesian solution by Lindley and EI-Sayyad (1968). Recently, interest has extended to binary regression and in particular probit regression. Burr (1985) performed frequentist analysis of Berkson's error in probit regression and found that the MLE does not ,always exist in finite samples. In this paper. we show that it is the tail behaviour of the likelihood that causes the problem and this in turn makes Bayesian estimation inadmissible if improper priors are used. Two non-informative priors are derived and simulation results indicate that the Bayesian solutions are generally superior to various likelihood based estimates, including the modified MLE proposed by Burr. It is further shown that the estimation problem vanishes if there are replicates and that the logistic model has the same behaviour as the probit model.