On Errors-in-Variables in Binary Regression—Berkson Case

Abstract

Abstract In binary regression, the predictor variables may be measured with error. The Berkson case of the errors-in-variables problem is considered, under which the values of the predictor variables are set by the experimenter but not achieved exactly. A particular model for this case is considered, with probit regression and normally distributed errors of observation. The regression parameters for intercept and slope are to be estimated. Two estimators are studied, the maximum likelihood estimator (MLE) and a modification of it. In a simulation study, the modified MLE is shown to improve on the MLE in a situation with substantial measurement error. Quantal bioassay is an important field of application of the Berkson case of the binary regression model. In quantal bioassay, there is a stimulus, perhaps a carcinogen or poison, with doses X to be determined by the experimenter. To address questions on carcinogenicity or toxicity of the stimulus, each experimental animal is assigned a dose of the stimulus, ...