Estimating from Misclassified Data.

A statistical method for estimating the proportions of items in each of several categories, based on an item-by-item classification in which many items may be misclassified. A specific case of interest is that in which the items are subjects being interviewed and the subjects may be hostile. Maximum likelihood estimators are developed for both the two-category and the multicategory response cases with respect to a group of noncooperative interviewees. An assessment is made, for each subject, of the probability that he is hostile. These probabilities are then combined with the actual responses to obtain the maximum likelihood estimators. Explicit evaluation of the estimators for a sample of n subjects and r categories requires solution of a simple concave programming problem involving a logarithmic objective function in variables confined to the unit interval. A Bayesian approach is used to evaluate the misclassification (or hostility) probabilities. It is assumed that the analysis applies to a single question only. For a survey containing many questions, the estimators would be evaluated separately for each question. The analysis can also be generalized to consider many questions simultaneously. 38 pp. Ref.