title: A New Extension of the Binomial Error Model for Responses to Items of Varying Difficulty in Educational Testing and Attitude Surveys.
abstract: We put forward a new item response model which is an extension of the binomial error model first introduced by Keats and Lord. Like the binomial error model, the basic latent variable can be interpreted as a probability of responding in a certain way to an arbitrarily specified item. For a set of dichotomous items, this model gives predictions that are similar to other single parameter IRT models (such as the Rasch model) but has certain advantages in more complex cases. The first is that in specifying a flexible two-parameter Beta distribution for the latent variable, it is easy to formulate models for randomized experiments in which there is no reason to believe that either the latent variable or its distribution vary over randomly composed experimental groups. Second, the elementary response function is such that extensions to more complex cases (e.g., polychotomous responses, unfolding scales) are straightforward. Third, the probability metric of the latent trait allows tractable extensions to cover a wide variety of stochastic response processes.
authors.affiliation: Department of Family and Community Medicine and Institute for Health Policy Studies, School of Medicine, University of California San Francisco, San Francisco, California, United States of America.
authors.forename: James A
authors.initials: JA
authors.lastname: Wiley
authors.affiliation: Sociology Department, University of Chicago, Chicago, Illinois, United States of America.
authors.forename: John Levi
authors.initials: JL
authors.lastname: Martin
authors.affiliation: Department of Mathematics, College of Staten Island, New York City, New York, United States of America.
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Herschkorn
authors.affiliation: Alcohol Research Group, Emeryville, California, United States of America.
authors.forename: Jason
authors.initials: J
authors.lastname: Bond
mesh_terms: D001290:Attitude; D004521:Educational Measurement; D015233:Models, Statistical; D013269:Stochastic Processes; D011795:Surveys and Questionnaires