In defense of retaining the "latent trait theory" term, instead of replacing it with "item response theory" as some recent research would have it, the following objectives are outlined: (1) investigation of theory and method for estimating the operating characteristics of discrete item responses using a minimum number of examinees and assuming no specific mathematical forms; (2) investigation of the random guessing behavior in testing, and the development of new models for the multiple-choice item; and (3) investigation of efficient methods of estimating the ability distribution for any specific group of examinees. Other topics pursued are: a new mathematical model for the binary item called Constant Information Model, the method of moments as the least squares solution for fitting a polynomial, Bayesian estimation of ability, and alternative estimates for the maximum liklihood estimator for the two extreme response patterns. Information functions interest researchers in getting the test items to provide the most information possible. The author proposes the Constant Information Model which aims at the consistency of item information and has practical implications and usefulness in the estimation of the operating characteristics of discrete item responses. (Author/CE)