In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent trait in terms of the operating density characteristic when the item response is continuous and by means of the operating characteristic when the item response is discrete. This paper is concerned solely with the unidimensional latent space and the discrete response level. An outline for a series of methods and approaches is introduced for estimating the operating characteristics of discrete item responses without assuming any mathematical form. Observations concerning computer programs and model validation, word/phrase comprehension tests and scale construction, and information loss caused by asumptotes are discussed. Numerous tables and figures are included, as well as three pages of references. (PN)