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…

The nonparametric approach to test theory discussed here has its roots in the early work of Guttman, Lazarsfeld, and Meredith; and more recently in the work of Cliff and in Tatsuoka and Tatsuoka. Mokken's extensive treatment of this subject concentrated on defining, constructing, and testing unidimensional scales, based on responses to dichotomous…

The focus of this study is on the estimation procedures implemented in BILOG, a computer program. One purpose is to compare the item parameter estimates produced by various procedures available in BILOG. Four different models are used: the one, two, and three parameter model and a three parameter model with common guessing parameters. The results…