Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. (Author/RC)

Using ordering theory, a boolean algebraic measurement model in which item response patterns are viewed as atoms in a boolean algebra with as many generators as there are items being considered, a hierarchy-generative procedure is developed. This procedure relates to the determination of prerequisite relationships between pairs of items. An…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…