Synopsis of Basic Theory and Techniques of Order Analysis. Occasional Paper No. 26.

Order analysis is a measurement technique for the quantitative and generalizable description of complex structures. Relations between the manifest elements of a data matrix and its underlying latent entities and attributes are considered in terms of magnitudes as basic scale units. Magnitude is conceptualized as a difference relation, translated into the binary units of information theory and linked with the functional relations of the propositional calculus of formal logic. Deterministic and probabilistic models of order analysis are developed. The deterministic model elaborates an algorithm for partitioning of binary relations within the context of Guttman-type scaling. The probabilistic model extends these principles within the framework of graph theory; it permits the generalization of ordered structures into their latent domains with a known degree of statistical certainty. Relation of order analysis to factor analysis is discussed, as well as components of isolated binary variation. Order analysis is validated on sets of prestructured, distorted and random data and its utility considered within the general framework of multivariate analysis models. (Author)