A Discrimination Model For Multivariate Q Representations

The proposed discrimination model for Q representation is a generalization of the method of unfolding in an algebraic rather than a geometric field. Placements of Q statements relative to one another in joint space so as to form a quasi-normal distribution of the q stimulus items are assigned Q values which form a bounded set of symbols with specified order in arithmetic progression; for example, a finite set from "one" to "nine" wherein "five" is the midpoint of an ordered metric within persons. An algebraic theory of numbers permits mathematical operations to be carried out with sets of sets of such symbols. Using illustrative data, a mathematical model is developed for the analysis of Q values, each of which represents the intersect of two or more dimensions of behavior structured into a Q set, and for testing its stability, consistency, and reliability. The Q check procedures permit comparisons among individuals and subsamples of population samples.