A New Model for Scaling Response Patterns: An Application of the Quasi-Independence Concept

Abstract

To analyze the “scalability” of the observed response patterns for a set of m dichotomous items, we introduce a model in which a given individual in the population is either “intrinsically scalable” or “intrinsically unscalable” (with respect to the m items), and there are d different types of “intrinsically scalable” individuals. With this model, using methods already developed for the study of quasi-independence in contingency tables, we show how to (a) test whether the model fits the observed data, (b) estimate the proportion of intrinsically scalable (and unscalable) individuals, and (c) estimate the distribution of the intrinsically scalable individuals among the d different scale types.