1991 Volume 18 Issue 30 Pages 1-21
In the present paper, scalogram analysis proposed by Guttman (1950) is developed into latent scalogram analysis, and a general discussion of the analysis is presented. The present paper deals with not only linear hierarchical structures but also branching hierarchical structures. In order to select a hierarchical structure which best fits the data set, model selection procedures are considered in both exploratory and confirmatory contexts. Concerning latent scales which exist in the population under consideration, a dynamic interpretation of latent scales is discussed through a mathematical viewpoint, and a method for evaluating the proportions of latent scales is proposed. Moreover in order to compare the latent scales, a latent space for locating the extracted latent classes is constructed by a technique similar to canonical analysis. Numerical examples are also presented to illustrate the present analysis.
