Nonlinear formulations of canonical correlation analysis and discriminant analysis are given, and it is shown that both reduce to the same eigen problem. Both problems can be regarded as a method to represent the probabilistic structure of data into a topological space(L-dimensional Euclindean space).Further, the usual linear cases are interpreted as linear approxi-mations of the nonlinear cases.
In order to analyze the result of a questionnaire using a rating scale method, it is important to clarify relational structure among questionnaire items. This paper presents a Semantic Structure Analysis method, called an SS Analysis. First, the author introduces an item odering coefficient between two items and shows fundamental properties on item relationships, such as ordering and equivalence. Next, a construction method of a synthesized item relational structure, called an SS digraph is presented, and its characteristics, such as hierachical struturing on ordering are discussed. An example of the SS digraph and effectiveness of this SS analysis are shown from apractical view point. Last, the relationship between SS analysis and Ordering Theory by Airasian & Bart(1973)is discussed. It is shown that SS analysis method is a generalization form of Ordering Theory.
A computer program MALIFA developed by Driel(1975)was implemented on a wide spread personal computer and was applied to several sets of data in the literature. MALIFA can obtain the maximum likelihood estimates of the parameters in the orthogonal common factor analysis model with different kind of constraints depending on the classical or non-classical approach.In the non-classical approach, even complex solution can be obtained.In this study, it is shown that when squared multiple correlation is used as a initial estimate of communality, MALIFA happened to yield a lower value of the objective function to be minimized in the classical approach than the non-classical approach. Although some care is needed in its use, MALIFA seemes to provide a useful tool for studying the cause of improper solution in maximum likelihood factor analysis.