Late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology, and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in linear algebra and multivariate analysis through his collaborative work with the present author, along with some untold episodes for the inception of key ideas underlying the work. The various topics covered include constrained principal component analysis, extensions of Khatri’s lemma, the Wedderburn-Guttman theorem, ridge operators, decompositions of the total association between two sets of variables, and ideal instruments. A common thread running through all of them is projectors and singular value decomposition (SVD), which are the main subject matters of a recent monograph by Yanai, Takeuchi, and Takane (2011).
On February 15 and 16 in 2014 a workshop was held under the auspices of The Behaviormetric Society of Japan on “The Problem Solving Through the Applications of Mathematics to Human Behaviors” by the aid of The Ministry of Education, Culture, Sports, Science, and Technology in Japan. In this note we shall briefly explain the reason why such a workshop was conducted, and summarize the talks presented at the workshop.
The role of mathematics in behavioral sciences is essential for the objective and logical descriptions of the phenomena under consideration. However, the question one must bear in mind is if it is used validly and justifiably. The paper was written in the hope that the basic premises for logical descriptions be well understood and put into practice of data analysis. The views presented here are based on my own observations of current practice in data analysis, and its preliminaries are already discussed in my paper entitled “Generating optimal data as regressions of measurement on data” (Bulletin of Data Analysis of Japanese Classification Society, 2011, Volume 1, No.1, 1-9) and my book “Data analysis for the behavioral sciences: Use of methods appropriate for data” (2010, Baifukan), both in Japanese. The current paper starts with these preliminaries and places special emphasis on the importance of the relations between data and measurement. Through the understanding of their relations, we discover that our data are enormously informative, leading to the important objective of exploratory data analysis: Capture as much information as possible from data in hand.
Network analysis is a method which explains an actor’s action and result from the network which surrounds the actor. Although network analysis is getting a result with many fields, practical use on marketing research is behind. The factor is because it is ambiguous how various network indices should be interpreted and utilized in marketing research. In this paper, summarizing network analysis indices, models, and previous works, the application possibility in marketing research is viewed by showing some examples of analysis in consideration of the above-mentioned factor.