Shin-ichi Mayekawa

RELATIONSHIPS AMONG SEVERAL METHODS OF LINEARLY CONSTRAINED CORRESPONDENCE ANALYSIS

This paper shows essential equivalences among several methods of linearly constrained correspondence analysis. They include Fishers method of additive scoring, Hayashis second type of quantification method, ter Braaks canonical correspondence analysis, Nishisatos type of quantification method, ter Braaks canonical correspondence analysis, Nishisatos ANOVA of categorical data, correspondence analysis of manipulated contingency tables, Böckenholt and Böckenholts least squares canonical analysis with linear constraints, and van der Heijden and Meijerinks zero average restrictions. These methods fall into one of two classes of methods corresponding to two alternative ways of imposing linear constraints, the reparametrization method and the null space method. A connection between the two is established through Khatris lemma.

A new biplot procedure with joint classification of objects and variables by fuzzy c-means clustering

Biplot is a technique for obtaining a low-dimensional configuration of the data matrix in which both the objects and the variables of the data matrix are jointly represented as points and vectors, respectively. However, biplots with a large number of objects and variables remain difficult to interpret. Therefore, in this research, we propose a new biplot procedure that allows us to interpret a large data matrix. In particular, the objects and variables are classified into a small number of clusters by using fuzzy

A COMPARISON OF EQUATING METHODS AND LINKING DESIGNS FOR DEVELOPING AN ITEM POOL UNDER ITEM RESPONSE THEORY

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MAXIMUM LIKELIHOOD SOLUTION TO THE PARAFAC MODEL

c-means clustering and the resulting clusters are simultaneously biplotted in lower-dimensional space. This procedure allows us to understand the configurations easily and to grasp the fuzzy memberships of the objects and variables to the clusters. A simulation study and real data example are also provided to demonstrate the effectiveness of the proposed procedure.

Review of Linear Algebra and Linear Models by R.B. Bapat

A number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory. This article presents the development of a new stochastic choice model based on multidimensional scaling. This allows decision-makers to have multiple viewpoints, whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint. The implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint. This paper also presents the maximum likelihood estimation of the proposed model, and reanalyzes Tversky’s gamble experiment data.