This paper proposes a model to analyze the symmetric dissimilarity matrix by an Euclidean distance model with additional terms. The proposed model is a restricted model of Weeks and Bentler's model. The symmetric dissimilarity is assumed to be induced from asymmetric dissimilarities. A Monte Carlo simulation study conducted demonstrated that the proposed least squares algorithm was effective in recovering the true number of dimensions and true configuration. This algorithm was applied to the real data set. The local minimum problem is discussed.
This study was designed to describe the growth and developmental distance curves of some physical fitness attributes chosen. The physical fitness attributes chosen were body linearity measured by stature, muscular strength by back strength, explosive strength and jumping ability by standing long jump, throwing ability by softball throw for distance, and running ability by 100m dash. These growth and developmental distance curves for 30 years could be described with considerably high precision by composite of three different functions; logistic function and 4th-degree polynomial for all attributes, and one of 2nd-degree polynomial, a type of truncated probability function and single vibration function. Then, each of these functions used was likely to reflect the nature of growth and developmental distance trend due to aging from childhood to maturity. The studies of this type have been reported only for physique attributes, so this was the first attempt regarding to physical fitness attributes.
Studies on intuitive perceptual judgment have shown central tendency of judgment on a series of stimuli. In those studies, it is critical that the range of judgmental objects be restricted. Therefore in a restricted range of judgmental objects, judgment with prize is also expected to have central tendency, although it has not been examined to date. This paper examines central tendency of decision making under uncertainty which consists of probability and prize. The decision making problem is the choice between two alternatives on the basis of an event observed in the restricted range. The optimal decision criterion was simulated by using statistical decision theory, and the decision criterion by subjects was experimentally investigated. The analysis comparing the experimental result to the simulation result showed that the criterion decided by subjects had central tendency. As a factor of central tendency, score for outcomes, or loss function, was shown to play an important role.
The ordinal equivalence of the Shapley-Shubik and Banzhaf-Coleman power indices in a simple game would be important to many applications, where consideration of “how much” more power one member has than another is irrelevant. The reason is that if the ordinal equivalence holds, then another question of which index to use goes out. To the ordinal equivalence problem, this paper gives the following answers. The ordinal equivalence holds true either in the weighted majority games as a subclass of simple games or in the five- or less-member simple games. However, it does not necessarily hold true in the six- or more-member simple games.
This article considers the analysis of association in connection with contingency tables having ordered categories. The restricted maximum likelihood methods are adopted to obtain the approximate confidence intervals and estimated asymptotic standard deviations for category scores. Furthermore, the testing of the equivalence of particular scores is illustrated in the context of potential application of the association models to analyze the ordered categorical data.