Yasumasa Baba

Measurement and Multivariate Analysis

Diversity is characteristic of the information age and also of statistics. To date, the social sciences have contributed greatly to the development of handling data under the rubric of measurement, while the statistical sciences have made phenomenal advances in theory and algorithms. Measurement and Multivariate Analysis promotes an effective interplay between those two realms of research-diversity with unity. The union and the intersection of those two areas of interest are reflected in the papers in this book, drawn from an international conference in Banff, Canada, with participants from 15 countries. In five major categories - scaling, structural analysis, statistical inference, algorithms, and data analysis - readers will find a rich variety of topics of current interest in the extended statistical community.

A measure of rotatability for second order response surface designs

The concept of rotatability introduced by Box and Hunter (1957,Ann. Math. Statist.,28, 195–241) is an important design criterion for response surface design. Recently, a few measures of rotatability that enable us to assess the degree of rotatability for a given response surface design have been introduced. In this paper, a new measure of rotatability for second order response surface designs is suggested, and illustrated for 3k factorial design and central composite design. Also a short comparison is made between the proposed measure with the previously suggested measures.

Graphical prediction method based on categorical data

Abstract A graphical representation method is proposed to represent individual response patterns visually on the constellation graph which can be used for the prediction of an objective variate from categorical data. The model for prediction is non-linear. Linear approximation and the non-linear solution are compared and illustrated with sample data.

Time Dependent Principal Component Analysis

Principal Component Analysis (PCA) is one of the useful descriptive methods for multivariate data. One aim of the methods is to construct new variables by a linear combination from original variables and illustrate the structure of variables and individuals on a new space based on new variables. In this method principal components have some meanings to summarize variables. Suppose that we obtained principal components at two time points. Then principal components obtained from data at different times will have different meanings if linear combinations of variables are different. For example, the first principal component at time 1 and that at time 2 do not always have the same meanings, as seen in the following example. The first principal component at time 1 may appear as the second or the third principal component at time 2, thus changing the meanings of the first principal components from two time points. Therefore care must be exercised for the interpretation of results from different time points.

New Approaches Based on Rankings in Sensory Evaluation

In sensory evaluation ranking is commonly used and plays an important role as a measure to evaluate something which cannot be measured on any objective scale. In this paper the data analytical techniques proposed by the present author are summarized. The following topics concerned with ranked observations will be shown; graphical analysis of ranked data, classification of items and judges on rank graph, classification by quantification method.