Tomoyuki Tarumi

Variable Selection in Principal Component Analysis

While there exist several criteria by which to select a reasonable subset of variables in the context of PCA, we introduce herein variable selection using criteria in Tanaka and Mori (1997)’s modified PCA (M.PCA) among others.

Statistical Software SAMMIF for Sensitivity Analysis in Multivariate Methods

SAMMIF (Sensitivity Analysis in Multivariate Methods based on Influence Functions) is a statistical package for sensitivity analysis in multivariate methods in which diagnostics statistics are obtained for detecting influential observations and influential directions on the basis of both influence function approach and Cook’s local influence approach. SAMMIF is designed to provide useful graphical user interface and some options for both beginners and specialists. The current version 1.0 performs sensitivity analysis fully in principal component analysis, canonical correlation analysis and exploratory and confirmatory factor analyses with some new diagnostics functions for the analyses. Practical examples illustrate that users can analyze the influence of observations without difficulties.

Principal Component Analysis Based on a Subset of Variables for Qualitative Data

A principal component analysis based on a subset of variables is proposed by Tanaka and Mori (1996) to derive principal components which are computed as linear combinations of a subset of quantitative variables but which can reproduce all the variables very well. The present paper discusses an extension of their modified principal component analysis so that it can deal with qualitative variables by using the idea of the alternating least squares method by Young et al.(1978). A backward elimination procedure is applied to find a suitable sequence of subsets of variables. A numerical example is shown to illustrate the performance of the proposed procedure.

Statistical Software VASMM for Variable Selection in Multivariate Methods

A statistical software package VASMM (VAriable Selection in Multivariate Methods) has been developed for selecting a subset of variables in multivariate methods without external variables. The current version is fully implemented for variable selection in principal component analysis and factor analysis. The system has been constructed with interactive architecture on Internet. The users can not only use the system via a web browser but can also obtain information related to variable selection in multivariate techniques of their choice. It allows for us to perform variable selection easily in a variety of practical applications.

Development of Statistical Software SAMMIF for Sensitivity Analysis in Multivariate Methods

Statistical software SAMMIF is being developed for sensitivity analysis in multivariate methods where influence functions or their analogues are available. It can be used for detecting jointly as well as singly influential observations and also for obtaining information on influential directions from the aspect of Cook’s local influence. A numerical example illustrates its performance in factor analysis.

Research and Applications of Quantification Methods in East Asian Countries

Quantification methods were established by Chikio Hayashi and his colleagues in 1950’s and have been widely used in Japan as tools for analyzing qualitative data. Applications in Japan and Korea are briefly reviewed, and some technical problems are discussed in detail concerning Quantification I and II.

Swap-Rate Analysis System: SRAS

When we select No students from N applicants using a result of an entrance examination, which consists of two step selection, the primary test and the secondary test. It is important to evaluate the contribution of each test. Swap-Rate is one of the measures of the contribution of stage test, and it is widely used. In this paper, first we describe a population swap-rate and sample swap-rate. Next, we consider the distribution of applicants from the point of view of swap of pass or fail. Finally, we introduce our system“SRAS: Swap-Rate Analysis System”, that can analyze the examination data on such point of view.

A Consultation System for Statistical Analysis on Hypertool

In this paper, we describe a statistical consultation system supporting non statisticians. There are many kinds of statistical software, but most of them require the knowledge and experience of statistics. So, developments of a consultation system with knowledge of data analyses are expected by many users.

OUTLIERS AND INFLUENTIAL OBSERVATIONS IN QUANTIFICATION THEORY

Publisher Summary This chapter discusses the methods for detection of outliers and influential observations in Hayashis first and second methods of quantification—quantification I, and quantification II. Quantification I is mathematically an extension of regression analysis to the case where the design matrix is not of full rank. Various measures for outliers and influential observations used in regression analysis can be applied in their original or modified forms. Quantification II is a discriminant analysis based on qualitative data and is mathematically equivalent to a certain type of correspondence analysis. A method of sensitivity analysis for quantification II has been proposed using the perturbation theory of eigenvalue problems. However, it requires high computing cost when the sample size and/or the number of categories are large. The chapter discusses simplified versions of diagnostic measures that are easily calculated. The idea is to fix the scores for the outside variable and then use the measures for quantification I as the approximate measures in quantification II. The chapter also discusses the properties of these measures.