Bücher der Reihe Behaviormetrics: Quantitative

This book offers a unique new look at the familiar quantification theory from the point of view of mathematical symmetry and spatial symmetry. Symmetry exists in many aspects of our life-for instance, in the arts and biology as an ingredient of beauty and equilibrium, and more importantly, for data analysis as an indispensable representation of functional optimality. This unique focus on symmetry clarifies the objectives of quantification theory and the demarcation of quantification space, something that has never caught the attention of researchers.Mathematical symmetry is well known, as can be inferred from Hirschfeld's simultaneous linear regressions, but spatial symmetry has not been discussed before, except for what one may infer from Nishisato's dual scaling. The focus on symmetry here clarifies the demarcation of quantification analysis and makes it easier to understand such a perennial problem as that of joint graphical display in quantification theory. The new framework will help advance the frontier of further developments of quantification theory. Many numerical examples are included to clarify the details of quantification theory, with a focus on symmetry as its operational principle. In this way, the book is useful not only for graduate students but also for researchers in diverse areas of data analysis.

This book provides methods and applications of latent class analysis, and the following topics are taken up in the focus of discussion: basic latent structure models in a framework of generalized linear models, exploratory latent class analysis, latent class analysis with ordered latent classes, a latent class model approach for analyzing learning structures, the latent Markov analysis for longitudinal data, and path analysis with latent class models. The maximum likelihood estimation procedures for latent class models are constructed via the expectation¿maximization (EM) algorithm, and along with it, latent profile and latent trait models are also treated. Entropy-based discussions for latent class models are given as advanced approaches, for example, comparison of latent classes in a latent class cluster model, assessing latent class models, path analysis, and so on. In observing human behaviors and responses to various stimuli and test items, it is valid to assume they are dominated by certain factors. This book plays a significant role in introducing latent structure analysis to not only young researchers and students studying behavioral sciences, but also to those investigating other fields of scientific research.

This edited book is the first one written in English that deals comprehensively with behavior metrics. The term ¿behaviormetrics¿ comprehends the research including all sorts of quantitative approaches to disclose human behavior. Researchers in behavior metrics have developed, extended, and improved methods such as multivariate statistical analysis, survey methods, cluster analysis, machine learning, multidimensional scaling, corresponding analysis or quantification theory, network analysis, clustering, factor analysis, test theory, and related factors. In the spirit of behavior metrics, researchers applied these methods to data obtained by surveys, experiments, or websites from a diverse range of fields. The purpose of this book is twofold. One is to represent studies that display how the basic elements of behavior metrics have developed into present-day behavior metrics. The other is to represent studies performed mainly by those who would like to pioneer new fieldsof behavior metrics and studies that display elements of future behavior metrics. These studies consist of various characteristics such as those dealing with theoretical or conceptual subjects, the algorithm, the model, the method, and the application to a wide variety of fields. This book helps readers to understand the present and future of behavior metrics.

The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.

This collection of essays is in honor of Shizuhiko Nishisato on his 88th birthday and consists of invited contributions only. The book contains essays on the analysis of categorical data, which includes quantification theory, cluster analysis, and other areas of multidimensional data analysis, covering more than half a century of research by the 41 interdisciplinary and international researchers who are contributors. Thus, it offers the wisdom and experience of work past and present and attracts a new generation of researchers to this field. Central to this wisdom and experience is that of Prof. Nishisato, who has spent much of the past 60 years mentoring and providing leadership in the research of quantification theory, especially that of ¿dual scaling¿. The book includes contributions by leading researchers who have worked alongside Prof. Nishisato, published with him, been mentored by him, or whose work has been influenced by the research he has undertaken over his illustrious career. This book inspires researchers young and old as it highlights the significant contributions, past and present, that Prof. Nishisato has made in his field.

This is the first technical book that considers tests as public tools and examines how to engineer and process test data, extract the structure within the data to be visualized, and thereby make test results useful for students, teachers, and the society. The author does not differentiate test data analysis from data engineering and information visualization. This monograph introduces the following methods of engineering or processing test data, including the latest machine learning techniques: classical test theory (CTT), item response theory (IRT), latent class analysis (LCA), latent rank analysis (LRA), biclustering (co-clustering), and Bayesian network model (BNM). CTT and IRT are methods for analyzing test data and evaluating students' abilities on a continuous scale. LCA and LRA assess examinees by classifying them into nominal and ordinal clusters, respectively, where the adequate number of clusters is estimated from the data. Biclustering classifies examinees into groups (latent clusters) while classifying items into fields (factors). Particularly, the infinite relational model discussed in this book is a biclustering method feasible under the condition that neither the number of groups nor the number of fields is known beforehand. Additionally, the local dependence LRA, local dependence biclustering, and bicluster network model are methods that search and visualize inter-item (or inter-field) network structure using the mechanism of BNM. As this book offers a new perspective on test data analysis methods, it is certain to widen readers' perspective on test data analysis.