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Author: Shizuhiko Nishisato
Publisher: CRC Press
ISBN: 1420011200
Category : Mathematics
Languages : en
Pages : 329
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Book Description
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sam
Author: Shizuhiko Nishisato
Publisher: CRC Press
ISBN: 1420011200
Category : Mathematics
Languages : en
Pages : 329
Get Book Here
Book Description
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sam
Author: Shizuhiko Nishisato
Publisher: CRC Press
ISBN: 9781584886129
Category : Mathematics
Languages : en
Pages : 336
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Book Description
Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for future progress. Covering both the early and later years of MUNDA research in the social sciences, psychology, ecology, biology, and statistics, this book provides a framework for potential developments in even more areas of study.
Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 9811691703
Category : Mathematics
Languages : en
Pages : 199
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Book Description
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.
Author: Shizuhiko Nishisato
Publisher: Springer Nature
ISBN: 9811624704
Category : Social Science
Languages : en
Pages : 242
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Book Description
This book offers a new look at well-established quantification theory for categorical data, referred to by such names as correspondence analysis, dual scaling, optimal scaling, and homogeneity analysis. These multiple identities are a consequence of its large number of properties that allow one to analyze and visualize the strength of variable association in an optimal solution. The book contains modern quantification theory for analyzing the association between two and more categorical variables in a variety of applicative frameworks. Visualization has attracted much attention over the past decades and given rise to controversial opinions. One may consider variations of plotting systems used in the construction of the classic correspondence plot, the biplot, the Carroll-Green-Schaffer scaling, or a new approach in doubled multidimensional space as presented in the book. There are even arguments for no visualization at all. The purpose of this book therefore is to shed new light on time-honored graphical procedures with critical reviews, new ideas, and future directions as alternatives. This stimulating volume is written with fresh new ideas from the traditional framework and the contemporary points of view. It thus offers readers a deep understanding of the ever-evolving nature of quantification theory and its practice. Part I starts with illustrating contingency table analysis with traditional joint graphical displays (symmetric, non-symmetric) and the CGS scaling and then explores logically correct graphs in doubled Euclidean space for both row and column variables. Part II covers a variety of mathematical approaches to the biplot strategy in graphing a data structure, providing a useful source for this modern approach to graphical display. Part II is also concerned with a number of alternative approaches to the joint graphical display such as bimodal cluster analysis and other statistical problems relevant to quantification theory.
Author: Wim J. van der Linden
Publisher: CRC Press
ISBN: 1315356902
Category : Mathematics
Languages : en
Pages : 785
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Book Description
Drawing on the work of internationally acclaimed experts in the field, Handbook of Item Response Theory, Volume One: Models presents all major item response models. This first volume in a three-volume set covers many model developments that have occurred in item response theory (IRT) during the last 20 years. It describes models for different response formats or response processes, the need of deeper parameterization due to a multilevel or hierarchical structure of the response data, and other extensions and insights. In Volume One, all chapters have a common format with each chapter focusing on one family of models or modeling approach. An introductory section in every chapter includes some history of the model and a motivation of its relevance. Subsequent sections present the model more formally, treat the estimation of its parameters, show how to evaluate its fit to empirical data, illustrate the use of the model through an empirical example, and discuss further applications and remaining research issues.
Author: Piet Wambacq
Publisher: Springer Science & Business Media
ISBN: 147575003X
Category : Technology & Engineering
Languages : en
Pages : 528
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Book Description
The analysis and prediction of nonlinear behavior in electronic circuits has long been a topic of concern for analog circuit designers. The recent explosion of interest in portable electronics such as cellular telephones, cordless telephones and other applications has served to reinforce the importance of these issues. The need now often arises to predict and optimize the distortion performance of diverse electronic circuit configurations operating in the gigahertz frequency range, where nonlinear reactive effects often dominate. However, there have historically been few sources available from which design engineers could obtain information on analysis tech niques suitable for tackling these important problems. I am sure that the analog circuit design community will thus welcome this work by Dr. Wambacq and Professor Sansen as a major contribution to the analog circuit design literature in the area of distortion analysis of electronic circuits. I am personally looking forward to hav ing a copy readily available for reference when designing integrated circuits for communication systems.
Author: Eric J. Beh
Publisher: John Wiley & Sons
ISBN: 1119041961
Category : Mathematics
Languages : en
Pages : 243
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Book Description
Master the fundamentals of correspondence analysis with this illuminating resource An Introduction to Correspondence Analysis assists researchers in improving their familiarity with the concepts, terminology, and application of several variants of correspondence analysis. The accomplished academics and authors deliver a comprehensive and insightful treatment of the fundamentals of correspondence analysis, including the statistical and visual aspects of the subject. Written in three parts, the book begins by offering readers a description of two variants of correspondence analysis that can be applied to two-way contingency tables for nominal categories of variables. Part Two shifts the discussion to categories of ordinal variables and demonstrates how the ordered structure of these variables can be incorporated into a correspondence analysis. Part Three describes the analysis of multiple nominal categorical variables, including both multiple correspondence analysis and multi-way correspondence analysis. Readers will benefit from explanations of a wide variety of specific topics, for example: Simple correspondence analysis, including how to reduce multidimensional space, measuring symmetric associations with the Pearson Ratio, constructing low-dimensional displays, and detecting statistically significant points Non-symmetrical correspondence analysis, including quantifying asymmetric associations Simple ordinal correspondence analysis, including how to decompose the Pearson Residual for ordinal variables Multiple correspondence analysis, including crisp coding and the indicator matrix, the Burt Matrix, and stacking Multi-way correspondence analysis, including symmetric multi-way analysis Perfect for researchers who seek to improve their understanding of key concepts in the graphical analysis of categorical data, An Introduction to Correspondence Analysis will also assist readers already familiar with correspondence analysis who wish to review the theoretical and foundational underpinnings of crucial concepts.
Author: Akinori Okada
Publisher: Springer Nature
ISBN: 9819922402
Category : Mathematics
Languages : en
Pages : 335
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Book Description
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 fields of 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.
Author: Yuichi Mori
Publisher: Springer
ISBN: 9811001596
Category : Mathematics
Languages : en
Pages : 87
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Book Description
This book expounds the principle and related applications of nonlinear principal component analysis (PCA), which is useful method to analyze mixed measurement levels data. In the part dealing with the principle, after a brief introduction of ordinary PCA, a PCA for categorical data (nominal and ordinal) is introduced as nonlinear PCA, in which an optimal scaling technique is used to quantify the categorical variables. The alternating least squares (ALS) is the main algorithm in the method. Multiple correspondence analysis (MCA), a special case of nonlinear PCA, is also introduced. All formulations in these methods are integrated in the same manner as matrix operations. Because any measurement levels data can be treated consistently as numerical data and ALS is a very powerful tool for estimations, the methods can be utilized in a variety of fields such as biometrics, econometrics, psychometrics, and sociology. In the applications part of the book, four applications are introduced: variable selection for mixed measurement levels data, sparse MCA, joint dimension reduction and clustering methods for categorical data, and acceleration of ALS computation. The variable selection methods in PCA that originally were developed for numerical data can be applied to any types of measurement levels by using nonlinear PCA. Sparseness and joint dimension reduction and clustering for nonlinear data, the results of recent studies, are extensions obtained by the same matrix operations in nonlinear PCA. Finally, an acceleration algorithm is proposed to reduce the problem of computational cost in the ALS iteration in nonlinear multivariate methods. This book thus presents the usefulness of nonlinear PCA which can be applied to different measurement levels data in diverse fields. As well, it covers the latest topics including the extension of the traditional statistical method, newly proposed nonlinear methods, and computational efficiency in the methods.
Author: Roger E Millsap
Publisher: SAGE
ISBN: 144620667X
Category : Psychology
Languages : en
Pages : 801
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Book Description
`I often... wonder to myself whether the field needs another book, handbook, or encyclopedia on this topic. In this case I think that the answer is truly yes. The handbook is well focused on important issues in the field, and the chapters are written by recognized authorities in their fields. The book should appeal to anyone who wants an understanding of important topics that frequently go uncovered in graduate education in psychology′ - David C Howell, Professor Emeritus, University of Vermont Quantitative psychology is arguably one of the oldest disciplines within the field of psychology and nearly all psychologists are exposed to quantitative psychology in some form. While textbooks in statistics, research methods and psychological measurement exist, none offer a unified treatment of quantitative psychology. The SAGE Handbook of Quantitative Methods in Psychology does just that. Each chapter covers a methodological topic with equal attention paid to established theory and the challenges facing methodologists as they address new research questions using that particular methodology. The reader will come away from each chapter with a greater understanding of the methodology being addressed as well as an understanding of the directions for future developments within that methodological area. Drawing on a global scholarship, the Handbook is divided into seven parts: Part One: Design and Inference: addresses issues in the inference of causal relations from experimental and non-experimental research, along with the design of true experiments and quasi-experiments, and the problem of missing data due to various influences such as attrition or non-compliance. Part Two: Measurement Theory: begins with a chapter on classical test theory, followed by the common factor analysis model as a model for psychological measurement. The models for continuous latent variables in item-response theory are covered next, followed by a chapter on discrete latent variable models as represented in latent class analysis. Part Three: Scaling Methods: covers metric and non-metric scaling methods as developed in multidimensional scaling, followed by consideration of the scaling of discrete measures as found in dual scaling and correspondence analysis. Models for preference data such as those found in random utility theory are covered next. Part Four: Data Analysis: includes chapters on regression models, categorical data analysis, multilevel or hierarchical models, resampling methods, robust data analysis, meta-analysis, Bayesian data analysis, and cluster analysis. Part Five: Structural Equation Models: addresses topics in general structural equation modeling, nonlinear structural equation models, mixture models, and multilevel structural equation models. Part Six: Longitudinal Models: covers the analysis of longitudinal data via mixed modeling, time series analysis and event history analysis. Part Seven: Specialized Models: covers specific topics including the analysis of neuro-imaging data and functional data-analysis.
