Latent Class and Latent Transition Analysis. With Applications in the Social, Behavioral, and Health Sciences

Latent Variable Models and Factor Analysis provides a comprehensive and unified approach to factor analysis and latent variable modeling from a statistical perspective. This book presents a general framework to enable the derivation of the commonly used models, along with updated numerical examples. Nature and interpretation of a latent variable is also introduced along with related techniques for investigating dependency. This book: Provides a unified approach showing how such apparently diverse methods as Latent Class Analysis and Factor Analysis are actually members of the same family. Presents new material on ordered manifest variables, MCMC methods, non-linear models as well as a new chapter on related techniques for investigating dependency. Includes new sections on structural equation models (SEM) and Markov Chain Monte Carlo methods for parameter estimation, along with new illustrative examples. Looks at recent developments on goodness-of-fit test statistics and on non-linear models and models with mixed latent variables, both categorical and continuous. No prior acquaintance with latent variable modelling is pre-supposed but a broad understanding of statistical theory will make it easier to see the approach in its proper perspective. Applied statisticians, psychometricians, medical statisticians, biostatisticians, economists and social science researchers will benefit from this book.

A comprehensive introduction to social network analysis that hones in on basic centrality measures, social links, subgroup analysis, data sources, and more Written by military, industry, and business professionals, this book introduces readers to social network analysis, the new and emerging topic that has recently become of significant use for industry, management, law enforcement, and military practitioners for identifying both vulnerabilities and opportunities in collaborative networked organizations. Focusing on models and methods for the analysis of organizational risk, Social Network Analysis with Applications provides easily accessible, yet comprehensive coverage of network basics, centrality measures, social link theory, subgroup analysis, relational algebra, data sources, and more. Examples of mathematical calculations and formulas for social network measures are also included. Along with practice problems and exercises, this easily accessible book covers: The basic concepts of networks, nodes, links, adjacency matrices, and graphs Mathematical calculations and exercises for centrality, the basic measures of degree, betweenness, closeness, and eigenvector centralities Graph-level measures, with a special focus on both the visual and numerical analysis of networks Matrix algebra, outlining basic concepts such as matrix addition, subtraction, multiplication, and transpose and inverse calculations in linear algebra that are useful for developing networks from relational data Meta-networks and relational algebra, social links, diffusion through networks, subgroup analysis, and more An excellent resource for practitioners in industry, management, law enforcement, and military intelligence who wish to learn and apply social network analysis to their respective fields, Social Network Analysis with Applications is also an ideal text for upper-level undergraduate and graduate level courses and workshops on the subject.

Analysis of Ordinal Categorical Data Alan Agresti Statistical Science Now has its first coordinated manual of methods for analyzing ordered categorical data. This book discusses specialized models that, unlike standard methods underlying nominal categorical data, efficiently use the information on ordering. It begins with an introduction to basic descriptive and inferential methods for categorical data, and then gives thorough coverage of the most current developments, such as loglinear and logit models for ordinal data. Special emphasis is placed on interpretation and application of methods and contains an integrated comparison of the available strategies for analyzing ordinal data. This is a case study work with illuminating examples taken from across the wide spectrum of ordinal categorical applications. 1984 (0 471-89055-3) 287 pp. Regression Diagnostics Identifying Influential Data and Sources of Collinearity David A. Belsley, Edwin Kuh and Roy E. Welsch This book provides the practicing statistician and econometrician with new tools for assessing the quality and reliability of regression estimates. Diagnostic techniques are developed that aid in the systematic location of data points that are either unusual or inordinately influential; measure the presence and intensity of collinear relations among the regression data and help to identify the variables involved in each; and pinpoint the estimated coefficients that are potentially most adversely affected. The primary emphasis of these contributions is on diagnostics, but suggestions for remedial action are given and illustrated. 1980 (0 471-05856-4) 292 pp. Applied Regression Analysis Second Edition Norman Draper and Harry Smith Featuring a significant expansion of material reflecting recent advances, here is a complete and up-to-date introduction to the fundamentals of regression analysis, focusing on understanding the latest concepts and applications of these methods. The authors thoroughly explore the fitting and checking of both linear and nonlinear regression models, using small or large data sets and pocket or high-speed computing equipment. Features added to this Second Edition include the practical implications of linear regression; the Durbin-Watson test for serial correlation; families of transformations; inverse, ridge, latent root and robust regression; and nonlinear growth models. Includes many new exercises and worked examples. 1981 (0 471-02995-5) 709 pp.

An effective technique for data analysis in the social sciences The recent explosion in longitudinal data in the social sciences highlights the need for this timely publication. Latent Curve Models: A Structural Equation Perspective provides an effective technique to analyze latent curve models (LCMs). This type of data features random intercepts and slopes that permit each case in a sample to have a different trajectory over time. Furthermore, researchers can include variables to predict the parameters governing these trajectories. The authors synthesize a vast amount of research and findings and, at the same time, provide original results. The book analyzes LCMs from the perspective of structural equation models (SEMs) with latent variables. While the authors discuss simple regression-based procedures that are useful in the early stages of LCMs, most of the presentation uses SEMs as a driving tool. This cutting-edge work includes some of the authors' recent work on the autoregressive latent trajectory model, suggests new models for method factors in multiple indicators, discusses repeated latent variable models, and establishes the identification of a variety of LCMs. This text has been thoroughly class-tested and makes extensive use of pedagogical tools to aid readers in mastering and applying LCMs quickly and easily to their own data sets. Key features include: Chapter introductions and summaries that provide a quick overview of highlights Empirical examples provided throughout that allow readers to test their newly found knowledge and discover practical applications Conclusions at the end of each chapter that stress the essential points that readers need to understand for advancement to more sophisticated topics Extensive footnoting that points the way to the primary literature for more information on particular topics With its emphasis on modeling and the use of numerous examples, this is an excellent book for graduate courses in latent trajectory models as well as a supplemental text for courses in structural modeling. This book is an excellent aid and reference for researchers in quantitative social and behavioral sciences who need to analyze longitudinal data.

A much-needed guide on how to use numerical methods to solve practical engineering problems Bridging the gap between mathematics and engineering, Numerical Analysis with Applications in Mechanics and Engineering arms readers with powerful tools for solving real-world problems in mechanics, physics, and civil and mechanical engineering. Unlike most books on numerical analysis, this outstanding work links theory and application, explains the mathematics in simple engineering terms, and clearly demonstrates how to use numerical methods to obtain solutions and interpret results. Each chapter is devoted to a unique analytical methodology, including a detailed theoretical presentation and emphasis on practical computation. Ample numerical examples and applications round out the discussion, illustrating how to work out specific problems of mechanics, physics, or engineering. Readers will learn the core purpose of each technique, develop hands-on problem-solving skills, and get a complete picture of the studied phenomenon. Coverage includes: How to deal with errors in numerical analysis Approaches for solving problems in linear and nonlinear systems Methods of interpolation and approximation of functions Formulas and calculations for numerical differentiation and integration Integration of ordinary and partial differential equations Optimization methods and solutions for programming problems Numerical Analysis with Applications in Mechanics and Engineering is a one-of-a-kind guide for engineers using mathematical models and methods, as well as for physicists and mathematicians interested in engineering problems.

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields. Michael Ruzhansky, Ph.D., is Professor in the Department of Mathematics at Imperial College London, UK. Dr. Ruzhansky was awarded the Ferran Sunyer I Balaguer Prize in 2014. Hemen Dutta, Ph.D., is Senior Assistant Professor of Mathematics at Gauhati University, India. Ravi P. Agarwal, Ph.D., is Professor and Chair of the Department of Mathematics at Texas A&M University-Kingsville, Kingsville, USA.

H andbook and reference guide for students and practitioners of statistical regression-based analyses in R   Handbook of Regression Analysis  with Applications in R, Second Edition  is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors’ thorough treatment of “classical” regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data.  The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include:  Regularization methods Smoothing methods Tree-based methods In the new edition of the  Handbook , the data analyst’s toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website.  Of interest to undergraduate and graduate students taking courses in statistics and regression, the  Handbook of Regression Analysis  will also be invaluable to practicing data scientists and statisticians.

An accessible introduction to performing meta-analysis across various areas of research The practice of meta-analysis allows researchers to obtain findings from various studies and compile them to verify and form one overall conclusion. Statistical Meta-Analysis with Applications presents the necessary statistical methodologies that allow readers to tackle the four main stages of meta-analysis: problem formulation, data collection, data evaluation, and data analysis and interpretation. Combining the authors' expertise on the topic with a wealth of up-to-date information, this book successfully introduces the essential statistical practices for making thorough and accurate discoveries across a wide array of diverse fields, such as business, public health, biostatistics, and environmental studies. Two main types of statistical analysis serve as the foundation of the methods and techniques: combining tests of effect size and combining estimates of effect size. Additional topics covered include: Meta-analysis regression procedures Multiple-endpoint and multiple-treatment studies The Bayesian approach to meta-analysis Publication bias Vote counting procedures Methods for combining individual tests and combining individual estimates Using meta-analysis to analyze binary and ordinal categorical data Numerous worked-out examples in each chapter provide the reader with a step-by-step understanding of the presented methods. All exercises can be computed using the R and SAS software packages, which are both available via the book's related Web site. Extensive references are also included, outlining additional sources for further study. Requiring only a working knowledge of statistics, Statistical Meta-Analysis with Applications is a valuable supplement for courses in biostatistics, business, public health, and social research at the upper-undergraduate and graduate levels. It is also an excellent reference for applied statisticians working in industry, academia, and government.

Guides readers through the quantitative data analysis process including contextualizing data within a research situation, connecting data to the appropriate statistical tests, and drawing valid conclusions Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences presents a clear and accessible introduction to the basics of quantitative data analysis and focuses on how to use statistical tests as a key tool for analyzing research data. The book presents the entire data analysis process as a cyclical, multiphase process and addresses the processes of exploratory analysis, decision-making for performing parametric or nonparametric analysis, and practical significance determination. In addition, the author details how data analysis is used to reveal the underlying patterns and relationships between the variables and connects those trends to the data’s contextual situation. Filling the gap in quantitative data analysis literature, this book teaches the methods and thought processes behind data analysis, rather than how to perform the study itself or how to perform individual statistical tests. With a clear and conversational style, readers are provided with a better understanding of the overall structure and methodology behind performing a data analysis as well as the needed techniques to make informed, meaningful decisions during data analysis. The book features numerous data analysis examples in order to emphasize the decision and thought processes that are best followed, and self-contained sections throughout separate the statistical data analysis from the detailed discussion of the concepts allowing readers to reference a specific section of the book for immediate solutions to problems and/or applications. Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences also features coverage of the following: • The overall methodology and research mind-set for how to approach quantitative data analysis and how to use statistics tests as part of research data analysis • A comprehensive understanding of the data, its connection to a research situation, and the most appropriate statistical tests for the data • Numerous data analysis problems and worked-out examples to illustrate the decision and thought processes that reveal underlying patterns and trends • Detailed examples of the main concepts to aid readers in gaining the needed skills to perform a full analysis of research problems • A conversational tone to effectively introduce readers to the basics of how to perform data analysis as well as make meaningful decisions during data analysis Introduction to Quantitative Data Analysis in the Behavioral and Social Sciences is an ideal textbook for upper-undergraduate and graduate-level research method courses in the behavioral and social sciences, statistics, and engineering. This book is also an appropriate reference for practitioners who require a review of quantitative research methods. Michael J. Albers, Ph.D., is Professor in the Department of English at East Carolina University. His research interests include information design with a focus on answering real-world questions, the presentation of complex information, and human–information interaction. Dr. Albers received his Ph.D. in Technical Communication and Rhetoric from Texas Tech University.

Survival analysis concerns sequential occurrences of events governed by probabilistic laws. Recent decades have witnessed many applications of survival analysis in various disciplines. This book introduces both classic survival models and theories along with newly developed techniques. Readers will learn how to perform analysis of survival data by following numerous empirical illustrations in SAS. Survival Analysis: Models and Applications: Presents basic techniques before leading onto some of the most advanced topics in survival analysis. Assumes only a minimal knowledge of SAS whilst enabling more experienced users to learn new techniques of data input and manipulation. Provides numerous examples of SAS code to illustrate each of the methods, along with step-by-step instructions to perform each technique. Highlights the strengths and limitations of each technique covered. Covering a wide scope of survival techniques and methods, from the introductory to the advanced, this book can be used as a useful reference book for planners, researchers, and professors who are working in settings involving various lifetime events. Scientists interested in survival analysis should find it a useful guidebook for the incorporation of survival data and methods into their projects.