Structural Equations with Latent Variables

This book presents an introduction to structural equation modeling (SEM) and facilitates the access of students and researchers in various scientific fields to this powerful statistical tool. It offers a didactic initiation to SEM as well as to the open-source software, lavaan, and the rich and comprehensive technical features it offers. Structural Equation Modeling with lavaan thus helps the reader to gain autonomy in the use of SEM to test path models and dyadic models, perform confirmatory factor analyses and estimate more complex models such as general structural models with latent variables and latent growth models. SEM is approached both from the point of view of its process (i.e. the different stages of its use) and from the point of view of its product (i.e. the results it generates and their reading).

A modern, comprehensive treatment of latent class and latent transition analysis for categorical data On a daily basis, researchers in the social, behavioral, and health sciences collect information and fit statistical models to the gathered empirical data with the goal of making significant advances in these fields. In many cases, it can be useful to identify latent, or unobserved, subgroups in a population, where individuals' subgroup membership is inferred from their responses on a set of observed variables. Latent Class and Latent Transition Analysis provides a comprehensive and unified introduction to this topic through one-of-a-kind, step-by-step presentations and coverage of theoretical, technical, and practical issues in categorical latent variable modeling for both cross-sectional and longitudinal data. The book begins with an introduction to latent class and latent transition analysis for categorical data. Subsequent chapters delve into more in-depth material, featuring: A complete treatment of longitudinal latent class models Focused coverage of the conceptual underpinnings of interpretation and evaluationof a latent class solution Use of parameter restrictions and detection of identification problems Advanced topics such as multi-group analysis and the modeling and interpretation of interactions between covariates The authors present the topic in a style that is accessible yet rigorous. Each method is presented with both a theoretical background and the practical information that is useful for any data analyst. Empirical examples showcase the real-world applications of the discussed concepts and models, and each chapter concludes with a «Points to Remember» section that contains a brief summary of key ideas. All of the analyses in the book are performed using Proc LCA and Proc LTA, the authors' own software packages that can be run within the SAS® environment. A related Web site houses information on these freely available programs and the book's data sets, encouraging readers to reproduce the analyses and also try their own variations. Latent Class and Latent Transition Analysis is an excellent book for courses on categorical data analysis and latent variable models at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners in the social, behavioral, and health sciences who conduct latent class and latent transition analysis in their everyday work.

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.

Since Lord Rayleigh introduced the idea of viscous damping in his classic work «The Theory of Sound» in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping. Over the past decade, extensive research has been undertaken on more general «non-viscous» damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Identification, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: dynamics of viscously damped systems; non-viscously damped single- and multi-degree of freedom systems; linear systems with non-local and non-viscous damping; reduced computational methods for damped systems; and finally a method for dealing with general asymmetric systems. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Contents 1. Introduction to Damping Models and Analysis Methods. 2. Dynamics of Undamped and Viscously Damped Systems. 3. Non-Viscously Damped Single-Degree-of-Freedom Systems. 4. Non-viscously Damped Multiple-Degree-of-Freedom Systems. 5. Linear Systems with General Non-Viscous Damping. 6. Reduced Computational Methods for Damped Systems

A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.

Since Lord Rayleigh introduced the idea of viscous damping in his classic work «The Theory of Sound» in 1877, it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering. However, in the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping. Over the past decade, extensive research has been undertaken on more general “non-viscous” damping models and vibration of non-viscously damped systems. This book, along with a related book Structural Dynamic Analysis with Generalized Damping Models: Analysis, is the first comprehensive study to cover vibration problems with general non-viscous damping. The author draws on his considerable research experience to produce a text covering: parametric senistivity of damped systems; identification of viscous damping; identification of non-viscous damping; and some tools for the quanitification of damping. The book is written from a vibration theory standpoint, with numerous worked examples which are relevant across a wide range of mechanical, aerospace and structural engineering applications. Contents 1. Parametric Sensitivity of Damped Systems. 2. Identification of Viscous Damping. 3. Identification of Non-viscous Damping. 4. Quantification of Damping. About the Authors Sondipon Adhikari is Chair Professor of Aerospace Engineering at Swansea University, Wales. His wide-ranging and multi-disciplinary research interests include uncertainty quantification in computational mechanics, bio- and nanomechanics, dynamics of complex systems, inverse problems for linear and nonlinear dynamics, and renewable energy. He is a technical reviewer of 97 international journals, 18 conferences and 13 funding bodies.He has written over 180 refereed journal papers, 120 refereed conference papers and has authored or co-authored 15 book chapters.

Presents a useful guide for applications of SEM whilst systematically demonstrating various SEM models using M plus Focusing on the conceptual and practical aspects of Structural Equation Modeling (SEM), this book demonstrates basic concepts and examples of various SEM models, along with updates on many advanced methods, including confirmatory factor analysis (CFA) with categorical items, bifactor model, Bayesian CFA model, item response theory (IRT) model, graded response model (GRM), multiple imputation (MI) of missing values, plausible values of latent variables, moderated mediation model, Bayesian SEM, latent growth modeling (LGM) with individually varying times of observations, dynamic structural equation modeling (DSEM), residual dynamic structural equation modeling (RDSEM), testing measurement invariance of instrument with categorical variables, longitudinal latent class analysis (LLCA), latent transition analysis (LTA), growth mixture modeling (GMM) with covariates and distal outcome, manual implementation of the BCH method and the three-step method for mixture modeling, Monte Carlo simulation power analysis for various SEM models, and estimate sample size for latent class analysis (LCA) model. The statistical modeling program Mplus Version 8. 2 is featured with all models updated. It provides researchers with a flexible tool that allows them to analyze data with an easy-to-use interface and graphical displays of data and analysis results. Intended as both a teaching resource and a reference guide, and written in non-mathematical terms, Structural Equation Modeling: Applications Using Mplus, 2nd edition provides step-by-step instructions of model specification, estimation, evaluation, and modification. Chapters cover: Confirmatory Factor Analysis (CFA); Structural Equation Models (SEM); SEM for Longitudinal Data; Multi-Group Models; Mixture Models; and Power Analysis and Sample Size Estimate for SEM. Presents a useful reference guide for applications of SEM while systematically demonstrating various advanced SEM models Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes Provides step-by-step instructions of model specification and estimation, as well as detailed interpretation of M plus results using real data sets Introduces different methods for sample size estimate and statistical power analysis for SEM Structural Equation Modeling is an excellent book for researchers and graduate students of SEM who want to understand the theory and learn how to build their own SEM models using M plus.

An authoritative view of Maxwell's Equations that takes theory to practice Maxwell's Equations is a practical guide to one of the most remarkable sets of equations ever devised. Professor Paul Huray presents techniques that show the reader how to obtain analytic solutions for Maxwell's equations for ideal materials and boundary conditions. These solutions are then used as a benchmark for solving real-world problems. Coverage includes: An historical overview of electromagnetic concepts before Maxwell and how we define fundamental units and universal constants today A review of vector analysis and vector operations of scalar, vector, and tensor products Electrostatic fields and the interaction of those fields with dielectric materials and good conductors A method for solving electrostatic problems through the use of Poisson's and Laplace's equations and Green's function Electrical resistance and power dissipation; superconductivity from an experimental perspective; and the equation of continuity An introduction to magnetism from the experimental inverse square of the Biot-Savart law so that Maxwell's magnetic flux equations can be deduced Maxwell's Equations serves as an ideal textbook for undergraduate students in junior/senior electromagnetics courses and graduate students, as well as a resource for electrical engineers.

***Winner of the 2008 Ziegel Prize for outstanding new book of the year*** Structural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account. As SEMs have grown in popularity in recent years, new models and statistical methods have been developed for more accurate analysis of more complex data. A Bayesian approach to SEMs allows the use of prior information resulting in improved parameter estimates, latent variable estimates, and statistics for model comparison, as well as offering more reliable results for smaller samples. Structural Equation Modeling introduces the Bayesian approach to SEMs, including the selection of prior distributions and data augmentation, and offers an overview of the subject’s recent advances. Demonstrates how to utilize powerful statistical computing tools, including the Gibbs sampler, the Metropolis-Hasting algorithm, bridge sampling and path sampling to obtain the Bayesian results. Discusses the Bayes factor and Deviance Information Criterion (DIC) for model comparison. Includes coverage of complex models, including SEMs with ordered categorical variables, and dichotomous variables, nonlinear SEMs, two-level SEMs, multisample SEMs, mixtures of SEMs, SEMs with missing data, SEMs with variables from an exponential family of distributions, and some of their combinations. Illustrates the methodology through simulation studies and examples with real data from business management, education, psychology, public health and sociology. Demonstrates the application of the freely available software WinBUGS via a supplementary website featuring computer code and data sets. Structural Equation Modeling: A Bayesian Approach is a multi-disciplinary text ideal for researchers and students in many areas, including: statistics, biostatistics, business, education, medicine, psychology, public health and social science.