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Large Scale Optimization in Supply Chains and Smart Manufacturing: Theory and Applications (Springer Optimization and Its Applications #149)
by Jesús M. Velásquez-Bermúdez Marzieh Khakifirooz Mahdi FathiIn this book, theory of large scale optimization is introduced with case studies of real-world problems and applications of structured mathematical modeling. The large scale optimization methods are represented by various theories such as Benders’ decomposition, logic-based Benders’ decomposition, Lagrangian relaxation, Dantzig –Wolfe decomposition, multi-tree decomposition, Van Roy’ cross decomposition and parallel decomposition for mathematical programs such as mixed integer nonlinear programming and stochastic programming. Case studies of large scale optimization in supply chain management, smart manufacturing, and Industry 4.0 are investigated with efficient implementation for real-time solutions. The features of case studies cover a wide range of fields including the Internet of things, advanced transportation systems, energy management, supply chain networks, service systems, operations management, risk management, and financial and sales management. Instructors, graduate students, researchers, and practitioners, would benefit from this book finding the applicability of large scale optimization in asynchronous parallel optimization, real-time distributed network, and optimizing the knowledge-based expert system for convex and non-convex problems.
Large Strain Finite Element Method
by Earl E. Knight Esteban Rougier Antonio MunjizaAn introductory approach to the subject of large strains and large displacements in finite elements.Large Strain Finite Element Method: A Practical Course, takes an introductory approach to the subject of large strains and large displacements in finite elements and starts from the basic concepts of finite strain deformability, including finite rotations and finite displacements. The necessary elements of vector analysis and tensorial calculus on the lines of modern understanding of the concept of tensor will also be introduced.This book explains how tensors and vectors can be described using matrices and also introduces different stress and strain tensors. Building on these, step by step finite element techniques for both hyper and hypo-elastic approach will be considered.Material models including isotropic, unisotropic, plastic and viscoplastic materials will be independently discussed to facilitate clarity and ease of learning. Elements of transient dynamics will also be covered and key explicit and iterative solvers including the direct numerical integration, relaxation techniques and conjugate gradient method will also be explored.This book contains a large number of easy to follow illustrations, examples and source code details that facilitate both reading and understanding. Takes an introductory approach to the subject of large strains and large displacements in finite elements. No prior knowledge of the subject is required.Discusses computational methods and algorithms to tackle large strains and teaches the basic knowledge required to be able to critically gauge the results of computational models.Contains a large number of easy to follow illustrations, examples and source code details.Accompanied by a website hosting code examples.
Large-Scale Cognitive Assessment: Analyzing PIAAC Data (Methodology of Educational Measurement and Assessment)
by Débora B. Maehler Beatrice RammstedtThis open access methodological book summarises existing analysing techniques using data from PIAAC, a study initiated by the OECD that assesses key cognitive and occupational skills of the adult population in more than 40 countries. The approximately 65 PIAAC datasets that has been published worldwide to date has been widely received and used by an interdisciplinary research community. Due to the complex structure of the data, analyses with PIAAC datasets are very challenging. To ensure the quality and significance of these data analyses, it is necessary to instruct users in the correct handling of the data. This methodological book provides a standardised approach to successfully implementing these data analyses. It contains examples of and tools for the analysis of the PIAAC data using different statistical approaches and software, and it offers perspectives from various disciplines. The contributing authors have hands-on experience of using PIAAC data, and/or they have conducted data analysis workshops with these data.
Large-Scale Computing Techniques for Complex System Simulations
by Werner Dubitzky Krzysztof Kurowski Bernard SchottComplex systems modeling and simulation approaches are being adopted in a growing number of sectors, including finance, economics, biology, astronomy, and many more. Technologies ranging from distributed computing to specialized hardware are explored and developed to address the computational requirements arising in complex systems simulations. The aim of this book is to present a representative overview of contemporary large-scale computing technologies in the context of complex systems simulations applications. The intention is to identify new research directions in this field and to provide a communications platform facilitating an exchange of concepts, ideas and needs between the scientists and technologist and complex system modelers. On the application side, the book focuses on modeling and simulation of natural and man-made complex systems. On the computing technology side, emphasis is placed on the distributed computing approaches, but supercomputing and other novel technologies are also considered.
Large-Scale Inference
by Bradley EfronWe live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.
Large-Scale Inverse Problems and Quantification of Uncertainty (Wiley Series in Computational Statistics #712)
by Lorenz Biegler Matthias Heinkenschloss Youssef Marzouk Karen Willcox Omar Ghattas George Biros Bart van Bloemen Waanders Luis Tenorio David Keyes Bani MallickThis book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Large-Scale Perturbations of Magnetohydrodynamic Regimes
by Vladislav ZheligovskyNew developments for hydrodynamical dynamo theory have been spurred by recent evidence of self-sustained dynamo activity in laboratory experiments with liquid metals. The emphasis in the present volume is on the introduction of powerful mathematical techniques required to tackle modern multiscale analysis of continous systems and there application to a number of realistic model geometries of increasing complexity. This introductory and self-contained research monograph summarizes the theoretical state-of-the-art to which the author has made pioneering contributions.
Large-Scale Quantum-Mechanical Enzymology
by Greg LeverThis work establishes linear-scaling density-functional theory (DFT) as a powerful tool for understanding enzyme catalysis, one that can complement quantum mechanics/molecular mechanics (QM/MM) and molecular dynamics simulations. The thesis reviews benchmark studies demonstrating techniques capable of simulating entire enzymes at the ab initio quantum-mechanical level of accuracy. DFT has transformed the physical sciences by allowing researchers to perform parameter-free quantum-mechanical calculations to predict a broad range of physical and chemical properties of materials. In principle, similar methods could be applied to biological problems. However, even the simplest biological systems contain many thousands of atoms and are characterized by extremely complex configuration spaces associated with a vast number of degrees of freedom. The development of linear-scaling density-functional codes makes biological molecules accessible to quantum-mechanical calculation, but has yet to resolve the complexity of the phase space. Furthermore, these calculations on systems containing up to 2,000 atoms can capture contributions to the energy that are not accounted for in QM/MM methods (for which the Nobel prize in Chemistry was awarded in 2013) and the results presented here reveal profound shortcomings in said methods.
Large-Scale Scientific Computations: 14th International Conference, LSSC 2023, Sozopol, Bulgaria, June 5–9, 2023, Revised Selected Papers (Lecture Notes in Computer Science #13952)
by Ivan Lirkov Svetozar MargenovThis book constitutes the refereed proceedings of the 14th International Conference on Large-Scale Scientific Computations, LSSC 2023, held in Sozopol, Bulgaria, during June 5–9, 2023. The 49 full papers included in this book were carefully reviewed and selected from 61 submissions. They were organized in topical sections as follows: preconditioning and multilevel methods; fractures and mixed dimensional modeling: discretizations, solvers, and methodology; machine learning and model order reduction for large scale predictive simulations; fractional differential problems: theoretical aspects, algorithms and applications; variational analysis and optimal control; stochastic optimal control and numerical methods in economics and finance; tensor methods for big data analytics and low-rank approximations of PDEs solutions; applications of metaheuristics to large-scale problems; large-scale models: numerical methods, parallel computations and applications; HPC and HPDA: algorithms and applications.
Large-Scale Scientific Computing
by Svetozar D. Margenov Ivan Lirkov Jerzy WaśniewskiThis book constitutes the thoroughly refereedpost-conference proceedings of the 10th International Conference on Large-ScaleScientific Computations, LSSC 2015, held in Sozopol, Bulgaria, in June 2015. The 49 revised full papers presented were carefullyreviewed and selected from 64 submissions. The general theme for LSSC 2015 wasLarge-Scale Scientific Computing with a particular focus on the organizedspecial sessions: enabling exascale computation; control and uncertain systems;computational microelectronics - from monte carlo to deterministic approaches;numerical methods for multiphysics problems; large-scale models: numericalmethods, parallel computations and applications; mathematical modeling andanalysis of PDEs describing physical problems; a posteriori error control anditerative methods for maxwell type problems; efficient algorithms for hybridHPC systems; multilevel methods on graphs; and applications of metaheuristicsto large-scale problems.
Large-Scale Studies in Mathematics Education
by Stephen Hwang James A. Middleton Jinfa CaiIn recent years, funding agencies like the Institute of Educational Sciences and the National Science Foundation have increasingly emphasized large-scale studies with experimental and quasi-experimental designs looking for 'objective truths' Educational researchers have recently begun to use large-scale studies to understand what really works, from developing interventions, to validation studies of the intervention, and then to efficacy studies and the final "scale-up" for large implementation of an intervention. Moreover, modeling student learning developmentally, taking into account cohort factors, issues of socioeconomics, local political context and the presence or absence of interventions requires the use of large data sets, wherein these variables can be sampled adequately and inferences made Inroads in quantitative methods have been made in the psychometric and sociometric literatures, but these methods are not yet common knowledge in the mathematics education community. In fact, currently there is no volume devoted to discussion of issues related to large-scale studies and to report findings from them This volume is unique as it directly discusses methodological issue in large-scale studies and reports empirical data from large-scale studies.
Large-Scale and Distributed Optimization (Lecture Notes in Mathematics #2227)
by Anders Rantzer Pontus GiselssonThis book presents tools and methods for large-scale and distributed optimization. Since many methods in "Big Data" fields rely on solving large-scale optimization problems, often in distributed fashion, this topic has over the last decade emerged to become very important. As well as specific coverage of this active research field, the book serves as a powerful source of information for practitioners as well as theoreticians.Large-Scale and Distributed Optimization is a unique combination of contributions from leading experts in the field, who were speakers at the LCCC Focus Period on Large-Scale and Distributed Optimization, held in Lund, 14th–16th June 2017. A source of information and innovative ideas for current and future research, this book will appeal to researchers, academics, and students who are interested in large-scale optimization.
Laser Beam Propagation: Generation and Propagation of Customized Light
by Andrew ForbesHow do laser beams propagate? Innovative discoveries involving laser beams and their propagation properties are at the heart of Laser Beam Propagation: Generation and Propagation of Customized Light. This book captures the essence of laser beam propagation. Divided into three parts, it explores the fundamentals of how laser beams propagate, and pro
Laser Interaction with Heterogeneous Biological Tissue: Mathematical Modeling (Biological and Medical Physics, Biomedical Engineering)
by Kirill Kulikov Tatiana KoshlanThis book introduces readers to the principles of laser interaction with biological cells and tissues with varying degrees of organization. In addition to considering the problems of biomedical cell diagnostics, and modeling the scattering of laser irradiation of blood cells for biological structures (dermis, epidermis, vascular plexus), it presents an analytic theory based on solving the wave equation for the electromagnetic field. It discusses a range of mathematical modeling topics, including optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers; heating blood vessels using laser irradiation on the outer surface of the skin; and thermo-chemical denaturation of biological structures based on the example of human skin. In this second edition, a new electrodynamic model of the interaction of laser radiation with blood cells is presented for the structure of cells and the in vitro prediction of optical properties. The approach developed makes it possible to determine changes in cell size as well as modifications in their internal structures, such as transformation and polymorphism nucleus scattering, which is of interest for cytological studies. The new model is subsequently used to calculate the size distribution function of irregular-shape particles with a variety of forms and structures, which allows a cytological analysis of the observed deviations from normal cells.
Lasso-MPC - Predictive Control with ℓ1-Regularised Least Squares
by Marco GallieriThis thesis proposes a novel Model Predictive Control (MPC) strategy, which modifies the usual MPC cost function in order to achieve a desirable sparse actuation. It features an ℓ1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. While standard control techniques lead to continuous movements of all actuators, this approach enables a selected subset of actuators to be used, the others being brought into play in exceptional circumstances. The same approach can also be used to obtain asynchronous actuator interventions, so that control actions are only taken in response to large disturbances. This thesis presents a straightforward and systematic approach to achieving these practical properties, which are ignored by mainstream control theory.
Latent Class Analysis of Survey Error
by Paul P. BiemerCombining theoretical, methodological, and practical aspects, Latent Class Analysis of Survey Error successfully guides readers through the accurate interpretation of survey results for quality evaluation and improvement. This book is a comprehensive resource on the key statistical tools and techniques employed during the modeling and estimation of classification errors, featuring a special focus on both latent class analysis (LCA) techniques and models for categorical data from complex sample surveys.Drawing from his extensive experience in the field of survey methodology, the author examines early models for survey measurement error and identifies their similarities and differences as well as their strengths and weaknesses. Subsequent chapters treat topics related to modeling, estimating, and reducing errors in surveys, including:Measurement error modeling forcategorical dataThe Hui-Walter model and othermethods for two indicatorsThe EM algorithm and its role in latentclass model parameter estimationLatent class models for three ormore indicatorsTechniques for interpretation of modelparameter estimatesAdvanced topics in LCA, including sparse data, boundary values, unidentifiability, and local maximaSpecial considerations for analyzing datafrom clustered and unequal probability samples with nonresponseThe current state of LCA and MLCA (multilevel latent class analysis), and an insightful discussion on areas for further researchThroughout the book, more than 100 real-world examples describe the presented methods in detail, and readers are guided through the use of lEM software to replicate the presented analyses. Appendices supply a primer on categorical data analysis, and a related Web site houses the lEM software.Extensively class-tested to ensure an accessible presentation, Latent Class Analysis of Survey Error is an excellent book for courses on measurement error and survey methodology at the graduate level. The book also serves as a valuable reference for researchers and practitioners working in business, government, and the social sciences who develop, implement, or evaluate surveys.
Latent Class and Latent Transition Analysis
by Stephanie T. Lanza Linda M. CollinsA modern, comprehensive treatment of latent class and latent transition analysis for categorical dataOn 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 modelsFocused coverage of the conceptual underpinnings of interpretation and evaluationof a latent class solutionUse of parameter restrictions and detection of identification problemsAdvanced topics such as multi-group analysis and the modeling and interpretation of interactions between covariatesThe 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.
Latent Curve Models: A Structural Equation Perspective
by Kenneth A. Bollen Patrick J. CurranAn 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. <p><p>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. <p><p>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.
Latent Factor Analysis for High-dimensional and Sparse Matrices: A particle swarm optimization-based approach (SpringerBriefs in Computer Science)
by Ye Yuan Xin LuoLatent factor analysis models are an effective type of machine learning model for addressing high-dimensional and sparse matrices, which are encountered in many big-data-related industrial applications. The performance of a latent factor analysis model relies heavily on appropriate hyper-parameters. However, most hyper-parameters are data-dependent, and using grid-search to tune these hyper-parameters is truly laborious and expensive in computational terms. Hence, how to achieve efficient hyper-parameter adaptation for latent factor analysis models has become a significant question.This is the first book to focus on how particle swarm optimization can be incorporated into latent factor analysis for efficient hyper-parameter adaptation, an approach that offers high scalability in real-world industrial applications. The book will help students, researchers and engineers fully understand the basic methodologies of hyper-parameter adaptation via particle swarm optimization in latent factor analysis models. Further, it will enable them to conduct extensive research and experiments on the real-world applications of the content discussed.
Latent Markov Models for Longitudinal Data (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences)
by Francesco Bartolucci Alessio Farcomeni Fulvia PennoniDrawing on the authors' extensive research in the analysis of categorical longitudinal data, this book focuses on the formulation of latent Markov models and the practical use of these models. It demonstrates how to use the models in three types of analysis, with numerous examples illustrating how latent Markov models are used in economics, education, sociology, and other fields. The R and MATLAB routines used for the examples are available on the authors' website.
Latent Variable Modeling Using R: A Step-by-Step Guide
by A. Alexander BeaujeanThis step-by-step guide is written for R and latent variable model (LVM) novices. Utilizing a path model approach and focusing on the lavaan package, this book is designed to help readers quickly understand LVMs and their analysis in R. The author reviews the reasoning behind the syntax selected and provides examples that demonstrate how to analyze data for a variety of LVMs.? Featuring examples applicable to psychology, education, business, and other social and health sciences, minimal text is devoted to theoretical underpinnings. The material is presented without?the use of matrix algebra. As a whole the book prepares readers to write about and interpret LVM results they obtain in R. Each chapter features background information, boldfaced key? terms defined in the glossary, detailed interpretations of R output, descriptions of how to write the analysis of results for publication, a summary, R based practice exercises (with solutions included in the back of the book), and references and related readings. Margin notes help readers better understand LVMs and write their own R syntax. Examples using data from published work across a variety of disciplines demonstrate how to use R syntax for analyzing and interpreting results. R functions, syntax, and the corresponding results appear in gray boxes to help readers quickly locate this material. A unique index helps readers quickly locate R?functions, packages, and datasets. The book and accompanying website at http://blogs.baylor.edu/rlatentvariable/ provides all of the data for the book’s examples and exercises as well as R syntax so readers can replicate the analyses. The book reviews how to enter the data into R, specify the LVMs, and obtain and interpret the estimated parameter values. The book opens with the fundamentals of using R including how to download the program, use functions, and enter and manipulate data. Chapters 2 and 3 introduce and then extend path models to include latent variables. Chapter 4 shows readers how to analyze a latent variable model with data from more than one group, while Chapter 5 shows how to analyze a latent variable model with data from more than one time period. Chapter 6 demonstrates the analysis of dichotomous variables, while Chapter 7 demonstrates how to analyze LVMs with missing data. Chapter 8 focuses on sample size determination using Monte Carlo methods, which can be used with a wide range of statistical models and account for missing data. The final chapter examines hierarchical LVMs, demonstrating both higher-order and bi-factor approaches. The book concludes with three Appendices: a review of common measures of model fit including their formulae and interpretation; syntax for other R latent variable models packages; and solutions for each chapter’s exercises. Intended as a supplementary text for graduate and/or advanced undergraduate courses on latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multivariate statistics taught in psychology, education, human development, business, economics, and social and health sciences, this book also appeals to researchers in these fields. Prerequisites include familiarity with basic statistical concepts, but knowledge of R is not assumed.
Latent Variable Modeling with R
by W. Holmes Finch Brian F. FrenchThis book demonstrates how to conduct latent variable modeling (LVM) in R by highlighting the features of each model, their specialized uses, examples, sample code and output, and an interpretation of the results. Each chapter features a detailed example including the analysis of the data using R, the relevant theory, the assumptions underlying the model, and other statistical details to help readers better understand the models and interpret the results. Every R command necessary for conducting the analyses is described along with the resulting output which provides readers with a template to follow when they apply the methods to their own data. The basic information pertinent to each model, the newest developments in these areas, and the relevant R code to use them are reviewed. Each chapter also features an introduction, summary, and suggested readings. A glossary of the text’s boldfaced key terms and key R commands serve as helpful resources. The book is accompanied by a website with exercises, an answer key, and the in-text example data sets. Latent Variable Modeling with R: -Provides some examples that use messy data providing a more realistic situation readers will encounter with their own data. -Reviews a wide range of LVMs including factor analysis, structural equation modeling, item response theory, and mixture models and advanced topics such as fitting nonlinear structural equation models, nonparametric item response theory models, and mixture regression models. -Demonstrates how data simulation can help researchers better understand statistical methods and assist in selecting the necessary sample size prior to collecting data. -www.routledge.com/9780415832458 provides exercises that apply the models along with annotated R output answer keys and the data that corresponds to the in-text examples so readers can replicate the results and check their work. The book opens with basic instructions in how to use R to read data, download functions, and conduct basic analyses. From there, each chapter is dedicated to a different latent variable model including exploratory and confirmatory factor analysis (CFA), structural equation modeling (SEM), multiple groups CFA/SEM, least squares estimation, growth curve models, mixture models, item response theory (both dichotomous and polytomous items), differential item functioning (DIF), and correspondance analysis. ?The book concludes with a discussion of how data simulation can be used to better understand the workings of a statistical method and assist researchers in deciding on the necessary sample size prior to collecting data.? A mixture of independently developed R code along with available libraries for simulating latent models in R are provided so readers can use these simulations to analyze data using the methods introduced in the previous chapters. Intended for use in graduate or advanced undergraduate courses in latent variable modeling, factor analysis, structural equation modeling, item response theory, measurement, or multivariate statistics taught in psychology, education, human development, and social and health sciences, researchers in these fields also appreciate this book’s practical approach. The book provides sufficient conceptual background information to serve as a standalone text.? Familiarity with basic statistical concepts is assumed but basic knowledge of R is not.
Latent Variable Models and Factor Analysis
by Irini Moustaki Martin Knott David J. BartholomewLatent 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.