Search results for: latent-variable-models-and-factor-analysis

Latent Variable Models and Factor Analysis

Author : David J. Bartholomew
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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.

Latent Variable Models

Author : John C. Loehlin
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Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis introduces latent variable models by utilizing path diagrams to explain the relationships in the models. This approach helps less mathematically-inclined readers to grasp the underlying relations among path analysis, factor analysis, and structural equation modeling, and to set up and carry out such analyses. This revised and expanded fifth edition again contains key chapters on path analysis, structural equation models, and exploratory factor analysis. In addition, it contains new material on composite reliability, models with categorical data, the minimum average partial procedure, bi-factor models, and communicating about latent variable models. The informal writing style and the numerous illustrative examples make the book accessible to readers of varying backgrounds. Notes at the end of each chapter expand the discussion and provide additional technical detail and references. Moreover, most chapters contain an extended example in which the authors work through one of the chapter’s examples in detail to aid readers in conducting similar analyses with their own data. The book and accompanying website provide all of the data for the book’s examples as well as syntax from latent variable programs so readers can replicate the analyses. The book can be used with any of a variety of computer programs, but special attention is paid to LISREL and R. An important resource for advanced students and researchers in numerous disciplines in the behavioral sciences, education, business, and health sciences, Latent Variable Models is a practical and readable reference for those seeking to understand or conduct an analysis using latent variables.

Language Policy in Schools

Author : David Corson
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School language policies are viewed by many in education as an integral and necessary part of the administration and the curriculum practice of schools. A language policy, like the many presented in this book, is a document compiled by school staff members, who often are assisted by other members of the school community, to which the staff give their assent and commitment.

Latent Variable Modeling with R

Author : W. Holmes Finch
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This 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. 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 and Latent Structure Models

Author : George A. Marcoulides
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This edited volume features cutting-edge topics from the leading researchers in the areas of latent variable modeling. Content highlights include coverage of approaches dealing with missing values, semi-parametric estimation, robust analysis, hierarchical data, factor scores, multi-group analysis, and model testing. New methodological topics are illustrated with real applications. The material presented brings together two traditions: psychometrics and structural equation modeling. Latent Variable and Latent Structure Models' thought-provoking chapters from the leading researchers in the area will help to stimulate ideas for further research for many years to come. This volume will be of interest to researchers and practitioners from a wide variety of disciplines, including biology, business, economics, education, medicine, psychology, sociology, and other social and behavioral sciences. A working knowledge of basic multivariate statistics and measurement theory is assumed.

Current Topics in the Theory and Application of Latent Variable Models

Author : Michael Charles Edwards
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This book presents recent developments in the theory and application of latent variable models (LVMs) by some of the most prominent researchers in the field. Topics covered involve a range of LVM frameworks including item response theory, structural equation modeling, factor analysis, and latent curve modeling, as well as various non-standard data structures and innovative applications. The book is divided into two sections, although several chapters cross these content boundaries. Part one focuses on complexities which involve the adaptation of latent variables models in research problems where real-world conditions do not match conventional assumptions. Chapters in this section cover issues such as analysis of dyadic data and complex survey data, as well as analysis of categorical variables. Part two of the book focuses on drawing real-world meaning from results obtained in LVMs. In this section there are chapters examining issues involving assessment of model fit, the nature of uncertainty in parameter estimates, inferences, and the nature of latent variables and individual differences. This book appeals to researchers and graduate students interested in the theory and application of latent variable models. As such, it serves as a supplementary reading in graduate level courses on latent variable models. Prerequisites include basic knowledge of latent variable models.

Generalized Latent Variable Modeling

Author : Anders Skrondal
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This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models. Following a gentle introduction to latent variable modeling, the authors clearly explain and contrast a wi

An Introduction to Latent Variable Models

Author : B. Everett
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Latent variable models are used in many areas of the social and behavioural sciences, and the increasing availability of computer packages for fitting such models is likely to increase their popularity. This book attempts to introduce such models to applied statisticians and research workers interested in exploring the structure of covari ance and correlation matrices in terms of a small number of unob servable constructs. The emphasis is on the practical application of the procedures rather than on detailed discussion of their mathe matical and statistical properties. It is assumed that the reader is familiar with the most commonly used statistical concepts and methods, particularly regression, and also has a fair knowledge of matrix algebra. My thanks are due to my colleagues Dr David Hand and Dr Graham Dunn for helpful comments on the book, to Mrs Bertha Lakey for her careful typing of a difficult manuscript and to Peter Cuttance for assistance with the LlSREL package. In addition the text clearly owes a great deal to the work on structural equation models published by Karl Joreskog, Dag Sorbom, Peter Bentler, Michael Browne and others.

Latent Variable Modeling Using R

Author : A. Alexander Beaujean
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This 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 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.

Random Effect and Latent Variable Model Selection

Author : David Dunson
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Random Effect and Latent Variable Model Selection In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of ?elds. For example, it is now standard pr- tice to routinely collect many response variables on each individual in a study. The different variables may correspond to repeated measurements over time, to a battery of surrogates for one or more latent traits, or to multiple types of outcomes having an unknown dependence structure. Hierarchical models that incorporate subje- speci?c parameters are one of the most widely-used tools for analyzing multivariate and correlated data. Such subject-speci?c parameters are commonly referred to as random effects, latent variables or frailties. There are two modeling frameworks that have been particularly widely used as hierarchical generalizations of linear regression models. The ?rst is the linear mixed effects model (Laird and Ware , 1982) and the second is the structural equation model (Bollen , 1989). Linear mixed effects (LME) models extend linear regr- sion to incorporate two components, with the ?rst corresponding to ?xed effects describing the impact of predictors on the mean and the second to random effects characterizing the impact on the covariance. LMEs have also been increasingly used for function estimation. In implementing LME analyses, model selection problems are unavoidable. For example, there may be interest in comparing models with and without a predictor in the ?xed and/or random effects component.

Handbook of Latent Variable and Related Models

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This Handbook covers latent variable models, which are a flexible class of models for modeling multivariate data to explore relationships among observed and latent variables. - Covers a wide class of important models - Models and statistical methods described provide tools for analyzing a wide spectrum of complicated data - Includes illustrative examples with real data sets from business, education, medicine, public health and sociology. - Demonstrates the use of a wide variety of statistical, computational, and mathematical techniques.

Hidden Variables

Author : Source Wikipedia
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 41. Chapters: Hidden variable theory, Latent variable models, Bell's theorem, Mixture model, Item response theory, Factor analysis, Latent Dirichlet allocation, Latent semantic analysis, Kochen-Specker theorem, Spekkens Toy Model, Local hidden variable theory, Partial least squares regression, Probabilistic latent semantic analysis, Latent class model, Local independence, Pachinko allocation, Nuisance variable, Topic model, Doubly stochastic model. Excerpt: In theoretical physics, Bell's theorem (a.k.a. Bell's inequality) is a no-go theorem, loosely stating that: no physical theory of local hidden variables can reproduce all of the predictions of quantum mechanics. The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness . It is the most famous legacy of the late physicist John Stewart Bell. Results of tests of Bell's theorem agree with the predictions of quantum mechanical theory, and demonstrate that some quantum effects appear to travel faster than light. Hence the class of tenable 'hidden variable' theories are limited to the non-local variety. However, none of the tests of the theorem performed to date has fulfilled all of the requisite conditions implicit in the theorem. Accordingly, none of the results are totally conclusive. Bell's theorem implies that the concept of local realism, favoured by Einstein, yields predictions that disagree with those of quantum mechanical theory. Because numerous experiments agree with the predictions of quantum mechanical theory, and show correlations that are stronger than could be explained by local hidden variables, the concept of local realism is thus refuted as an explanation of the physical phenomena under test, and superluminal effects are...

Discrete Latent Variable Models

Author : Ton Heinen
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Unobserved Variables

Author : David J. Bartholomew
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​The classical statistical problem typically involves a probability distribution which depends on a number of unknown parameters. The form of the distribution may be known, partially or completely, and inferences have to be made on the basis of a sample of observations drawn from the distribution; often, but not necessarily, a random sample. This brief deals with problems where some of the sample members are either unobserved or hypothetical, the latter category being introduced as a means of better explaining the data. Sometimes we are interested in these kinds of variable themselves and sometimes in the parameters of the distribution. Many problems that can be cast into this form are treated. These include: missing data, mixtures, latent variables, time series and social measurement problems. Although all can be accommodated within a Bayesian framework, most are best treated from first principles.

Latent Variable Models for Longitudinal Data with Multiple Outcomes Informative Dropouts and Missing Covariates

Author : Jason Roy
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Encyclopedia of Educational Research

Author : Marvin C. Alkin
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Confirmatory Factor Analysis for Applied Research Second Edition

Author : Timothy A. Brown
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This accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA) for its emphasis on practical and conceptual aspects rather than mathematics or formulas. Detailed, worked-through examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities ...

Latent Variables Analysis

Author : Alexander von Eye
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In this volume, leading researchers examine how latent variables can be incorporated in a variety of data-analysis strategies, such as structural equation modelling, regression analysis, log-linear modelling and prediction analysis. The contributors also discuss how latent variables analysis can be applied in developmental psychology research using methods such as cohort-time of measurement-age analysis, log-linear modelling of behaviour genetics hypothesis and analyses of repeatedly observed state measures. Detailed explanations of computations and software packages are included with each statistical method.

Statistical Modelling and Latent Variables

Author : Klaus Haagen
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Statistical methods based on models with latent variables play an important role in the analysis of multivariate data. The subject can be approached theoretically or in an empirical, pragmatic way. The statistical problem is to make inferences about the latent variables and the relationships between them. Errors-in-variables models, factor analysis and latent structure models are all examples of this approach. This volume presents a selection of invited and contributed papers which address the problems involved in developing a unifying statistical theory for latent variable models.

Advances in Latent Class Analysis

Author : Gregory R. Hancock
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What is latent class analysis? If you asked that question thirty or forty years ago you would have gotten a different answer than you would today. Closer to its time of inception, latent class analysis was viewed primarily as a categorical data analysis technique, often framed as a factor analysis model where both the measured variable indicators and underlying latent variables are categorical. Today, however, it rests within much broader mixture and diagnostic modeling framework, integrating measured and latent variables that may be categorical and/or continuous, and where latent classes serve to define the subpopulations for whom many aspects of the focal measured and latent variable model may differ. For latent class analysis to take these developmental leaps required contributions that were methodological, certainly, as well as didactic. Among the leaders on both fronts was C. Mitchell “Chan” Dayton, at the University of Maryland, whose work in latent class analysis spanning several decades helped the method to expand and reach its current potential. The current volume in the Center for Integrated Latent Variable Research (CILVR) series reflects the diversity that is latent class analysis today, celebrating work related to, made possible by, and inspired by Chan’s noted contributions, and signaling the even more exciting future yet to come.