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Structural Equations with Latent Variables

Author : Kenneth A. Bollen

Publisher : John Wiley & Sons

Page : 528 pages

File Size : 26,67 MB

Release : 2014-08-28

Category : Mathematics

ISBN : 111861903X

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Book Description

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.



Latent Variable Models and Factor Analysis

Author : David J. Bartholomew

Publisher : Wiley

Page : 214 pages

File Size : 48,62 MB

Release : 1999-08-10

Category : Mathematics

ISBN : 9780340692431

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Book Description

Hitherto latent variable modelling has hovered on the fringes of the statistical mainstream but if the purpose of statistics is to deal with real problems, there is every reason for it to move closer to centre stage. In the social sciences especially, latent variables are common and if they are to be handled in a truly scientific manner, statistical theory must be developed to include them. This book aims to show how that should be done. This second edition is a complete re-working of the book of the same name which appeared in the Griffin’s Statistical Monographs in 1987. Since then there has been a surge of interest in latent variable methods which has necessitated a radical revision of the material but the prime object of the book remains the same. It provides a unified and coherent treatment of the field from a statistical perspective. This is achieved by setting up a sufficiently general framework to enable the derivation of the commonly used models. The subsequent analysis is then done wholly within the realm of probability calculus and the theory of statistical inference. Numerical examples are provided as well as the software to carry them out ( where this is not otherwise available). Additional data sets are provided in some cases so that the reader can aquire a wider experience of analysis and interpretation.



Latent Variable Models

Author : John C. Loehlin

Publisher : Psychology Press

Page : 303 pages

File Size : 32,2 MB

Release : 2004-05-20

Category : Business & Economics

ISBN : 1135614342

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Book Description

This book introduces multiple-latent variable models by utilizing path diagrams to explain the underlying relationships in the models. This approach helps less mathematically inclined students grasp the underlying relationships between path analysis, factor analysis, and structural equation modeling more easily. A few sections of the book make use of elementary matrix algebra. An appendix on the topic is provided for those who need a review. The author maintains an informal style so as to increase the book's accessibility. Notes at the end of each chapter provide some of the more technical details. The book is not tied to a particular computer program, but special attention is paid to LISREL, EQS, AMOS, and Mx. New in the fourth edition of Latent Variable Models: *a data CD that features the correlation and covariance matrices used in the exercises; *new sections on missing data, non-normality, mediation, factorial invariance, and automating the construction of path diagrams; and *reorganization of chapters 3-7 to enhance the flow of the book and its flexibility for teaching. Intended for advanced students and researchers in the areas of social, educational, clinical, industrial, consumer, personality, and developmental psychology, sociology, political science, and marketing, some prior familiarity with correlation and regression is helpful.



Measurement Error and Latent Variables in Econometrics

Author : T. Wansbeek

Publisher : North Holland

Page : 464 pages

File Size : 32,83 MB

Release : 2000-12-08

Category : Business & Economics

ISBN :

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Book Description

The book first discusses in depth various aspects of the well-known inconsistency that arises when explanatory variables in a linear regression model are measured with error. Despite this inconsistency, the region where the true regression coeffecients lies can sometimes be characterized in a useful way, especially when bounds are known on the measurement error variance but also when such information is absent. Wage discrimination with imperfect productivity measurement is discussed as an important special case. Next, it is shown that the inconsistency is not accidental but fundamental. Due to an identification problem, no consistent estimators may exist at all. Additional information is desirable. This information can be of various types. One type is exact prior knowledge about functions of the parameters. This leads to the CALS estimator. Another major type is in the form of instrumental variables. Many aspects of this are discussed, including heteroskedasticity, combination of data from different sources, construction of instruments from the available data, and the LIML estimator, which is especially relevant when the instruments are weak. The scope is then widened to an embedding of the regression equation with measurement error in a multiple equations setting, leading to the exploratory factor analysis (EFA) model. This marks the step from measurement error to latent variables. Estimation of the EFA model leads to an eigenvalue problem. A variety of models is reviewed that involve eignevalue problems as their common characteristic. EFA is extended to confirmatory factor analysis (CFA) by including restrictions on the parameters of the factor analysis model, and next by relating the factors to background variables. These models are all structural equation models (SEMs), a very general and important class of models, with the LISREL model as its best-known representation, encompassing almost all linear equation systems with latent variables. Estimation of SEMs can be viewed as an application of the generalized method of moments (GMM). GMM in general and for SEM in particular is discussed at great length, including the generality of GMM, optimal weighting, conditional moments, continuous updating, simulation estimation, the link with the method of maximum likelihood, and in particular testing and model evaluation for GMM. The discussion concludes with nonlinear models. The emphasis is on polynomial models and models that are nonlinear due to a filter on the dependent variables, like discrete choice models or models with ordered categorical variables.



Advances in Latent Variables

Author : Maurizio Carpita

Publisher :

Page : pages

File Size : 34,78 MB

Release : 2015

Category :

ISBN : 9783319029689

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Book Description

The book, belonging to the series "Studies in Theoretical and Applied Statistics - Selected Papers from the Statistical Societies", presents a peer-reviewed selection of contributions on relevant topics organized by the editors on the occasion of the SIS 2013 Statistical Conference "Advances in Latent Variables. Methods, Models and Applications", held at the Department of Economics and Management of the University of Brescia from June 19 to 21, 2013. The focus of the book is on advances in statistical methods for analyses with latent variables. In fact, in recent years, there has been increasing interest in this broad research area from both a theoretical and an applied point of view, as the statistical latent variable approach allows the effective modeling of complex real-life phenomena in a wide range of research fields. A major goal of the volume is to bring together articles written by statisticians from different research fields, which present different approaches and experiences related to the analysis of unobservable variables and the study of the relationships between them.



Handbook of Latent Variable and Related Models

Author :

Publisher : Elsevier

Page : 458 pages

File Size : 31,73 MB

Release : 2011-08-11

Category : Mathematics

ISBN : 0080471269

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Book Description

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.



Generalized Latent Variable Modeling

Author : Anders Skrondal

Publisher : CRC Press

Page : 528 pages

File Size : 22,79 MB

Release : 2004-05-11

Category : Mathematics

ISBN : 0203489438

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Book Description

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



Latent Class and Latent Transition Analysis

Author : Linda M. Collins

Publisher : John Wiley & Sons

Page : 273 pages

File Size : 35,38 MB

Release : 2013-05-20

Category : Mathematics

ISBN : 111821076X

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Book Description

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.



Latent Variable Modeling Using R

Author : A. Alexander Beaujean

Publisher : Routledge

Page : 337 pages

File Size : 27,88 MB

Release : 2014-05-09

Category : Psychology

ISBN : 1317970721

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Book Description

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 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.



Longitudinal Research with Latent Variables

Author : Kees van Montfort

Publisher : Springer Science & Business Media

Page : 311 pages

File Size : 46,4 MB

Release : 2010-05-17

Category : Mathematics

ISBN : 3642117600

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Book Description

Since Charles Spearman published his seminal paper on factor analysis in 1904 and Karl Joresk ̈ og replaced the observed variables in an econometric structural equation model by latent factors in 1970, causal modelling by means of latent variables has become the standard in the social and behavioural sciences. Indeed, the central va- ables that social and behavioural theories deal with, can hardly ever be identi?ed as observed variables. Statistical modelling has to take account of measurement - rors and invalidities in the observed variables and so address the underlying latent variables. Moreover, during the past decades it has been widely agreed on that serious causal modelling should be based on longitudinal data. It is especially in the ?eld of longitudinal research and analysis, including panel research, that progress has been made in recent years. Many comprehensive panel data sets as, for example, on human development and voting behaviour have become available for analysis. The number of publications based on longitudinal data has increased immensely. Papers with causal claims based on cross-sectional data only experience rejection just for that reason.



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