Advances In Latent Variable Mixture Models

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Advances in Latent Variable Mixture Models

Author : Gregory R. Hancock
Publisher : IAP
ISBN 13 : 1607526344
Total Pages : 382 pages
Book Rating : 4.6/5 (75 download)

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Book Synopsis Advances in Latent Variable Mixture Models by : Gregory R. Hancock

Download or read book Advances in Latent Variable Mixture Models written by Gregory R. Hancock and published by IAP. This book was released on 2007-11-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current volume, Advances in Latent Variable Mixture Models, contains chapters by all of the speakers who participated in the 2006 CILVR conference, providing not just a snapshot of the event, but more importantly chronicling the state of the art in latent variable mixture model research. The volume starts with an overview chapter by the CILVR conference keynote speaker, Bengt Muthén, offering a “lay of the land” for latent variable mixture models before the volume moves to more specific constellations of topics. Part I, Multilevel and Longitudinal Systems, deals with mixtures for data that are hierarchical in nature either due to the data’s sampling structure or to the repetition of measures (of varied types) over time. Part II, Models for Assessment and Diagnosis, addresses scenarios for making judgments about individuals’ state of knowledge or development, and about the instruments used for making such judgments. Finally, Part III, Challenges in Model Evaluation, focuses on some of the methodological issues associated with the selection of models most accurately representing the processes and populations under investigation. It should be stated that this volume is not intended to be a first exposure to latent variable methods. Readers lacking such foundational knowledge are encouraged to consult primary and/or secondary didactic resources in order to get the most from the chapters in this volume. Once armed with the basic understanding of latent variable methods, we believe readers will find this volume incredibly exciting.

Advances in Latent Class Analysis

Author : Gregory R. Hancock
Publisher : IAP
ISBN 13 : 1641135638
Total Pages : 276 pages
Book Rating : 4.6/5 (411 download)

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Book Synopsis Advances in Latent Class Analysis by : Gregory R. Hancock

Download or read book Advances in Latent Class Analysis written by Gregory R. Hancock and published by IAP. This book was released on 2019-05-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Higher-Order Growth Curves and Mixture Modeling with Mplus

Author : Kandauda A.S. Wickrama
Publisher : Routledge
ISBN 13 : 1317283929
Total Pages : 345 pages
Book Rating : 4.3/5 (172 download)

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Book Synopsis Higher-Order Growth Curves and Mixture Modeling with Mplus by : Kandauda A.S. Wickrama

Download or read book Higher-Order Growth Curves and Mixture Modeling with Mplus written by Kandauda A.S. Wickrama and published by Routledge. This book was released on 2016-04-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical introduction to second-order and growth mixture models using Mplus introduces simple and complex techniques through incremental steps. The authors extend latent growth curves to second-order growth curve and mixture models and then combine the two. To maximize understanding, each model is presented with basic structural equations, figures with associated syntax that highlight what the statistics mean, Mplus applications, and an interpretation of results. Examples from a variety of disciplines demonstrate the use of the models and exercises allow readers to test their understanding of the techniques. A comprehensive introduction to confirmatory factor analysis, latent growth curve modeling, and growth mixture modeling is provided so the book can be used by readers of various skill levels. The book’s datasets are available on the web. Highlights include: -Illustrative examples using Mplus 7.4 include conceptual figures, Mplus program syntax, and an interpretation of results to show readers how to carry out the analyses with actual data. -Exercises with an answer key allow readers to practice the skills they learn. -Applications to a variety of disciplines appeal to those in the behavioral, social, political, educational, occupational, business, and health sciences. -Data files for all the illustrative examples and exercises at www.routledge.com/9781138925151 allow readers to test their understanding of the concepts. -Point to Remember boxes aid in reader comprehension or provide in-depth discussions of key statistical or theoretical concepts. Part 1 introduces basic structural equation modeling (SEM) as well as first- and second-order growth curve modeling. The book opens with the basic concepts from SEM, possible extensions of conventional growth curve models, and the data and measures used throughout the book. The subsequent chapters in part 1 explain the extensions. Chapter 2 introduces conventional modeling of multidimensional panel data, including confirmatory factor analysis (CFA) and growth curve modeling, and its limitations. The logical and theoretical extension of a CFA to a second-order growth curve, known as curve-of-factors model (CFM), are explained in Chapter 3. Chapter 4 illustrates the estimation and interpretation of unconditional and conditional CFMs. Chapter 5 presents the logical and theoretical extension of a parallel process model to a second-order growth curve, known as factor-of-curves model (FCM). Chapter 6 illustrates the estimation and interpretation of unconditional and conditional FCMs. Part 2 reviews growth mixture modeling including unconditional growth mixture modeling (Ch. 7) and conditional growth mixture models (Ch. 8). How to extend second-order growth curves (curve-of-factors and factor-of-curves models) to growth mixture models is highlighted in Chapter 9. Ideal as a supplement for use in graduate courses on (advanced) structural equation, multilevel, longitudinal, or latent variable modeling, latent growth curve and mixture modeling, factor analysis, multivariate statistics, or advanced quantitative techniques (methods) taught in psychology, human development and family studies, business, education, health, and social sciences, this book’s practical approach also appeals to researchers. Prerequisites include a basic knowledge of intermediate statistics and structural equation modeling.

Latent Variable Modeling with R

Author : W. Holmes Finch
Publisher :
ISBN 13 : 9781315869797
Total Pages : 0 pages
Book Rating : 4.8/5 (697 download)

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Book Synopsis Latent Variable Modeling with R by : W. Holmes Finch

Download or read book Latent Variable Modeling with R written by W. Holmes Finch and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. -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.

The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis

Author : Todd D. Little
Publisher : Oxford University Press
ISBN 13 : 0199934908
Total Pages : 784 pages
Book Rating : 4.1/5 (999 download)

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Book Synopsis The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis by : Todd D. Little

Download or read book The Oxford Handbook of Quantitative Methods, Vol. 2: Statistical Analysis written by Todd D. Little and published by Oxford University Press. This book was released on 2013-02-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research today demands the application of sophisticated and powerful research tools. Fulfilling this need, The Oxford Handbook of Quantitative Methods is the complete tool box to deliver the most valid and generalizable answers to todays complex research questions. It is a one-stop source for learning and reviewing current best-practices in quantitative methods as practiced in the social, behavioral, and educational sciences. Comprising two volumes, this handbook covers a wealth of topics related to quantitative research methods. It begins with essential philosophical and ethical issues related to science and quantitative research. It then addresses core measurement topics before delving into the design of studies. Principal issues related to modern estimation and mathematical modeling are also detailed. Topics in the handbook then segway into the realm of statistical inference and modeling with chapters dedicated to classical approaches as well as modern latent variable approaches. Numerous chapters associated with longitudinal data and more specialized techniques round out this broad selection of topics. Comprehensive, authoritative, and user-friendly, this two-volume set will be an indispensable resource for serious researchers across the social, behavioral, and educational sciences.

Multilevel Modeling

Author : Steven P. Reise
Publisher : Psychology Press
ISBN 13 : 1135655367
Total Pages : 276 pages
Book Rating : 4.1/5 (356 download)

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Book Synopsis Multilevel Modeling by : Steven P. Reise

Download or read book Multilevel Modeling written by Steven P. Reise and published by Psychology Press. This book was released on 2003-01-30 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book appeals to researchers who work with nested data structures or repeated measures data, including biomed & health researchers, clinical/intervention researchers and developmental & educational psychologists. Also some potential as a grad lvl tex

Generalized Latent Variable Modeling

Author : Anders Skrondal
Publisher : CRC Press
ISBN 13 : 0203489438
Total Pages : 523 pages
Book Rating : 4.2/5 (34 download)

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Book Synopsis Generalized Latent Variable Modeling by : Anders Skrondal

Download or read book Generalized Latent Variable Modeling written by Anders Skrondal and published by CRC Press. This book was released on 2004-05-11 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

New Developments and Techniques in Structural Equation Modeling

Author : George A. Marcoulides
Publisher : Psychology Press
ISBN 13 : 1410601854
Total Pages : 354 pages
Book Rating : 4.4/5 (16 download)

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Book Synopsis New Developments and Techniques in Structural Equation Modeling by : George A. Marcoulides

Download or read book New Developments and Techniques in Structural Equation Modeling written by George A. Marcoulides and published by Psychology Press. This book was released on 2001-03-01 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring contributions from some of the leading researchers in the field of SEM, most chapters are written by the author(s) who originally proposed the technique and/or contributed substantially to its development. Content highlights include latent variable mixture modeling, multilevel modeling, interaction modeling, models for dealing with nonstandard and noncompliance samples, the latest on the analysis of growth curve and longitudinal data, specification searches, item parceling, and equivalent models. This volume will appeal to educators, psychologists, biologists, business professionals, medical researchers, and other social and health scientists. It is assumed that the reader has mastered the equivalent of a graduate-level multivariate statistics course that included coverage of introductory SEM techniques.

Applied Latent Class Analysis

Author : Jacques A. Hagenaars
Publisher : Cambridge University Press
ISBN 13 : 1139439235
Total Pages : 478 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Applied Latent Class Analysis by : Jacques A. Hagenaars

Download or read book Applied Latent Class Analysis written by Jacques A. Hagenaars and published by Cambridge University Press. This book was released on 2002-06-24 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Latent Class Analysis introduces several innovations in latent class analysis to a wider audience of researchers. Many of the world's leading innovators in the field of latent class analysis contributed essays to this volume, each presenting a key innovation to the basic latent class model and illustrating how it can prove useful in situations typically encountered in actual research.

Handbook of Latent Variable and Related Models

Author :
Publisher : Elsevier
ISBN 13 : 0080471269
Total Pages : 458 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Latent Variable and Related Models by :

Download or read book Handbook of Latent Variable and Related Models written by and published by Elsevier. This book was released on 2011-08-11 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Model-Based Clustering and Classification for Data Science

Author : Charles Bouveyron
Publisher : Cambridge University Press
ISBN 13 : 1108640591
Total Pages : 447 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Model-Based Clustering and Classification for Data Science by : Charles Bouveyron

Download or read book Model-Based Clustering and Classification for Data Science written by Charles Bouveyron and published by Cambridge University Press. This book was released on 2019-07-25 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cluster analysis finds groups in data automatically. Most methods have been heuristic and leave open such central questions as: how many clusters are there? Which method should I use? How should I handle outliers? Classification assigns new observations to groups given previously classified observations, and also has open questions about parameter tuning, robustness and uncertainty assessment. This book frames cluster analysis and classification in terms of statistical models, thus yielding principled estimation, testing and prediction methods, and sound answers to the central questions. It builds the basic ideas in an accessible but rigorous way, with extensive data examples and R code; describes modern approaches to high-dimensional data and networks; and explains such recent advances as Bayesian regularization, non-Gaussian model-based clustering, cluster merging, variable selection, semi-supervised and robust classification, clustering of functional data, text and images, and co-clustering. Written for advanced undergraduates in data science, as well as researchers and practitioners, it assumes basic knowledge of multivariate calculus, linear algebra, probability and statistics.

Explanatory Item Response Models

Author : Paul de Boeck
Publisher : Springer Science & Business Media
ISBN 13 : 1475739907
Total Pages : 394 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Explanatory Item Response Models by : Paul de Boeck

Download or read book Explanatory Item Response Models written by Paul de Boeck and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume gives a new and integrated introduction to item response models (predominantly used in measurement applications in psychology, education, and other social science areas) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. It also includes a chapter on the statistical background and one on useful software.

Longitudinal Structural Equation Modeling

Author : Todd D. Little
Publisher : Guilford Press
ISBN 13 : 1462510272
Total Pages : 411 pages
Book Rating : 4.4/5 (625 download)

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Book Synopsis Longitudinal Structural Equation Modeling by : Todd D. Little

Download or read book Longitudinal Structural Equation Modeling written by Todd D. Little and published by Guilford Press. This book was released on 2013-02-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been replaced by Longitudinal Structural Equation Modeling, Second Edition, ISBN 978-1-4625-5314-3.

Advances in Multilevel Modeling for Educational Research

Author : Jeffrey R. Harring
Publisher : IAP
ISBN 13 : 1681233290
Total Pages : 413 pages
Book Rating : 4.6/5 (812 download)

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Book Synopsis Advances in Multilevel Modeling for Educational Research by : Jeffrey R. Harring

Download or read book Advances in Multilevel Modeling for Educational Research written by Jeffrey R. Harring and published by IAP. This book was released on 2015-12-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significance that practitioners are placing on the use of multilevel models is undeniable as researchers want to both accurately partition variance stemming from complex sampling designs and understand relations within and between variables describing the hierarchical levels of these nested data structures. Simply scan the applied literature and one can see evidence of this trend by noticing the number of articles adopting multilevel models as their primary modeling framework. Helping to drive the popularity of their use, governmental funding agencies continue to advocate the use of multilevel models as part of a comprehensive analytic strategy for conducting rigorous and relevant research to improve our nation’s education system. Advances in Multilevel Modeling for Educational Research: Addressing Practical Issues Found in Real?World Applications is a resource intended for advanced graduate students, faculty and/or researchers interested in multilevel data analysis, especially in education, social and behavioral sciences. The chapters are written by prominent methodological researchers across diverse research domains such as educational statistics, quantitative psychology, and psychometrics. Each chapter exposes the reader to some of the latest methodological innovations, refinements and state?of?the?art developments and perspectives in the analysis of multilevel data including current best practices of standard techniques. We believe this volume will be particularly appealing to researchers in domains including but not limited to: educational policy and administration, educational psychology including school psychology and special education, and clinical psychology. In fact, we believe this volume will be a desirable resource for any research area that uses hierarchically nested data. The book will likely be attractive to applied and methodological researchers in several professional organizations such as the American Educational Research Association (AERA), the American Psychological Association (APA), the American Psychological Society (APS), the Society for Research on Educational Effectiveness (SREE), and other related organizations.

Longitudinal Structural Equation Modeling

Author : Jason T. Newsom
Publisher : Routledge
ISBN 13 : 1317975340
Total Pages : 657 pages
Book Rating : 4.3/5 (179 download)

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Book Synopsis Longitudinal Structural Equation Modeling by : Jason T. Newsom

Download or read book Longitudinal Structural Equation Modeling written by Jason T. Newsom and published by Routledge. This book was released on 2015-06-19 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive resource reviews structural equation modeling (SEM) strategies for longitudinal data to help readers see which modeling options are available for which hypotheses. The author demonstrates how SEM is related to other longitudinal data techniques throughout. By exploring connections between models, readers gain a better understanding of when to choose one analysis over another. The book explores basic models to sophisticated ones including the statistical and conceptual underpinnings that are the building blocks of the analyses. Accessibly written, research examples from the behavioral and social sciences and results interpretations are provided throughout. The emphasis is on concepts and practical guidance for applied research rather than on mathematical proofs. New terms are highlighted and defined in the glossary. Figures are included for every model along with detailed discussions of model specification and implementation issues. Each chapter also includes examples of each model type, comment sections that provide practical guidance, model extensions, and recommended readings. Highlights include: Covers the major SEM approaches to longitudinal analysis in one resource. Explores connections between longitudinal SEM models to enhance integration. Numerous examples that help readers match research questions to appropriate analyses and interpret results. Reviews practical issues related to model specification and estimation to reinforce connections. Analyzes continuous and discrete (binary and ordinal) variables throughout for breadth not found in other sources. Reviews key SEM concepts for those who need a refresher (Ch. 1). Emphasizes how to apply and interpret each model through realistic data examples. Provides the book’s data sets at www.longitudinalsem.com along with the Mplus and R-lavaan syntax used to generate the results. Introduces the LISREL notation system used throughout (Appendix A). The chapters can be read out of order but it is best to read chapters 1 – 4 first because most of the later chapters refer back to them. The book opens with a review of latent variables and analysis of binary and ordinal variables. Chapter 2 applies this information to assessing longitudinal measurement invariance. SEM tests of dependent means and proportions over time points are explored in Chapter 3, and stability and change, difference scores, and lagged regression are covered in Chapter 4. The remaining chapters are each devoted to one major type of longitudinal SEM -- repeated measures analysis models, full cross-lagged panel models and simplex models, modeling stability with state-trait models, linear and nonlinear growth curve models, latent difference score models, latent transition analysis, time series analysis, survival analysis, and attrition. Missing data is discussed in the context of many of the preceding models in Chapter 13. Ideal for graduate courses on longitudinal (data) analysis, advanced SEM, longitudinal SEM, and/or advanced data (quantitative) analysis taught in the behavioral, social, and health sciences, this text also appeals to researchers in these fields. Intended for those without an extensive math background, prerequisites include familiarity with basic SEM. Matrix algebra is avoided in all but a few places.

Finite Mixture Models

Author : Geoffrey McLachlan
Publisher : John Wiley & Sons
ISBN 13 : 047165406X
Total Pages : 419 pages
Book Rating : 4.4/5 (716 download)

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Book Synopsis Finite Mixture Models by : Geoffrey McLachlan

Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.

Latent Variable Models and Factor Analysis

Author : David J. Bartholomew
Publisher : Wiley
ISBN 13 : 9780340692431
Total Pages : 214 pages
Book Rating : 4.6/5 (924 download)

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Book Synopsis Latent Variable Models and Factor Analysis by : David J. Bartholomew

Download or read book Latent Variable Models and Factor Analysis written by David J. Bartholomew and published by Wiley. This book was released on 1999-08-10 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.