Advances In Latent Variable Mixture Models

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.

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.

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 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.

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.

The Oxford Handbook of Quantitative Methods in Psychology provides an accessible and comprehensive review of the current state-of-the-science and a one-stop source for learning and reviewing current best-practices in a quantitative methods across the social, behavioral, and educational sciences.

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

The revision of this edited volume introduces the latest issues and developments in SEM techniques. The book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. Includes cases & examples.