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.
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.
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.
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
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.
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.
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.
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.
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.
