This book provides a comprehensive introduction to latent variable growth curve modeling (LGM) for analyzing repeated measures. It presents the statistical basis for LGM and its various methodological extensions, including a number of practical examples of its use. It is designed to take advantage of the reader’s familiarity with analysis of variance and structural equation modeling (SEM) in introducing LGM techniques. Sample data, syntax, input and output, are provided for EQS, Amos, LISREL, and Mplus on the book’s CD. Throughout the book, the authors present a variety of LGM techniques that are useful for many different research designs, and numerous figures provide helpful diagrams of the examples. Updated throughout, the second edition features three new chapters—growth modeling with ordered categorical variables, growth mixture modeling, and pooled interrupted time series LGM approaches. Following a new organization, the book now covers the development of the LGM, followed by chapters on multiple-group issues (analyzing growth in multiple populations, accelerated designs, and multi-level longitudinal approaches), and then special topics such as missing data models, LGM power and Monte Carlo estimation, and latent growth interaction models. The model specifications previously included in the appendices are now available on the CD so the reader can more easily adapt the models to their own research. This practical guide is ideal for a wide range of social and behavioral researchers interested in the measurement of change over time, including social, developmental, organizational, educational, consumer, personality and clinical psychologists, sociologists, and quantitative methodologists, as well as for a text on latent variable growth curve modeling or as a supplement for a course on multivariate statistics. A prerequisite of graduate level statistics is recommended.
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.
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.
After Karl Jöreskog's first presentation in 1970, Structural Equation Modelling or SEM has become a main statistical tool in many fields of science. It is the standard approach of factor analytic and causal modelling in such diverse fields as sociology, education, psychology, economics, management and medical sciences. In addition to an extension of its application area, Structural Equation Modelling also features a continual renewal and extension of its theoretical background. The sixteen contributions to this book, written by experts from many countries, present important new developments and interesting applications in Structural Equation Modelling. The book addresses methodologists and statisticians professionally dealing with Structural Equation Modelling to enhance their knowledge of the type of models covered and the technical problems involved in their formulation. In addition, the book offers applied researchers new ideas about the use of Structural Equation Modeling in solving their problems. Finally, methodologists, mathematicians and applied researchers alike are addressed, who simply want to update their knowledge of recent approaches in data analysis and mathematical modelling.
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 dissertation proposes longitudinal growth curve cognitive diagnosis models (GC-CDM) to incorporate learning over time into the cognitive assessment framework. The approach was motivated by higher-order latent trait models (de la Torre & Douglas, 2004), which define a higher-order continuous latent trait that affects all the latent skills. The higher-order latent trait can be viewed as the more broadly defined general ability; and the skills can be viewed as the specific knowledge arising from the higher-order latent trait. GC-CDMs trace changes in the higher-order latent traits over time by using latent growth curve model with respondent-specific random intercept and random slope of time, and simultaneously trace students' skill mastery through the CDM measurement model. GC-CDMs are estimated using marginal maximum likelihood (MML) estimation in Mplus. Relevant issues for estimating GC-CDMs are addressed, e.g., the high-dimensional computation problem, model specification for the relationship between the higher-order latent trait and the multiple skills, and model identification. In simulation studies, we use the DINA measurement model, and examine parameter recovery of the GC-DINA model under differing conditions. Particularly, the effects of the design of the Q-matrix, the number of respondents and the number of time points are discussed. Overall, MML estimation in Mplus shows good parameter recovery; especially, the average growth, which is the parameter of most interest, is well estimated in all conditions. We also illustrate the application of the GC-DINA model to real data using two datasets from multi-wave experiments designed to assess the effects of the Enhanced Anchored Instruction (EAI; Bottge et al., 2003) on mathematics achievement. In addition, the GC-DINA model is compared to the latent transition analysis DINA model (LTA-DINA) (Li et al., 2016; Kaya & Leite, 2016) and a longitudinal item response theory (IRT) model (Andersen, 1985) using a simulated data. The results suggest that the GC-DINA model and the LTA-DINA model are similar in terms of the predicted skill mastery; and the GC-DINA model and the longitudinal IRT model are similar in terms of the predicted higher-order latent trait.
An effective technique for data analysis in the social sciences The recent explosion in longitudinal data in the social scienceshighlights the need for this timely publication. Latent CurveModels: A Structural Equation Perspective provides an effectivetechnique to analyze latent curve models (LCMs). This type of datafeatures random intercepts and slopes that permit each case in asample to have a different trajectory over time. Furthermore,researchers can include variables to predict the parametersgoverning these trajectories. The authors synthesize a vast amount of research and findingsand, at the same time, provide original results. The book analyzesLCMs from the perspective of structural equation models (SEMs) withlatent variables. While the authors discuss simple regression-basedprocedures that are useful in the early stages of LCMs, most of thepresentation uses SEMs as a driving tool. This cutting-edge workincludes some of the authors' recent work on the autoregressivelatent trajectory model, suggests new models for method factors inmultiple indicators, discusses repeated latent variable models, andestablishes the identification of a variety of LCMs. This text has been thoroughly class-tested and makes extensiveuse of pedagogical tools to aid readers in mastering and applyingLCMs quickly and easily to their own data sets. Key featuresinclude: Chapter introductions and summaries that provide a quickoverview of highlights Empirical examples provided throughout that allow readers totest their newly found knowledge and discover practicalapplications Conclusions at the end of each chapter that stress theessential points that readers need to understand for advancement tomore sophisticated topics Extensive footnoting that points the way to the primaryliterature for more information on particular topics With its emphasis on modeling and the use of numerous examples,this is an excellent book for graduate courses in latent trajectorymodels as well as a supplemental text for courses in structuralmodeling. This book is an excellent aid and reference forresearchers in quantitative social and behavioral sciences who needto analyze longitudinal data.
This bestselling text provides a practical guide to the basic concepts of structural equation modeling (SEM) and the AMOS program (Versions 17 & 18). The author reviews SEM applications based on actual data taken from her research. Noted for its non-mathematical language, this book is written for the novice SEM user. With each chapter, the author "walks" the reader through all steps involved in testing the SEM model including: an explanation of the issues addressed an illustration of the hypothesized and posthoc models tested AMOS input and output with accompanying interpretation and explanation The function of the AMOS toolbar icons and their related pull-down menus The data and published reference upon which the model was based. With over 50% new material, highlights of the new edition include: All new screen shots featuring Version 17 of the AMOS program All data files now available at www.psypress.com/sem-with-amos Application of a multitrait-mulitimethod model, latent growth curve model, and second-order model based on categorical data All applications based on the most commonly used graphical interface The automated multi-group approach to testing for equivalence The book opens with an introduction to the fundamental concepts of SEM and the basics of the AMOS program. The next 3 sections present applications that focus on single-group, multiple-group, and multitrait-mutimethod and latent growth curve models. The book concludes with a discussion about non-normal and missing (incomplete) data and two applications capable of addressing these issues. Intended for researchers, practitioners, and students who use SEM and AMOS in their work, this book is an ideal resource for graduate level courses on SEM taught in departments of psychology, education, business, and other social and health sciences and/or as a supplement in courses on applied statistics, multivariate statistics, statistics II, intermediate or advanced statistics, and/or research design. Appropriate for those with limited or no previous exposure to SEM, a prerequisite of basic statistics through regression analysis is recommended.