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Estimation Methods In Multilevel Structural Equation Modeling
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Book Synopsis Estimation Methods in Multilevel Structural Equation Modeling by : Jimmy Byrd
Download or read book Estimation Methods in Multilevel Structural Equation Modeling written by Jimmy Byrd and published by LAP Lambert Academic Publishing. This book was released on 2010-04 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text examines multilevel regression models in the context of multilevel structural equation modeling (SEM) in terms of accuracy of parameter estimates, standard errors, and fit indices in normal and nonnormal data under various sample sizes and differing estimators (maximum likelihood, generalized least squares, and weighted least squares). The finding revealed that the regression coefficients were estimated with little to no bias among the study design conditions investigated. However, the number of clusters (group level) appeared to have the greatest impact on bias among the parameter estimate standard errors at both level- 1 and level-2. Regarding fit statistics, negative bias was noted among each of the fit indices investigated when the number of clusters ranged from 30 to 50 and cluster size was fixed at 10. Recommendations for the substantive researcher are presented and areas of future research are discussed.
Book Synopsis A Monte Carlo Investigation of Three Different Estimation Methods in Multilevel Structural Equation Modeling Under Conditions of Data Nonnormality and Varied Sample Sizes by : Jimmy Byrd
Download or read book A Monte Carlo Investigation of Three Different Estimation Methods in Multilevel Structural Equation Modeling Under Conditions of Data Nonnormality and Varied Sample Sizes written by Jimmy Byrd and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the study was to examine multilevel regression models in the context of multilevel structural equation modeling (SEM) in terms of accuracy of parameter estimates, standard errors, and fit indices in normal and nonnormal data under various sample sizes and differing estimators (maximum likelihood, generalized least squares, and weighted least squares). The finding revealed that the regression coefficients were estimated with little to no bias among the study design conditions investigated. However, the number of clusters (group level) appeared to have the greatest impact on bias among the parameter estimate standard errors at both level-1 and level-2. In small sample sizes (i.e., 300 and 500) the standard errors were negatively biased. When the number of clusters was 30 and cluster size was held at 10, the level-1 standard errors were biased downward by approximately 20% for the maximum likelihood and generalized least squares estimators, while the weighted least squares estimator produced level-1 standard errors that were negatively biased by 25%. Regarding the level-2 standard errors, the level-2 standard errors were biased downward by approximately 24% in nonnormal data, especially when the correlation among variables was fixed at .5 and kurtosis was held constant at 7. In this same setting (30 clusters with cluster size fixed at 10), when kurtosis was fixed at 4 and the correlation among variables was held at .7, both the maximum likelihood and generalized least squares estimators resulted in standard errors that were biased downward by approximately 11%. Regarding fit statistics, negative bias was noted among each of the fit indices investigated when the number of clusters ranged from 30 to 50 and cluster size was fixed at 10. The least amount of bias was associated with the maximum likelihood estimator in each of the data normality conditions examined. As sample size increased, bias decreased to near zero when the sample size was equal to or greater than 1,500 with similar results reported across estimation methods. Recommendations for the substantive researcher are presented and areas of future research are presented.
Book Synopsis Structural Equation Modeling by : David Kaplan
Download or read book Structural Equation Modeling written by David Kaplan and published by SAGE Publications. This book was released on 2008-07-23 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using detailed, empirical examples, Structural Equation Modeling, Second Edition, presents a thorough and sophisticated treatment of the foundations of structural equation modeling (SEM). It also demonstrates how SEM can provide a unique lens on the problems social and behavioral scientists face. Intended Audience While the book assumes some knowledge and background in statistics, it guides readers through the foundations and critical assumptions of SEM in an easy-to-understand manner.
Book Synopsis A Monte Carlo investigation of three different estimation methods in multilevel structural equation modeling under conditions of data nonnormality and varied sample sizes by : Jimmy Kent Byrd
Download or read book A Monte Carlo investigation of three different estimation methods in multilevel structural equation modeling under conditions of data nonnormality and varied sample sizes written by Jimmy Kent Byrd and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Estimating Multilevel Structural Equation Models with Random Slopes for Latent Covariates by : Nicholas J. Rockwood
Download or read book Estimating Multilevel Structural Equation Models with Random Slopes for Latent Covariates written by Nicholas J. Rockwood and published by . This book was released on 2019 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multilevel structural equation modeling (MSEM) is an emerging statistical framework for the analysis of hierarchically structured data, such as data corresponding to students nested within classrooms or repeated measurements nested within individuals. The MSEM framework provides several advantages over the traditional multilevel modeling (MLM) and structural equation modeling (SEM) frameworks, including the ability to model multivariate responses, level-2 response variables, measurement error via factor models, and structural relations (e.g., regressions) among the random effects/latent variables. Although several formulations of the MSEM have been presented (see, e.g., Liang & Bentler, 2004; Rabe-Hesketh, Skrondal, & Pickles, 2004; Mehta & Neale, 2005), the framework of B. Muthen and Asparouhov (2008) as implemented in Mplus (L. K. Muthen & Muthen, 2017) has the advantage that the relationship between lower-level (i.e., level-1) latent variables can be modeled as randomly varying across upper-level (i.e., level-2) units. Unfortunately, maximum likelihood (ML) estimation of the parameters for such models, as implemented in Mplus, is computationally demanding due to the likelihood function having to be approximated, as the function cannot be computed in closed-form. Mplus numerically integrates over all of the random effects/latent variables using quadrature-based methods. This approach is not feasible for high-dimensional latent variable models, which reduces the potential models that can practically be fit. In this dissertation, I develop a more computationally efficient and accurate ML estimation routine for MSEMs with random slopes for latent variables. The method relies on a reformulation of the likelihood function so that some of the integrals can be computed analytically, reducing the dimension of numerical integration required. Specifically, only the random slopes for latent variables need to be numerically integrated, as the integrals corresponding to the other random effects can be computed in closed-form. For most models implemented in practice, this method results in a function that typically requires less than four dimensions of numerical integration. Thus, the estimation routine I develop here allows for many models within the MSEM framework to be estimated that would otherwise be impractical to fit using currently implemented methods. In addition to developing this new ML estimation algorithm, three example MSEMs are fit to real-world datasets to demonstrate the generality of the MSEM framework. Further, I assess the performance of this estimation routine using three small-scale simulation studies based on the examples. Overall, the estimation routine appears to recover the true parameters well, highlighting the utility of this new method. I also discuss limitations of the proposed method, possible ways of extending the methodology to account for other types of data (e.g., categorical and count outcomes), and the importance of future research to assess the performance of the ML estimates for such models relative to other modeling frameworks.
Book Synopsis Meta-Analysis by : Mike W.-L. Cheung
Download or read book Meta-Analysis written by Mike W.-L. Cheung and published by John Wiley & Sons. This book was released on 2015-04-07 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the importance of SEM and meta-analysis in answering research questions. Key ideas in meta-analysis and SEM are briefly reviewed, and various meta-analytic models are then introduced and linked to the SEM framework. Fixed-, random-, and mixed-effects models in univariate and multivariate meta-analyses, three-level meta-analysis, and meta-analytic structural equation modeling, are introduced. Advanced topics, such as using restricted maximum likelihood estimation method and handling missing covariates, are also covered. Readers will learn a single framework to apply both meta-analysis and SEM. Examples in R and in Mplus are included. This book will be a valuable resource for statistical and academic researchers and graduate students carrying out meta-analyses, and will also be useful to researchers and statisticians using SEM in biostatistics. Basic knowledge of either SEM or meta-analysis will be helpful in understanding the materials in this book.
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.
Book Synopsis Handbook of Advanced Multilevel Analysis by : Joop Hox
Download or read book Handbook of Advanced Multilevel Analysis written by Joop Hox and published by Psychology Press. This book was released on 2011-01-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new handbook is the definitive resource on advanced topics related to multilevel analysis. The editors assembled the top minds in the field to address the latest applications of multilevel modeling as well as the specific difficulties and methodological problems that are becoming more common as more complicated models are developed. Each chapter features examples that use actual datasets. These datasets, as well as the code to run the models, are available on the book’s website http://www.hlm-online.com . Each chapter includes an introduction that sets the stage for the material to come and a conclusion. Divided into five sections, the first provides a broad introduction to the field that serves as a framework for understanding the latter chapters. Part 2 focuses on multilevel latent variable modeling including item response theory and mixture modeling. Section 3 addresses models used for longitudinal data including growth curve and structural equation modeling. Special estimation problems are examined in section 4 including the difficulties involved in estimating survival analysis, Bayesian estimation, bootstrapping, multiple imputation, and complicated models, including generalized linear models, optimal design in multilevel models, and more. The book’s concluding section focuses on statistical design issues encountered when doing multilevel modeling including nested designs, analyzing cross-classified models, and dyadic data analysis. Intended for methodologists, statisticians, and researchers in a variety of fields including psychology, education, and the social and health sciences, this handbook also serves as an excellent text for graduate and PhD level courses in multilevel modeling. A basic knowledge of multilevel modeling is assumed.
Book Synopsis Multilevel Analysis by : Joop J. Hox
Download or read book Multilevel Analysis written by Joop J. Hox and published by Routledge. This book was released on 2010-09-13 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical introduction helps readers apply multilevel techniques to their research. Noted as an accessible introduction, the book also includes advanced extensions, making it useful as both an introduction and as a reference to students, researchers, and methodologists. Basic models and examples are discussed in non-technical terms with an emphasis on understanding the methodological and statistical issues involved in using these models. The estimation and interpretation of multilevel models is demonstrated using realistic examples from various disciplines. For example, readers will find data sets on stress in hospitals, GPA scores, survey responses, street safety, epilepsy, divorce, and sociometric scores, to name a few. The data sets are available on the website in SPSS, HLM, MLwiN, LISREL and/or Mplus files. Readers are introduced to both the multilevel regression model and multilevel structural models. Highlights of the second edition include: Two new chapters—one on multilevel models for ordinal and count data (Ch. 7) and another on multilevel survival analysis (Ch. 8). Thoroughly updated chapters on multilevel structural equation modeling that reflect the enormous technical progress of the last few years. The addition of some simpler examples to help the novice, whilst the more complex examples that combine more than one problem have been retained. A new section on multivariate meta-analysis (Ch. 11). Expanded discussions of covariance structures across time and analyzing longitudinal data where no trend is expected. Expanded chapter on the logistic model for dichotomous data and proportions with new estimation methods. An updated website at http://www.joophox.net/ with data sets for all the text examples and up-to-date screen shots and PowerPoint slides for instructors. Ideal for introductory courses on multilevel modeling and/or ones that introduce this topic in some detail taught in a variety of disciplines including: psychology, education, sociology, the health sciences, and business. The advanced extensions also make this a favorite resource for researchers and methodologists in these disciplines. A basic understanding of ANOVA and multiple regression is assumed. The section on multilevel structural equation models assumes a basic understanding of SEM.
Book Synopsis An Introduction to Multilevel Modeling Techniques by : Ronald H. Heck
Download or read book An Introduction to Multilevel Modeling Techniques written by Ronald H. Heck and published by Psychology Press. This book was released on 1999-11-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of basic multilevel modeling issues and illustrates techniques building analyses around several organizational data sets. Although the focus is primarily on educational and organizational settings, the examples will help the reader discover other applications for these techniques. Two basic classes of multilevel models are developed: multilevel regression models and multilevel models for covariance structures--are used to develop the rationale behind these models and provide an introduction to the design and analysis of research studies using two multilevel analytic techniques--hierarchical linear modeling and structural equation modeling.
Book Synopsis Structural Equation Modeling by : Gregory R. Hancock
Download or read book Structural Equation Modeling written by Gregory R. Hancock and published by IAP. This book was released on 2013-03-01 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sponsored by the American Educational Research Association's Special Interest Group for Educational Statisticians This volume is the second edition of Hancock and Mueller’s highly-successful 2006 volume, with all of the original chapters updated as well as four new chapters. The second edition, like the first, is intended to serve as a didactically-oriented resource for graduate students and research professionals, covering a broad range of advanced topics often not discussed in introductory courses on structural equation modeling (SEM). Such topics are important in furthering the understanding of foundations and assumptions underlying SEM as well as in exploring SEM, as a potential tool to address new types of research questions that might not have arisen during a first course. Chapters focus on the clear explanation and application of topics, rather than on analytical derivations, and contain materials from popular SEM software.
Book Synopsis Advanced Structural Equation Modeling by : George A. Marcoulides
Download or read book Advanced Structural Equation Modeling written by George A. Marcoulides and published by Psychology Press. This book was released on 2013-10-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: By focusing primarily on the application of structural equation modeling (SEM) techniques in example cases and situations, this book provides an understanding and working knowledge of advanced SEM techniques with a minimum of mathematical derivations. The book was written for a broad audience crossing many disciplines, assumes an understanding of graduate level multivariate statistics, including an introduction to SEM.
Book Synopsis An Evaluation of Parameter Estimation when Using Multilevel Structural Equation Modeling for Mediation Analysis by : Xin Li
Download or read book An Evaluation of Parameter Estimation when Using Multilevel Structural Equation Modeling for Mediation Analysis written by Xin Li and published by . This book was released on 2011 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handling of clustered or nested data structures requires the use of multilevel modeling techniques. One such multilevel modeling technique is multilevel structural equation modeling (MLSEM). While estimation of indirect effect parameters and standard errors based on the conventional multilevel model (MMM) has been assessed, this is not the case for the use of the MLSEM model for estimating indirect effects. This simulation study was designed to investigate the use of the MLSEM for estimating mediated effects for the "upper-level" mediation model as compared with the MMM. The following conditions were manipulated: number of clusters (G), within-cluster sample size (nj), intra-class correlation, measurement error in the mediator, and the true value of the mediated effect derived from various patterns of true values for a and b. The generating model entailed an upper-level mediation model for a cluster-randomized trial that included a dichotomous level two independent variable, a cluster-level latent mediator and an individual-level latent dependent variable both with four indicators. Relative parameter and standard error bias, obtained using the MLSEM and the MMM were evaluated and compared. Percent coverage was calculated and compared when PRODCLIN was used to calculate the confidence interval estimates of the ab effect. Finally, Type I error rates for conditions when ab = 0 were assessed and compared. In addition, statistical power for detecting a truly non-zero mediated effect was tallied and compared across models. Results showed that use of the MMM provided inaccurate and misleading parameter and standard error estimates for the estimates of the mediated effect, especially when the true values of a, b and ab were not zero and the measurement error for M was large. However, the MLSEM estimates were also unacceptable in some of the conditions with small values for G and nj. Researchers are encouraged to use the MLSEM for assessing the multilevel mediated effects when either or both paths a and b are expected to be non-zero, if G is at least 40 and nj is also greater than 40. Results are presented and discussed along with implications for applied researchers intending to assess mediated effect with clustered data.
Book Synopsis Multilevel Structural Equation Modeling by : Bruno Castanho Silva
Download or read book Multilevel Structural Equation Modeling written by Bruno Castanho Silva and published by SAGE Publications. This book was released on 2019-02-28 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multilevel Structural Equation Modeling serves as a minimally technical overview of multilevel structural equation modeling (MSEM) for applied researchers and advanced graduate students in the social sciences. As the first book of its kind, this title is an accessible, hands-on introduction for beginners of the topic. The authors predict a growth in this area, fueled by both data availability and also the availability of new and improved software to run these models. The applied approach, combined with a graphical presentation style and minimal reliance on complex matrix algebra guarantee that this volume will be useful to social science graduate students wanting to utilize such models.
Book Synopsis Multilevel Analysis by : Joop J. Hox
Download or read book Multilevel Analysis written by Joop J. Hox and published by Routledge. This book was released on 2017-09-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applauded for its clarity, this accessible introduction helps readers apply multilevel techniques to their research. The book also includes advanced extensions, making it useful as both an introduction for students and as a reference for researchers. Basic models and examples are discussed in nontechnical terms with an emphasis on understanding the methodological and statistical issues involved in using these models. The estimation and interpretation of multilevel models is demonstrated using realistic examples from various disciplines including psychology, education, public health, and sociology. Readers are introduced to a general framework on multilevel modeling which covers both observed and latent variables in the same model, while most other books focus on observed variables. In addition, Bayesian estimation is introduced and applied using accessible software.
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 528 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
