Hierarchical Linear Models

Applications and Data Analysis Methods

Author: Stephen W. Raudenbush,Anthony S. Bryk

Publisher: SAGE

ISBN: 9780761919049

Category: Mathematics

Page: 485

View: 4856

Popular in its first edition for its rich, illustrative examples and lucid explanations of the theory and use of hierarchical linear models (HLM), the book has been updated to include: an intuitive introductory summary of the basic procedures for estimation and inference used with HLM models that only requires a minimal level of mathematical sophistication; a new section on multivariate growth models; a discussion of research synthesis or meta-analysis applications; aata analytic advice on centering of level-1 predictors, and new material on plausible value intervals and robust standard estimators.

Multilevel Models

Applications using SAS®

Author: Jichuan Wang,Haiyi Xie,James F. Fisher

Publisher: Walter de Gruyter

ISBN: 3110267705

Category: Mathematics

Page: 274

View: 2718

This book covers a broad range of topics about multilevel modeling. The goal is to help readers to understand the basic concepts, theoretical frameworks, and application methods of multilevel modeling. It is at a level also accessible to non-mathematicians, focusing on the methods and applications of various multilevel models and using the widely used statistical software SAS®. Examples are drawn from analysis of real-world research data.

Multilevel Analysis for Applied Research

It's Just Regression!

Author: Robert Bickel

Publisher: Guilford Press

ISBN: 1609181069

Category: Psychology

Page: 355

View: 7456

This book provides a uniquely accessible introduction to multilevel modeling, a powerful tool for analyzing relationships between an individual-level dependent variable, such as student reading achievement, and individual-level and contextual explanatory factors, such as gender and neighborhood quality. Helping readers build on the statistical techniques they already know, Robert Bickel emphasizes the parallels with more familiar regression models, shows how to do multilevel modeling using SPSS, and demonstrates how to interpret the results. He discusses the strengths and limitations of multilevel analysis and explains specific circumstances in which it offers (or does not offer) methodological advantages over more traditional techniques. Over 300 dataset examples from research on educational achievement, income attainment, voting behavior, and other timely issues are presented in numbered procedural steps.

Multilevel Analysis

An Introduction to Basic and Advanced Multilevel Modeling

Author: Tom A B Snijders,Roel J Bosker

Publisher: SAGE

ISBN: 144625433X

Category: Reference

Page: 368

View: 6508

The Second Edition of this classic text introduces the main methods, techniques and issues involved in carrying out multilevel modeling and analysis. Snijders and Bosker's book is an applied, authoritative and accessible introduction to the topic, providing readers with a clear conceptual and practical understanding of all the main issues involved in designing multilevel studies and conducting multilevel analysis. This book provides step-by-step coverage of: • multilevel theories • ecological fallacies • the hierarchical linear model • testing and model specification • heteroscedasticity • study designs • longitudinal data • multivariate multilevel models • discrete dependent variables There are also new chapters on: • missing data • multilevel modeling and survey weights • Bayesian and MCMC estimation and latent-class models. This book has been comprehensively revised and updated since the last edition, and now discusses modeling using HLM, MLwiN, SAS, Stata including GLLAMM, R, SPSS, Mplus, WinBugs, Latent Gold, and SuperMix. This is a must-have text for any student, teacher or researcher with an interest in conducting or understanding multilevel analysis. Tom A.B. Snijders is Professor of Statistics in the Social Sciences at the University of Oxford and Professor of Statistics and Methodology at the University of Groningen. Roel J. Bosker is Professor of Education and Director of GION, Groningen Institute for Educational Research, at the University of Groningen.

Applied Bayesian Hierarchical Methods

Author: Peter D. Congdon

Publisher: CRC Press

ISBN: 9781584887218

Category: Mathematics

Page: 604

View: 9436

The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach to data sets involving inferences for collections of related units or variables and in methods where parameters can be treated as random collections. Emphasizing computational issues, the book provides examples of the following application settings: meta-analysis, data structured in space or time, multilevel and longitudinal data, multivariate data, nonlinear regression, and survival time data. For the worked examples, the text mainly employs the WinBUGS package, allowing readers to explore alternative likelihood assumptions, regression structures, and assumptions on prior densities. It also incorporates BayesX code, which is particularly useful in nonlinear regression. To demonstrate MCMC sampling from first principles, the author includes worked examples using the R package. Through illustrative data analysis and attention to statistical computing, this book focuses on the practical implementation of Bayesian hierarchical methods. It also discusses several issues that arise when applying Bayesian techniques in hierarchical and random effects models.

Applied Regression Analysis and Generalized Linear Models

Author: John Fox

Publisher: SAGE Publications

ISBN: 1483321312

Category: Social Science

Page: 816

View: 3951

Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book.

Hierarchical Linear Modeling

Guide and Applications

Author: G. David Garson

Publisher: SAGE

ISBN: 1412998859

Category: Computers

Page: 371

View: 9974

This book provides a brief, easy-to-read guide to implementing hierarchical linear modelling using the three leading software platforms, followed by a set of application articles based on recent work published in leading journals and as part of doctoral dissertations. The "guide" portion consists of three chapters by the editor, covering basic to intermediate use of SPSS, SAS, and HLM for purposes for hierarchical linear modelling, while the "applications" portion consists of a dozen contributions in which the authors emphasize how-to and methodological aspects and show how they have used these techniques in practice.

Teaching Statistics

A Bag of Tricks

Author: Andrew Gelman,Deborah Nolan

Publisher: Oxford University Press

ISBN: 0191088641

Category: Mathematics

Page: 384

View: 2004

Students in the sciences, economics, social sciences, and medicine take an introductory statistics course. And yet statistics can be notoriously difficult for instructors to teach and for students to learn. To help overcome these challenges, Gelman and Nolan have put together this fascinating and thought-provoking book. Based on years of teaching experience the book provides a wealth of demonstrations, activities, examples, and projects that involve active student participation. Part I of the book presents a large selection of activities for introductory statistics courses and has chapters such as 'First week of class'— with exercises to break the ice and get students talking; then descriptive statistics, graphics, linear regression, data collection (sampling and experimentation), probability, inference, and statistical communication. Part II gives tips on what works and what doesn't, how to set up effective demonstrations, how to encourage students to participate in class and to work effectively in group projects. Course plans for introductory statistics, statistics for social scientists, and communication and graphics are provided. Part III presents material for more advanced courses on topics such as decision theory, Bayesian statistics, sampling, and data science.

Linear Models with R, Second Edition

Author: Julian J. Faraway

Publisher: CRC Press

ISBN: 1439887349

Category: Mathematics

Page: 286

View: 2093

A Hands-On Way to Learning Data Analysis Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates Extensive use of the ggplot2 graphics package in addition to base graphics Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Multilevel Modeling

Author: Douglas A. Luke

Publisher: SAGE

ISBN: 9780761928799

Category: Mathematics

Page: 79

View: 9487

A practical introduction to multi-level modelling, this book offers an introduction to HLM & illustrations of how to use this technique to build models for hierarchical & longitudinal data.

Hierarchical Modeling and Inference in Ecology

The Analysis of Data from Populations, Metapopulations and Communities

Author: J. Andrew Royle,Robert M. Dorazio

Publisher: Elsevier

ISBN: 0080559255

Category: Science

Page: 464

View: 2939

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics * Wide variety of examples involving many taxa (birds, amphibians, mammals, insects, plants) * Development of classical, likelihood-based procedures for inference, as well as Bayesian methods of analysis * Detailed explanations describing the implementation of hierarchical models using freely available software such as R and WinBUGS * Computing support in technical appendices in an online companion web site

Bayesian Data Analysis, Third Edition

Author: Andrew Gelman,John B. Carlin,Hal S. Stern,David B. Dunson,Aki Vehtari,Donald B. Rubin

Publisher: CRC Press

ISBN: 1439840954

Category: Mathematics

Page: 675

View: 1623

Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Multilevel Modeling in Plain Language

Author: Karen Robson,David Pevalin

Publisher: SAGE

ISBN: 1473934311

Category: Social Science

Page: 160

View: 4482

Have you been told you need to do multilevel modeling, but you can't get past the forest of equations? Do you need the techniques explained with words and practical examples so they make sense? Help is here! This book unpacks these statistical techniques in easy-to-understand language with fully annotated examples using the statistical software Stata. The techniques are explained without reliance on equations and algebra so that new users will understand when to use these approaches and how they are really just special applications of ordinary regression. Using real life data, the authors show you how to model random intercept models and random coefficient models for cross-sectional data in a way that makes sense and can be retained and repeated. This book is the perfect answer for anyone who needs a clear, accessible introduction to multilevel modeling.

Multilevel Modeling Using R

Author: W. Holmes Finch,Jocelyn E. Bolin,Ken Kelley

Publisher: CRC Press

ISBN: 1466515864

Category: Mathematics

Page: 230

View: 8155

A powerful tool for analyzing nested designs in a variety of fields, multilevel/hierarchical modeling allows researchers to account for data collected at multiple levels. Multilevel Modeling Using R provides you with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data. The book concludes with Bayesian fitting of multilevel models. For those new to R, the appendix provides an introduction to this system that covers basic R knowledge necessary to run the models in the book. Through the R code and detailed explanations provided, this book gives you the tools to launch your own investigations in multilevel modeling and gain insight into your research.

Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives

Author: Donald B. Rubin,Andrew Gelman,Xiao-Li Meng

Publisher: John Wiley & Sons

ISBN: 9780470090435

Category: Mathematics

Page: 407

View: 5689

This book brings together a collection of articles onstatistical methods relating to missing data analysis, includingmultiple imputation, propensity scores, instrumental variables, andBayesian inference. Covering new research topicsand real-world examples which do not feature in manystandard texts. The book is dedicated to Professor Don Rubin(Harvard). Don Rubin has made fundamental contributions tothe study of missing data. Key features of the book include: Comprehensive coverage of an imporant area for both researchand applications. Adopts a pragmatic approach to describing a wide range ofintermediate and advanced statistical techniques. Covers key topics such as multiple imputation, propensityscores, instrumental variables and Bayesian inference. Includes a number of applications from the social and healthsciences. Edited and authored by highly respected researchers in thearea.

Multilevel and Longitudinal Modeling Using Stata, Second Edition

Author: Sophia Rabe-Hesketh,Anders Skrondal

Publisher: Stata Press

ISBN: 1597180408

Category: Business & Economics

Page: 562

View: 6619

This is a book about applied multilevel and longitudinal modeling. Other terms for multilevel models include hierarchical models, random-effects or random-coefficient models, mixed-effects models, or simply mixed models. Longitudinal data are also referred to as panel data, repeated measures, or cross-sectional time series. A popular type of multilevel model for longitudinal data is the growth-curve model. Our emphasis is on explaining the models and their assumptions, applying the methods to real data, and interpreting results.

Multilevel Analysis

Techniques and Applications, Third Edition

Author: Joop J. Hox,Mirjam Moerbeek,Rens van de Schoot

Publisher: Routledge

ISBN: 1317308670

Category: Psychology

Page: 348

View: 2858

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.

Doing Bayesian Data Analysis

A Tutorial with R, JAGS, and Stan

Author: John Kruschke

Publisher: Academic Press

ISBN: 0124059163

Category: Mathematics

Page: 776

View: 7132

Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan, Second Edition provides an accessible approach for conducting Bayesian data analysis, as material is explained clearly with concrete examples. Included are step-by-step instructions on how to carry out Bayesian data analyses in the popular and free software R and WinBugs, as well as new programs in JAGS and Stan. The new programs are designed to be much easier to use than the scripts in the first edition. In particular, there are now compact high-level scripts that make it easy to run the programs on your own data sets. The book is divided into three parts and begins with the basics: models, probability, Bayes’ rule, and the R programming language. The discussion then moves to the fundamentals applied to inferring a binomial probability, before concluding with chapters on the generalized linear model. Topics include metric-predicted variable on one or two groups; metric-predicted variable with one metric predictor; metric-predicted variable with multiple metric predictors; metric-predicted variable with one nominal predictor; and metric-predicted variable with multiple nominal predictors. The exercises found in the text have explicit purposes and guidelines for accomplishment. This book is intended for first-year graduate students or advanced undergraduates in statistics, data analysis, psychology, cognitive science, social sciences, clinical sciences, and consumer sciences in business. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and JAGS software Comprehensive coverage of all scenarios addressed by non-Bayesian textbooks: t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis) Coverage of experiment planning R and JAGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment Provides step-by-step instructions on how to conduct Bayesian data analyses in the popular and free software R and WinBugs

Doing Bayesian Data Analysis

A Tutorial Introduction with R

Author: John Kruschke

Publisher: Academic Press

ISBN: 9780123814869

Category: Mathematics

Page: 672

View: 6082

There is an explosion of interest in Bayesian statistics, primarily because recently created computational methods have finally made Bayesian analysis tractable and accessible to a wide audience. Doing Bayesian Data Analysis, A Tutorial Introduction with R and BUGS, is for first year graduate students or advanced undergraduates and provides an accessible approach, as all mathematics is explained intuitively and with concrete examples. It assumes only algebra and ‘rusty’ calculus. Unlike other textbooks, this book begins with the basics, including essential concepts of probability and random sampling. The book gradually climbs all the way to advanced hierarchical modeling methods for realistic data. The text provides complete examples with the R programming language and BUGS software (both freeware), and begins with basic programming examples, working up gradually to complete programs for complex analyses and presentation graphics. These templates can be easily adapted for a large variety of students and their own research needs.The textbook bridges the students from their undergraduate training into modern Bayesian methods. Accessible, including the basics of essential concepts of probability and random sampling Examples with R programming language and BUGS software Comprehensive coverage of all scenarios addressed by non-bayesian textbooks- t-tests, analysis of variance (ANOVA) and comparisons in ANOVA, multiple regression, and chi-square (contingency table analysis). Coverage of experiment planning R and BUGS computer programming code on website Exercises have explicit purposes and guidelines for accomplishment