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      SAGE Publications Asia-Pacific Pte. Ltd.

      3 Church Street

      #10–04 Samsung Hub

      Singapore 049483

      Printed in the United States of America

      This book is printed on acid-free paper.

      ISBN: 978-1-5443-1030-5

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      Acquisitions Editor: Helen Salmon

      Editorial Assistant: Megan O’Hefferman

      Production Editor: Karen Wiley

      Copy Editor: QuADs

      Typesetter: Integra

      Proofreader: Jen Grubba

      Indexer: Naomi Linzer

      Cover Designer: Candice Harman

      Marketing Manager: Shari Countrymen

      Praise for The Second Edition

       Because of the author’s pedagogically masterful presentation of multi-level modeling, the otherwise challenging journey to this topic now becomes not only smooth but also enjoyable.

      —Lin Ding, Ohio State University

       The book offers insights and explanations from which both newcomers and seasoned experts can find benefit.

      —Timothy Ford, Ohio University

       This is a thorough and accessible introduction to multilevel models. Through extensive examples, the author expertly guides the reader through the material addressing interpretation, graphical presentation, and diagnostics along the way.

      —Jennifer Hayes Clark, University of Houston

       The Second Edition is even better than the first. The models presented are closely linked to an extended example that students can readily identify with.

      —Richard R. Sudweeks, Brigham Young University

      About the Author

      Douglas A. Lukeis Professor and Director of the Center for Public Health Systems Science at the Brown School at Washington University in St. Louis. Dr. Luke is a leading researcher in the areas of public health policy, implementation science, and systems science. Most of the work that Dr. Luke directs at the Center focuses on the evaluation, dissemination, and implementation of evidence-based public health policies. During the past decade, Dr. Luke has worked on applying systems science methods to important public health problems, especially social network analysis. He has published two systems science review papers in the Annual Review of Public Health, and the first study to employ new statistical network modeling techniques on public health data was published in the American Journal of Public Health in 2010. He was also a member of a National Academy of Sciences panel that produced a recent report, “Assessing the Use of Agent-Based Models for Tobacco Regulation,” which provided the FDA and other public health scientists with guidance on how best to use computational models to inform tobacco control regulation and policy. Dr. Luke directs the doctoral progam in Public Health Sciences at the Brown School, where he also teaches doctoral courses in multilevel and longitudinal modeling, social network analysis, and philosophy of social science. Dr. Luke received his PhD in clinical and community psychology in 1990 from the University of Illinois at Urbana-Champaign.

      Series Editor’s Introduction

      How people see and act in the world reflect the contexts within which they function. Social scientists would not hesitate to agree with this statement. But they differ in the contexts that they emphasize. In sociology, these contexts might be neighborhoods or communities; in political science, voting precincts, legislative districts, or states; in economics, markets of various types; in education, classrooms, schools, and school districts. In each instance, level-one units, e.g., individuals, operate within and are constrained by level-two units, e.g., the contexts just enumerated. Multilevel models are designed for such situations, where independent variables measured at two (or more) levels are hypothesized to affect a level-one outcome.

      Multilevel Modeling, 2nd edition, by Douglas Luke, provides a step-by-step introduction to multilevel statistical models. As in the first edition, the volume targets users already familiar with linear regression but new to multilevel concepts and analysis. Professor Luke lays a firm foundation, giving the most attention to two-level hierarchical linear models where level-one units are neatly nested within level-two units. He explains how to conceptualize, build, and assess these models in Chapters 2, 1, and 4, respectively. Chapters 5 and 6 take up various extensions of the two-level hierarchical linear model, including nonlinear multilevel models, three-level and cross-classified models, and longitudinal models that allow for intra-individual change and inter-individual variability. Chapter 7 provides guidance on the presentation of results as well as a curated list of references for those wanting to learn more.

      Examples are critical to the pedagogy of the volume. One involves influences on tobacco-related legislation by members of Congress. Members of Congress are nested in states (two levels), with the outcome measured as the percentage of time that members voted in a “pro-tobacco” direction over a four-year period. Professor Luke uses this example to illustrate different model specifications, explain measures of fit and model performance, and discuss centering and its impact. A related binary model predicts the outcome of votes on particular bills, for or against. Professor Luke uses an extension of this example, to introduce the generalized linear mixed-effects model. This version of the model nests votes on particular bills within members, nested within states. A different example is used to illustrate the multilevel approach to latent trajectory modeling. This example draws on the Longitudinal

      Study of Aging to investigate change in the activities of daily living as an elderly population ages. There are other examples as well. Data and software code (in R and Stata) are provided in an online appendix so that readers can gain experience with the methods by reproducing the examples. Professor Luke provides lots of practical general advice about multilevel modeling as well as advice specific to these examples.

      Since the first edition of Multilevel Modeling was published 15 years ago, it has become straightforward to link sample survey data to measures of relevant contexts. Indeed, in some instances, ancillary data for this purpose has already been created and made available to users. For example, the Health and Retirement Survey (HRS) has assembled and makes available to qualified users measures of sociodemographic characteristics, the built environment, health care, the food environment, physical hazards, and social stressors at multiple levels of census geography with links to HRS respondents. The possibilities are limitless, with much still to be done. With Multilevel Modeling, 2nd edition in hand, graduate students and others are well equipped to begin their journey.

      Barbara Entwisle

       Series Editor

      Preface

      Since the first edition of this monograph was published in 2004, there have been numerous developments in the statistical and computational methods used in multilevel and longitudinal modeling. Mixed-effects modeling has been solidified as a primary means for accurately and efficiently estimating a wide variety of multilevel and longitudinal models. More complex models that include cross-level interactions, cross-classified random effects, alternative covariances structures, and the like appear much more frequently in the health and social sciences research literature. Sophisticated mixed-effects modeling procedures are now incorporated

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