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 in most comprehensive statistical software packages (including R, Stata, and SAS), and thus there is less need for specialized multilevel software. During this same period, I have taught graduate multilevel classes and trainings over a dozen times, and I have learned a thing or two about how to think about mixed-effects models, how to correctly interpret their results, and maybe most important how to communicate those results to interested audiences. My students in these classes have always been patient with me and have been my most important collaborators in my own statistical training.
The second edition of Multilevel Modeling has been improved and expanded in ways too numerous to list in detail. However, the major changes in this new version are as follows:
Longitudinal methods are expanded and get their own new chapter.
Diagnostic procedures are expanded with an emphasis on influence statistics.
Coverage of models of counts (Poisson) has been added.
A short new section on power analysis has been added.
Cross-classified models are now discussed.
The coverage of centering has been updated to reflect current statistical knowledge and practices.
A new section has been added that makes recommendations for presenting modeling results.
A new support website has been developed for the book that provides the data and the statistical code (both R and Stata) used for all of the presented analyses.
I hope that with these changes, this book will remain useful and relevant for students and researchers for many years to come.
In developing this second edition, I would like to particularly thank the following people who all provided extremely detailed and helpful reviews of the earlier edition, and drafts of this second edition.
Edward Brent, Department of Sociology, University of Missouri
Brian V. Carolan, Department of Educational Foundations, Montclair State University
Timothy Ford, Department of Curriculum, Instruction, and Learning, University of Louisiana
Jennifer Hayes Clark, Department of Political Science, University of Houston
Changjoo Kim, Department of Geography, University of Cincinnati
David LaHuis, Department of Psychology, Wright State University
I dedicated the first edition of this book to my parents. I would like to dedicate this updated version to my daughter, Alina Luke. Alina was in first grade when I started work on the original volume. As time passes, daughters grow up. She recently received her MPH with a concentration in biostatistics and epidemiology, and is herself a skilled analyst with training in mixed-effects models. In fact, she has helped with
