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Multilevel Analysis for Applied Research

It's Just Regression!

• By Robert Bickel

Please order this title fromGuilford Press

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• Binding: Paperback (also available in Hardback)
• Pages: 428
• Published by: Guilford Press
• Publication Date: 26th April 2007
• ISBN: 978-1-59385-191-0

About the Book

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.

Reviews

'This book is one of the best statistical texts that I have ever read, and I would highly recommend using it for an advanced data analysis course. The examples and the step-by-step methods using SPSS are superb and statistically accurate. The author does a tremendous job of linking concepts to statistical procedures, as well as giving great examples! The listings for how to interpret the coefficients will really help graduate students make sense of their results.' - Alison J. Bianchi, Department of Sociology, Kent State University , USA

'This would be a good reference for sticky issues, and I really like that this book addresses issues that researchers actually struggle with when they are working on a project, such as effective sample size and maximum likelihood. I also like the writing style - casual but authoritative.' - Julia McQuillan, Bureau of Sociological Research and Department of Sociology, University of Nebraska -Lincoln , USA

'The writing style is excellent for students and for applied researchers who don't consider themselves experts in statistics. One of the particular strengths of the book is how the author writes about the interpretation of results that may lead to the respecification of models and their tests. The figures of the models tested, the to-do lists, and interpretation of the corresponding output allow readers to integrate cognitively the concepts and procedures pertaining to very difficult topics. It is clear that the author spent significant amounts of time considering how best to present this information. I would tell my colleagues who don't consider themselves experts in measurement and statistics to buy themselves a present -this book.' - Jonna M. Kulikowich, Department of Educational and School Psychology and Special Education, Penn State, USA

'This is a lucid and well-written text that cuts directly to the important issues in multilevel modeling. The regression approach is highly desirable as it builds on methods commonly taught in graduate programs in the social sciences. The text is appropriate for graduate-level teaching and could easily be used as the primary text in a multilevel modeling seminar. In addition, applied researchers with a background in multiple regression will find this an excellent resource for modeling nested data in cross-sectional and longitudinal studies.' - Jeffrey D. Long, Department of Educational Psychology, University of Minnesota, USA

'Unparalleled as an introduction to multilevel methods. For anyone who wants to learn or teach these methods using a text built on examples rather than equations, who prefers demonstrations over derivations, and who wants to begin analyzing data right away, this is the book to use.' - Daniel Ozer, Department of Psychology, University of California, Riverside, USA

'With this rigorous and detailed book, Bickel provides an unparalleled introduction to multilevel methods. This is a practical text both for experienced researchers who need to catch up with these newer methods and for students who have completed a regression course and are ready for the next step. The approach taken is conceptual and data-analytic, with extended examples analyzed in detail. There is extensive use of tables and figures to display data and report the worked examples, and each chapter's brief discussion of additional resources and readings is very useful. All examples reference the SPSS software package, and specific instructions for using this software are included as boxed text that does not interrupt the flow of ideas but is easily found when needed. While the book is designed for the data analyst rather than the methodologist, technical issues are not ignored. For anyone who wants to learn or teach multilevel modeling using a text built on examples rather than equations, who prefers demonstrations over derivations, and who wants to begin analyzing data right away, this is the book to use.' - Daniel Ozer, Department of Psychology, University of California, Riverside, USA

'This is a very accessible and terrifically useful book.' - Lisa Feldman Barrett, PhD, Department of Psychology, Boston College, USA

Table of Contents

Part I: Broadening the Scope of Regression Analysis. 1.1.Chapter Introduction. 1.2. Why Use Multilevel Regression Analysis? 1.3. Limitations of Available Instructional Material. 1.4. Multilevel Regression Analysis in Suggestive Historical Context. 1.5. It’s Just Regression under Specific Circumstances. 1.6. Jumping the Gun to a Multilevel Illustration. 1.7. Summing Up. 1.8. Useful Resources. Part II: The Meaning of Nesting. 2.1. Chapter Introduction. 2.2. Nesting Illustrated: School Achievement and Neighborhood Quality. 2.3. Nesting Illustrated: Comparing Public and Private Schools. 2.4. Cautionary Comment on Residuals in Multilevel Analysis. 2.5. Nesting and Correlated Residuals. 2.6. Nesting and Effective Sample Size. 2.7. Summing Up. 2.8. Useful Resources. Part III: Contextual Variables. 3.1. Chapter Introduction. 3.2. Contextual Variables and Analytical Opportunities. 3.3. Contextual Variables and Independent Observations. 3.4. Contextual Variables and Independent Observations: A Nine-Category Dummy Variable. 3.5. Contextual Variables, Intraclass Correlation, and Misspecification. 3.6. Contextual Variables and Varying Parameter Estimates. 3.7. Contextual Variables and Covariance Structure. 3.8. Contextual Variables and Degrees of Freedom. 3.9. Summing Up. 3.10. Useful Resources. Part IV: From OLS to Random Coefficient to Multilevel Regression. 4.1. Chapter Introduction. 4.2. Simple Regression Equation. 4.3. Simple Regression with an Individual-Level Variable. 4.4. Multiple Regression: Adding a Contextual Variable. 4.5. Nesting (Again!) with a Contextual Variable. 4.6. Is There a Problem with Degrees of Freedom? 4.7. Is There a Problem with Dependent Observations? 4.8. Alternatives to OLS Estimators. 4.9. The Conceptual Basis of ML Estimators. 4.10. Desirable Properties of REML Estimators. 4.11. Applying REML Estimators with Random Coefficient Regression Models. 4.12. Fixed Components and Random Components. 4.13. Interpreting Random Coefficients: Developing a Cautionary Comment. 4.14. Subscript Conventions. 4.15. Percentage of Variance Explained for Random Coefficient and Multilevel Models. 4.16. Grand-Mean Centering. 4.17. Grand-Mean Centering, Group-Mean Centering, and Raw Scores Compared. 4.18. Summing Up. 4.19. Useful Resources. Part V: Developing the Multilevel Regression Model. 5.1. Chapter Introduction. 5.2. From Random Coefficient Regression to Multilevel Regression. 5.3. Equations for a Random Intercept and Random Slope. 5.4. Subscript Conventions for Two-Level Models: Gamma Coefficients. 5.5. The Full Equation. 5.6. An Implied Cross-Level Interaction Term. 5.7. Estimating a Multilevel Model: The Full Equation. 5.8. A Multilevel Model with a Random Slope and Fixed Slopes at Level One. 5.9. Complexity and Confusion: Too Many Random Components. 5.10. Interpreting Multilevel Regression Equations. 5.11. Comparing Interpretations of Alternative Specifications. 5.12. What Happened to the Error Term? 5.13. Summing Up. 5.14. Useful Resources. Part VI: Giving OLS Regression Its Due. 6.1. Chapter Introduction. 6.2. An Extended Exercise with County-Level Data. 6.3. Tentative Specification of an OLS Regression Model. 6.4. Preliminary Regression Results. 6.5. Surprise Results and Possible Violation of OLS Assumptions. 6.6. Curvilinear Relationships: Y_BUSH by X_BLACK, X_HISPANIC, X_NATIVE. 6.7. Quadratic Functional Form. 6.8. A Respecified OLS Regression Model. 6.9. Interpreting Quadratic Relationships. 6.10. Nonadditivity and Interaction Terms. 6.11. Further Respecification of the Regression Model. 6.12. Clarifying OLS Interaction Effects. 6.13. Results for the Respecified OLS Regression Equation for County-Level Data. 6.14. Summing Up. 6.15. Useful Resources. Part VII: Does Multilevel Regression Have Anything to Contribute? 7.1. Chapter Introduction. 7.2. Contextual Effects in OLS Regression. 7.3. Respecification and Changing Functional Form. 7.4. Addressing the Limitations of OLS. 7.5. Counties Nested within States: Intraclass Correlation. 7.6. Multilevel Regression Model Specification: Learning from OLS. 7.7. Interpreting the Multilevel Regression Equation for County-Level Data. 7.8. Knowing When to Stop. 7.9. Summing Up. 7.10. Useful Resources. Part VIII: Multilevel Regression Models with Three Levels. 8.1. Chapter Introduction. 8.2. Students Nested within Schools and within Districts. 8.3. Level One: Students. 8.4. Level Two: Schools. 8.5. Level Three: Districts. 8.6. Notation and Subscript Conventions for Specifying a Three-Level Model. 8.7. Estimating a Three-Level Random Coefficient Model. 8.8. Adding a Second Level-One Predictor. 8.9. Adding a Level-Two Predictor. 8.10. Adding a Second Predictor at Level Two and a Predictor at Level Three. 8.11. Discretionary Use of Same-Level Interaction Terms. 8.12. Ongoing Respecification of a Three-Level Model. 8.13. A Level-Two Random Slope at Level Three. 8.14. Summing Up. 8.15. Useful Resources. Part IX: Familiar Measures Applied to a Three-Level Model. 9.1. Chapter Introduction. 9.2. The Intraclass Correlation Coefficient Revisited. 9.3. Percentage of Variance Explained in a Level-One Dependent Variable. 9.4. Other Summary Measures Used with Multilevel Regression. 9.5. Summing Up. 9.6. Useful Resources. Part X: Determining Sample Sizes for Multilevel Regression. 10.1. Chapter Introduction. 10.2. Interest in Sample Size in OLS and Multiple Regression. 10.3. Sample Size: Rules of Thumb and Data Constraints. 10.4. Estimation and Inference for Unstandardized Regression Coefficients. 10.5. More Than One Level of Analysis Means More Than One Sample Size. 10.6. An Individual-Level OLS Analysis with a Large Sample. 10.7. A Group-Level OLS Analysis with a Small Sample. 10.8. Standard Errors: Corrected and Uncorrected, Individual and Group Levels. 10.9. When Output Is Not Forthcoming!10.10. Sample Sizes and OLS-Based Commonsense in Multilevel Regression. 10.11. Sample Size Generalizations Peculiar to Multilevel Regression. 10.12. Level-One Sample Size and Level-Two Statistical Power. 10.13. The Importance of Sample Size at Higher Levels. 10.14. Summing Up. 10.15. Useful Resources. Part XI: Multilevel Regression Growth Models. 11.1. Chapter Introduction. 11.2. Analyzing Longitudinal Data: Pretest–Posttest. 11.3. Nested Measures: Growth in Student Vocabulary Achievement. 11.4. Nested Measures: Growth in NCLEX Pass Rates. 11.5. Developing Multilevel Regression Growth Models. 11.6. Summary Statistics with Growth Models. 11.7. Sample Sizes. 11.8. The Multilevel Regression Growth Model Respecified. 11.9. The Multilevel Regression Growth Model: Further Respecification. 11.10. Residual Covariance Structures. 11.11. Multilevel Regression Growth Models with Three Levels. 11.12. Nonlinear Growth Curves. 11.13. NCLEX Pass Rates with a Time-Dependent Predictor. 11.14. Summing Up. 1.15. Useful Resources.

About the Author(s)

Robert Bickel, College of Education and Human Services, Marshall University, Huntington, WV, USA

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