Multilevel Model Foundations

This book introduces the foundations of multilevel models, using Monopoly (R) rent data, from the classic board game, and the statistical program Stata (R). Widespread experience with the game means many readers have a head start on understanding these models. The small-data set, 132 rent values for 22 properties clustered by the four sides of the playing board, combines with extensive graphical displays of data and results so all readers can see core multilevel ideas in action at a granular level. Two chapters on standard statistical models, one-way analysis of variance and multiple regression, help readers see how multilevel models rely on but also extend these monolevel ideas. Chapters present three basic multilevel models for cross-sectional analyses - analysis of variance, analysis of covariance, and random coefficients regression - and one basic developmental model for longitudinal analyses. Troubleshooting guidance, combined with close examination of data patterns, and careful inspection of model parameters, all help readers better grasp what model results mean, when model results should or should not be trusted, and how model results link back to core theoretical questions. Consequently, readers will develop a sense of best practices for building and diagnosing their own multilevel models. Those who complete the volume can readily apply what they have learned to more complex datasets and models and adapt available online Stata do files to those projects. Any social scientist working with data clustered in time, in space, or in both, and seeking to learn more about how to use, interpret, or teach these models, will find the book useful.