Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fixed-Effects Models
- 3 Models with Random Effects
- 4 Prediction and Bayesian Inference
- 5 Multilevel Models
- 6 Stochastic Regressors
- 7 Modeling Issues
- 8 Dynamic Models
- 9 Binary Dependent Variables
- 10 Generalized Linear Models
- 11 Categorical Dependent Variables and Survival Models
- Appendix A Elements of Matrix Algebra
- Appendix B Normal Distribution
- Appendix C Likelihood-Based Inference
- Appendix D State Space Model and the Kalman Filter
- Appendix E Symbols and Notation
- Appendix F Selected Longitudinal and Panel Data Sets
- References
- Index
5 - Multilevel Models
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Fixed-Effects Models
- 3 Models with Random Effects
- 4 Prediction and Bayesian Inference
- 5 Multilevel Models
- 6 Stochastic Regressors
- 7 Modeling Issues
- 8 Dynamic Models
- 9 Binary Dependent Variables
- 10 Generalized Linear Models
- 11 Categorical Dependent Variables and Survival Models
- Appendix A Elements of Matrix Algebra
- Appendix B Normal Distribution
- Appendix C Likelihood-Based Inference
- Appendix D State Space Model and the Kalman Filter
- Appendix E Symbols and Notation
- Appendix F Selected Longitudinal and Panel Data Sets
- References
- Index
Summary
Abstract. This chapter describes a conditional modeling framework that takes into account hierarchical and clustered data structures. The data and models, known as multilevel, are used extensively in educational science and related disciplines in the social and behavioral sciences. We show that a multilevel model can be viewed as a linear mixed-effects model, and hence the statistical inference techniques introduced in Chapter 3 are readily applicable. By considering multilevel data and models as a separate unit, we expand the breadth of applications that linear mixed-effects models enjoy.
Cross-Sectional Multilevel Models
Educational systems are often described by structures in which the units of observation at one level are grouped within units at a higher level of structure. To illustrate, suppose that we are interested in assessing student performance based on an achievement test. Students are grouped into classes, classes are grouped into schools, and schools are grouped into districts. At each level, there are variables that may affect responses from a student. For example, at the class level, education of the teacher may be important, at the school level, the school size may be important, and at the district level, funding may be important. Further, each level of grouping may be of scientific interest. Finally, there may be not only relationships among variables within each group but also across groups that should be considered.
- Type
- Chapter
- Information
- Longitudinal and Panel DataAnalysis and Applications in the Social Sciences, pp. 166 - 198Publisher: Cambridge University PressPrint publication year: 2004
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