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
2 - Fixed-Effects 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 introduces the analysis of longitudinal and panel data using the general linear model framework. Here, longitudinal data modeling is cast as a regression problem by using fixed parameters to represent the heterogeneity; nonrandom quantities that account for the heterogeneity are known as fixed effects. In this way, ideas of model representation and data exploration are introduced using regression analysis, a toolkit that is widely known. Analysis of covariance, from the general linear model, easily handles the many parameters needed to represent the heterogeneity.
Although longitudinal and panel data can be analyzed using regression techniques, it is also important to emphasize the special features of these data. Specifically, the chapter emphasizes the wide cross section and the short time series of many longitudinal and panel data sets, as well as the special model specification and diagnostic tools needed to handle these features.
Basic Fixed-Effects Model
Data
Suppose that we are interested in explaining hospital costs for each state in terms of measures of utilization, such as the number of discharged patients and the average hospital stay per discharge. Here, we consider the state to be the unit of observation, or subject. We differentiate among states with the index i, where i may range from 1 to n, and n is the number of subjects. Each state is observed Ti times and we use the index t to differentiate the observation times. With these indices, let yit denote the response of the ith subject at the tth time point.
- Type
- Chapter
- Information
- Longitudinal and Panel DataAnalysis and Applications in the Social Sciences, pp. 18 - 71Publisher: Cambridge University PressPrint publication year: 2004
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