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
6 - Stochastic Regressors
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. In many applications of interest, explanatory variables, or regressors, cannot be thought of as fixed quantities but, rather, they are modeled stochastically. In some applications, it can be difficult to determine which variables are being predicted and which are doing the prediction! This chapter summarizes several models that incorporate stochastic regressors. The first consideration is to identify under what circumstances we can safely condition on stochastic regressors and to use the results from prior chapters. We then discuss exogeneity, formalizing the idea that a regressor influences the response variable and not the other way around. Finally, this chapter introduces situations where more than one response is of interest, thus permitting us to investigate complex relationships among responses.
Stochastic Regressors in Nonlongitudinal Settings
Up to this point, we have assumed that the explanatory variables, Xi and Zi, are nonstochastic. This convention follows a long-standing tradition in the statistics literature. Pedagogically, this tradition allows for simpler verification of properties of estimators than the stochastic convention. Moreover, in classical experimental or laboratory settings, treating explanatory variables as nonstochastic allows for intuitive interpretations, such as when X is under the control of the analyst.
However, for other applications, such as the analysis of survey data drawn as a probability sample from a population, the assumption of nonstochastic variables is more difficult to interpret.
- Type
- Chapter
- Information
- Longitudinal and Panel DataAnalysis and Applications in the Social Sciences, pp. 199 - 241Publisher: Cambridge University PressPrint publication year: 2004