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Two-Step Hierarchical Estimation: Beyond Regression Analysis

Published online by Cambridge University Press:  04 January 2017

Christopher H. Achen*
Affiliation:
Department of Politics, Princeton University, Princeton, NJ 08544. e-mail: achen@princeton.edu

Abstract

Two-step estimators for hierarchical models can be constructed even when neither stage is a conventional linear regression model. For example, the first stage might consist of probit models, or duration models, or event count models. The second stage might be a nonlinear regression specification. This note sketches some of the considerations that arise in ensuring that two-step estimators are consistent in such cases.

Type
Research Article
Copyright
Copyright © The Author 2005. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Bartels, Larry M. 1996. “Pooling Disparate Observations.” American Journal of Political Science 40: 905942.Google Scholar
Belsley, David A., Kuh, Edwin, and Welsch, Roy E. 1980. Regression Diagnostics New York: Wiley.Google Scholar
Borjas, George J., and Sueyoshi, Glenn T. 1994. “A Two-Stage Estimator for Probit Models with Structural Group Effects.” Journal of Econometrics 64: 165182.Google Scholar
Bowers, Jake, and Drake, Katherine W. 2005. “EDA for HLM: Visualization When Probabilistic Inference Fails.” Political Analysis doi:10.1093/pan/mpi031.Google Scholar
Bryk, Anthony S., and Raudenbush, Stephen W. 2001. Hierarchical Linear Models, 2nd ed. Newbury Park, CA: Sage.Google Scholar
Duch, Raymond, and Stevenson, Randy. 2005. “Context and the Economic Vote: A Multi-Level Analysis.” Political Analysis doi:10.1093/pan/mpi028.CrossRefGoogle Scholar
Franzese, Robert J. Jr. 2005. “Empirical Strategies for Various Manifestations of Multilevel Data.” Political Analysis doi:10.1093/pan/mpi024.CrossRefGoogle Scholar
Gibbons, Robert D., and Hedeker, Donald. 1997. “Random Effects Probit and Logistic Regression Models for Three-Level Data.” Biometrics 53: 15271537.Google Scholar
Hanushek, Erik A. 1974. “Efficient Estimators for Regressing Regression Coefficients.” American Statistician 28: 6667.Google Scholar
Huber, John D., Kernell, Georgia, and Leoni, Eduardo. 2005. “Institutional Context, Cognitive Resources and Partisan Attachments Across Democracies.” Political Analysis doi:10.1093/pan/mpi025.Google Scholar
Jusko, Karen Long. 2005. “A Two-Step Binary Response Model for Cross-National Public Opinion Data: A Research Note.” Presented at the Midwest Political Science Association National Conference, April 7–10, 2005, Chicago.Google Scholar
Jusko, Karen Long, and Shively, Phillips W. 2005. “A Two-Step Strategy for the Analysis of Cross-National Public Opinion Data.” Political Analysis doi:10.1093/pan/mpi030.Google Scholar
Kedar, Orit. 2005. “How Diffusion of Power in Parliaments Affects Voter Choice.” Political Analysis doi:10.1093/pan/mpi029.Google Scholar
Lewis, Jeffrey B., and Linzer, Drew A. 2005. “Estimating Regression Models in which the Dependent Variable Is Based on Estimates.” Political Analysis doi:10.1093/pan/mpi026.Google Scholar
Lindley, Dennis V., and Smith, A. F. M. 1972. “Bayes Estimates for the Linear Model.” Journal of the Royal Statistical Society, Series B 34: 141.Google Scholar
Saxonhouse, Gary R. 1976. “Estimated Parameters as Dependent Varibles.” American Economic Review 66: 178183.Google Scholar
Saxonhouse, Gary R. 1977. “Regressions from Samples Having Different Characteristics.” Review of Economics and Statistics 59: 234237.Google Scholar
Snijders, Tom A.B., and Bosker, Roel J. 1999. Multilevel Analysis. London: Sage.Google Scholar
Western, Bruce. 1998. “Causal Heterogeneity in Comparative Research.” American Journal of Political Science 42: 12331259.Google Scholar