Hostname: page-component-74656f9884-npj9w Total loading time: 0 Render date: 2026-11-09T21:23:44.830Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Distribution-Free Test for Nonnested Model Selection

Published online by Cambridge University Press:  04 January 2017

Kevin A. Clarke
Kevin A. Clarke*
Affiliation:
Department of Political Science, University of Rochester, Rochester, NY 14627-0146. e-mail: kevin.clarke@rochester.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper considers a simple distribution-free test for nonnested model selection. The new test is shown to be asymptotically more efficient than the well-known Vuong test when the distribution of individual log-likelihood ratios is highly peaked. Monte Carlo results demonstrate that for many applied research situations, this distribution is indeed highly peaked. The simulation further demonstrates that the proposed test has greater power than the Vuong test under these conditions. The substantive application addresses the effect of domestic political institutions on foreign policy decision making. Do domestic institutions have effects because they hold political leaders accountable, or do they simply promote political norms that shape elite bargaining behavior? The results indicate that the latter model has greater explanatory power.

Information

Type
Research Article
Information
Political Analysis , Volume 15 , Issue 3 , Summer 2007 , pp. 347 - 363
Copyright
Copyright © The Author 2007. Published by Oxford University Press on behalf of the Society for Political Methodology 

References

Akaike, H. 1973. Information theory and an extension of the likelihood ratio principle. In Second international symposium of information theory, ed. Petrov, B. N. and Csaki, F. Minnesota Studies in the Philosophy of Science, Budapest: Akademinai Kiado.Google Scholar
Albert, James H. 1996. Bayesian selection of log-linear models. Canadian Journal of Statistics 24: 327–47.Google Scholar
Berger, James O., and Pericchi, Luis R. 1996. The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91: 109–122.Google Scholar
Brown, P. J., Vannucci, M., and Fearn, T. 1998. Multivariate Bayesian variable selection and prediction. Journal of the Royal Statistical Society, Series B 60: 627–41.Google Scholar
Cameron, A. Colin, and Trived, Pravin K. 2005. Microeconometrics: Methods and applications. Cambridge: Cambridge University Press.Google Scholar
Carlin, B. P., and Chibb, S. 1995. Bayesian model choice via Markov Chain Monte Carlo. Journal of the Royal Statisitcal Society, Series B 77: 473–84.Google Scholar
Chipman, Hugh, George, Edward I., and McCulloch, Robert E. 2001. The practical implementation of Bayesian model selection. In Model selection, ed. Lahiri, P. Institute of mathematical statistics lecture notes. Vol. 38, 67–116. Beachwood, OH: Institute of Mathematical Statistics.Google Scholar
Clarke, Kevin A. 2001. Testing nonnested models of international relations: Reevaluating realism. American Journal of Political Science 45: 724–74.CrossRefGoogle Scholar
Clarke, Kevin A. 2003. Nonparametric model discrimination in international relations. Journal of Conflict Resolution 47: 72–93.Google Scholar
Clarke, Kevin A. 2007. Data experiments: Model specifications as treatments. Unpublished manuscript.Google Scholar
Clarke, Kevin A., and Signorino, Curt S. 2006. Discriminating methods: Nonnested tests for strategic choice models. Unpublished manuscript.Google Scholar
Davidson, Russell, and MacKinnon, James G. 1993. Estimation and inference in econometrics. Oxford: Oxford University Press.Google Scholar
Efron, Bradley. 1986. Why isn't everyone a Bayesian? The American Statistician 40: 1–5.Google Scholar
Fernandez, Carmen, Ley, Eduardo, and Steel, Mark F. J. 2001. Benchmark priors for Bayesian model averaging. Journal of Econometrics 100: 381–427.Google Scholar
George, Edward I., and Foster, Dean P. 2000. Calibration and empirical Bayes variable selection. Biometrika 87: 731–47.Google Scholar
Gibbons, Jean Dickinson, and Chakraborti, Subhabrata. 1992. Nonparametric statistical inference. 3rd ed. New York: Marcel Dekker, Inc.Google Scholar
Greene, William H. 2003. Econometric analysis. 5th ed. Upper Saddle River, NJ: Prentice Hall.Google Scholar
Hodges, J. L., and Lehmann, E. L. 1956. The efficiency of some nonparametric competitors of the t-test. Annals of Mathematical Statistics 27: 324–35.Google Scholar
Hollander, Myles, and Wolfe, Douglas A. 1999. Nonparametric statistical methods. 2nd ed. New York: John Wiley and Sons.Google Scholar
Huth, Paul K., and Allee, Todd. 2002. The democratic peace and territorial conflict in the twentieth century. Cambridge studies in international relations, Cambridge: Cambridge University Press.Google Scholar
Johnston, Jack, and DiNardo, John. 1997. Econometric methods. 4th ed. New York: McGraw Hill.Google Scholar
Judge, George G., Griffiths, W. E., Carter Hill, R., Lutkepohl, Helmut, and Lee, Tsoung-Chao. 1985. The theory and practice of econometrics. 2nd ed. New York: John Wiley and Sons.Google Scholar
Kaiser, Henry F., and Dickman, Kern. 1962. Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika 27: 179–82.CrossRefGoogle Scholar
Kmenta, Jan. 1986. Elements of econometrics. 2nd ed. New York: Macmillan Publishing Company.Google Scholar
Kullback, Solomon, and Leibler, R. A. 1951. On information and sufficiency. Annals of Mathematical Statistics 22: 79–86.Google Scholar
Laud, Purushottam W., and Ibrahim, Joseph G. 1995. Predictive model selection. Journal of the Royal Statisitcal Society, Series B 57: 247–62.Google Scholar
Lehmann, E. L. 1986. Testing statistical hypotheses. 2nd ed. New York: John Wiley and Sons.Google Scholar
Maoz, Zeev, and Russett, Bruce. 1993. Normative and structural causes of democratic peace, 1946-1986. American Political Science Review 87: 624–38.Google Scholar
McAleer, Michael. 1987. Specification tests for separate models: A survey. In specification analysis in the linear model, ed. King, M. L. and Giles, D. E. A. London: Routledge and Kegan Paul.Google Scholar
Noether, Gottfried E. 1955. On a theorem of Pitman. Annals of Mathematical Statistics 26: 64–8.Google Scholar
Noether, Gottfried E. 1967. Elements of nonparametric statistics. New York: John Wiley and Sons.Google Scholar
Pesaran, M. H. 1974. On the general problem of model selection. Review of Economic Studies 41: 153–71.CrossRefGoogle Scholar
Pesaran, M. H. 1987. Global and partial non-nested hypotheses and asymptotic local power. Econometric Theory 3: 69–97.Google Scholar
Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–4.Google Scholar
Spanos, Aris. 1999. Probability theory and statistical inference. Cambridge: Cambridge University Press.Google Scholar
Vuong, Quang. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57: 307–33.Google Scholar
White, Halbert. 1982. Maximum likelihood estimator of misspecified models. Econometrica 50: 1–25.Google Scholar
Supplementary material: PDF

Clarke Supplementary Material

Supplementary Material

Download Clarke Supplementary Material(PDF)
PDF 114.6 KB
Supplementary material: File

Clarke Supplementary Material

Supplementary Material

Download Clarke Supplementary Material(File)
File 2.2 KB