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A Simple Distribution-Free Test for Nonnested Model Selection

  • Kevin A. Clarke (a1)

Abstract

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.

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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.
Albert, James H. 1996. Bayesian selection of log-linear models. Canadian Journal of Statistics 24: 327–47.
Berger, James O., and Pericchi, Luis R. 1996. The intrinsic Bayes factor for model selection and prediction. Journal of the American Statistical Association 91: 109122.
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.
Cameron, A. Colin, and Trived, Pravin K. 2005. Microeconometrics: Methods and applications. Cambridge: Cambridge University Press.
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.
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, 67116. Beachwood, OH: Institute of Mathematical Statistics.
Clarke, Kevin A. 2001. Testing nonnested models of international relations: Reevaluating realism. American Journal of Political Science 45: 724–74.
Clarke, Kevin A. 2003. Nonparametric model discrimination in international relations. Journal of Conflict Resolution 47: 7293.
Clarke, Kevin A. 2007. Data experiments: Model specifications as treatments. Unpublished manuscript.
Clarke, Kevin A., and Signorino, Curt S. 2006. Discriminating methods: Nonnested tests for strategic choice models. Unpublished manuscript.
Davidson, Russell, and MacKinnon, James G. 1993. Estimation and inference in econometrics. Oxford: Oxford University Press.
Efron, Bradley. 1986. Why isn't everyone a Bayesian? The American Statistician 40: 15.
Fernandez, Carmen, Ley, Eduardo, and Steel, Mark F. J. 2001. Benchmark priors for Bayesian model averaging. Journal of Econometrics 100: 381427.
George, Edward I., and Foster, Dean P. 2000. Calibration and empirical Bayes variable selection. Biometrika 87: 731–47.
Gibbons, Jean Dickinson, and Chakraborti, Subhabrata. 1992. Nonparametric statistical inference. 3rd ed. New York: Marcel Dekker, Inc.
Greene, William H. 2003. Econometric analysis. 5th ed. Upper Saddle River, NJ: Prentice Hall.
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.
Hollander, Myles, and Wolfe, Douglas A. 1999. Nonparametric statistical methods. 2nd ed. New York: John Wiley and Sons.
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.
Johnston, Jack, and DiNardo, John. 1997. Econometric methods. 4th ed. New York: McGraw Hill.
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.
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.
Kmenta, Jan. 1986. Elements of econometrics. 2nd ed. New York: Macmillan Publishing Company.
Kullback, Solomon, and Leibler, R. A. 1951. On information and sufficiency. Annals of Mathematical Statistics 22: 7986.
Laud, Purushottam W., and Ibrahim, Joseph G. 1995. Predictive model selection. Journal of the Royal Statisitcal Society, Series B 57: 247–62.
Lehmann, E. L. 1986. Testing statistical hypotheses. 2nd ed. New York: John Wiley and Sons.
Maoz, Zeev, and Russett, Bruce. 1993. Normative and structural causes of democratic peace, 1946-1986. American Political Science Review 87: 624–38.
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.
Noether, Gottfried E. 1955. On a theorem of Pitman. Annals of Mathematical Statistics 26: 64–8.
Noether, Gottfried E. 1967. Elements of nonparametric statistics. New York: John Wiley and Sons.
Pesaran, M. H. 1974. On the general problem of model selection. Review of Economic Studies 41: 153–71.
Pesaran, M. H. 1987. Global and partial non-nested hypotheses and asymptotic local power. Econometric Theory 3: 6997.
Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–4.
Spanos, Aris. 1999. Probability theory and statistical inference. Cambridge: Cambridge University Press.
Vuong, Quang. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57: 307–33.
White, Halbert. 1982. Maximum likelihood estimator of misspecified models. Econometrica 50: 125.
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A Simple Distribution-Free Test for Nonnested Model Selection

  • Kevin A. Clarke (a1)

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