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Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression

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  • Petzold, Max

    (Department of Statistics,)

  • Jonsson, Robert

    (Department of Economics, School of Economics and Commercial Law, Göteborg University)

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    Abstract

    Two small-sample tests for random coefficients in linear regression are derived from the Maximum Likelihood Ratio. The first test has previously been proposed for testing equality of fixed effects, but is here shown to be suitable also for random coefficients. The second test is based on the multiple coefficient of determination from regressing the observed subject means on the estimated slopes. The properties and relations of the tests are examined in detail, followed by a simulation study of the power functions. The two tests are found to complement each other depending on the study design: The first test is preferred for a large number of observations from a small number of subjects, and the second test is preferred for the opposite situation. Finally, the robustness of the tests to violations of the distributional assumptions is examined.

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    File URL: http://hdl.handle.net/2077/2813
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    Bibliographic Info

    Paper provided by University of Gothenburg, Department of Economics in its series Working Papers in Economics with number 102.

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    Length: 21 pages
    Date of creation: 25 Aug 2003
    Date of revision:
    Handle: RePEc:hhs:gunwpe:0102

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    Postal: Department of Economics, School of Business, Economics and Law, University of Gothenburg, Box 640, SE 405 30 GÖTEBORG, Sweden
    Phone: 031-773 10 00
    Web page: http://www.handels.gu.se/econ/
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    Related research

    Keywords: Exact test; Hypothesis test; Maximum Likelihood; Pre-test; Random coefficient regression;

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    1. Boozer, Michael A., 1997. "Econometric Analysis of Panel Data Badi H. Baltagi Wiley, 1995," Econometric Theory, Cambridge University Press, vol. 13(05), pages 747-754, October.
    2. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    3. V. V. Anh, 1999. "Estimated Generalized Least Squares for Random Coefficient Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 31-46.
    4. Honda, Yuzo, 1985. "Testing the Error Components Model with Non-normal Disturbances," Review of Economic Studies, Wiley Blackwell, vol. 52(4), pages 681-90, October.
    5. Fujikoshi, Yasunori & von Rosen, Dietrich, 2000. "LR Tests for Random-Coefficient Covariance Structures in an Extended Growth Curve Model," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 245-268, November.
    6. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
    7. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-23, March.
    8. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
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    Cited by:
    1. Jonsson, Robert, 2003. "On the problem of optimal inference for time heterogeneous data with error components regression structure," Working Papers in Economics 110, University of Gothenburg, Department of Economics.

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