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

Author

Listed:
  • Petzold, Max

    (Department of Statistics,)

  • Jonsson, Robert

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

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.

Suggested Citation

  • Petzold, Max & Jonsson, Robert, 2003. "Maximum Likelihood Ratio based small-sample tests for random coefficients in linear regression," Working Papers in Economics 102, University of Gothenburg, Department of Economics.
    • Handle: RePEc:hhs:gunwpe:0102
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    File URL: http://hdl.handle.net/2077/2813
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    References listed on IDEAS

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    1. Yuzo Honda, 1985. "Testing the Error Components Model with Non-Normal Disturbances," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 681-690.
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    3. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    4. V. V. Anh & T. Chelliah, 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, March.
    5. Mundlak, Yair, 1978. "On the Pooling of Time Series and Cross Section Data," Econometrica, Econometric Society, vol. 46(1), pages 69-85, January.
    6. Erling Häggström, 2002. "Properties of Honda’s test of random individual effects in non-linear regressions," Statistical Papers, Springer, vol. 43(2), pages 177-196, April.
    7. 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.
    8. Boozer, Michael A., 1997. "Econometric Analysis of Panel DataBadi H. Baltagi Wiley, 1995," Econometric Theory, Cambridge University Press, vol. 13(5), pages 747-754, October.
    9. 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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    More about this item

    Keywords

    Exact test; Hypothesis test; Maximum Likelihood; Pre-test; Random coefficient regression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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