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Testing the equality of several linear regression models

Author

Listed:
  • Filipe J. Marques

    (NOVA University of Lisbon
    Universidade Nova de Lisboa)

  • Carlos A. Coelho

    (NOVA University of Lisbon
    Universidade Nova de Lisboa)

  • Paulo C. Rodrigues

    (Federal University of Bahia
    University of Tampere)

Abstract

The linear regression models are widely used in different research fields, and often there is the need to analyze if there are similarities between two or more different linear models or to verify if a given relation between two variables remains the same in different intervals of time, in particular in cases where small differences might make a big difference. Motivated by these problems the authors consider a test of equality of k linear regression models which is a simultaneous test of equality of slopes, intercepts and variances. In order to overcome the extreme difficulties that exist in the use of the exact distribution of the likelihood ratio test (LRT) statistic and to make this test reliable and easy to use, we propose the use of near-exact distributions to approximate the distribution of the LRT statistic, under $$H_0$$ H 0 , in the balanced case, and of new asymptotic approximations for the unbalanced case. The near-exact approximations are built by approximating one factor of an adequate factorization of the characteristic function of the logarithm of the LRT statistic and may be easily implemented. The asymptotic approximations are developed using an expansion for the ratio of gamma functions. The quality of these approximations is analyzed and confirmed. Power studies are conducted in order to better assess the performance of the test. Finally to illustrate the applicability of the test we consider a real data set of gross domestic product at market prices and final consumption expenditure in European countries and one tests the existence of similarities between countries.

Suggested Citation

  • Filipe J. Marques & Carlos A. Coelho & Paulo C. Rodrigues, 2017. "Testing the equality of several linear regression models," Computational Statistics, Springer, vol. 32(4), pages 1453-1480, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0703-1
    DOI: 10.1007/s00180-016-0703-1
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    References listed on IDEAS

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    1. Johansen, Søren, 2000. "A Bartlett Correction Factor For Tests On The Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 16(5), pages 740-778, October.
    2. Filipe Marques & Carlos Coelho, 2013. "Obtaining the exact and near-exact distributions of the likelihood ratio statistic to test circular symmetry through the use of characteristic functions," Computational Statistics, Springer, vol. 28(5), pages 2091-2115, October.
    3. Coelho, Carlos A., 1998. "The Generalized Integer Gamma Distribution--A Basis for Distributions in Multivariate Statistics," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 86-102, January.
    4. Coelho, Carlos A., 2004. "The generalized near-integer Gamma distribution: a basis for 'near-exact' approximations to the distribution of statistics which are the product of an odd number of independent Beta random variables," Journal of Multivariate Analysis, Elsevier, vol. 89(2), pages 191-218, May.
    5. Coelho, Carlos A. & Marques, Filipe J., 2010. "Near-exact distributions for the independence and sphericity likelihood ratio test statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 583-593, March.
    6. Junyong Park & Bimal Sinha & Arvind Shah & Dihua Xu & Jianxin Lin, 2015. "Likelihood Ratio Tests for Interval Hypotheses with Applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(11), pages 2351-2370, June.
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