IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i4d10.1007_s00180-016-0703-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0703-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-016-0703-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Deaton, Angus, 1992. "Understanding Consumption," OUP Catalogue, Oxford University Press, number 9780198288244.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Filipe Marques & Carlos Coelho & Barry Arnold, 2011. "A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 180-203, May.
    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. & 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.
    4. Carlos A. Coelho & Anuradha Roy, 2020. "Testing the hypothesis of a doubly exchangeable covariance matrix," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 45-68, January.
    5. Carlos A. Coelho & Anuradha Roy, 2017. "Testing the hypothesis of a block compound symmetric covariance matrix for elliptically contoured distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 308-330, June.
    6. Filipe J. Marques & Carlos A. Coelho & Barry C. Arnold, 2011. "A general near-exact distribution theory for the most common likelihood ratio test statistics used in Multivariate Analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 180-203, May.
    7. Marques, Filipe J. & Loingeville, Florence, 2016. "Improved near-exact distributions for the product of independent Generalized Gamma random variables," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 55-66.
    8. Carlos Coelho & Filipe Marques, 2012. "Near-exact distributions for the likelihood ratio test statistic to test equality of several variance-covariance matrices in elliptically contoured distributions," Computational Statistics, Springer, vol. 27(4), pages 627-659, December.
    9. Jonathan Gruber & Aaron Yelowitz, 1999. "Public Health Insurance and Private Savings," Journal of Political Economy, University of Chicago Press, vol. 107(6), pages 1249-1274, December.
    10. Cristóbal Huneeus & Andrea Repetto, 2005. "The Dynamics of Earnings in Chile," Central Banking, Analysis, and Economic Policies Book Series, in: Jorge Restrepo & Andrea Tokman R. & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series Edi (ed.),Labor Markets and Institutions, edition 1, volume 8, chapter 12, pages 383-410, Central Bank of Chile.
    11. Lusardi, Annamaria, 1997. "Precautionary saving and subjective earnings variance," Economics Letters, Elsevier, vol. 57(3), pages 319-326, December.
    12. Fatih Ozatay, 2008. "Expansionary Fiscal Consolidations: New Evidence from Turkey," Working Papers 0805, TOBB University of Economics and Technology, Department of Economics.
    13. Guy Stecklov & Paul Winters & Marco Stampini & Benjamin Davis, 2003. "Can Public Transfers Reduce Mexican Migration? A study based on randomized experimental data," Working Papers 03-16, Agricultural and Development Economics Division of the Food and Agriculture Organization of the United Nations (FAO - ESA).
    14. Das, Marcel & van Soest, Arthur, 1999. "A panel data model for subjective information on household income growth," Journal of Economic Behavior & Organization, Elsevier, vol. 40(4), pages 409-426, December.
    15. Francesco Devicienti & Valentina Gualtieri & Mariacristina Rossi, 2014. "The Persistence Of Income Poverty And Lifestyle Deprivation: Evidence From Italy," Bulletin of Economic Research, Wiley Blackwell, vol. 66(3), pages 246-278, July.
    16. repec:spo:wpmain:info:hdl:2441/765 is not listed on IDEAS
    17. Zhao, Weimin & Chen, Na, 2024. "Does old-age security promote rural residents' consumption? A decomposition based on contribution and replacement rates," Economic Analysis and Policy, Elsevier, vol. 82(C), pages 817-830.
    18. Augendra BHUKUTH & Jérôme BALLET & Bako Nirina RABEVOHITRA & Patrick RASOLOFO, 2014. "Analysing the Effects of Crop Shocks on Child Work: the Case of the Morondava District in Madagascar," Cahiers du GREThA (2007-2019) 2014-17, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    19. Luc Arrondel & André Masson, 2013. "Measuring savers' preferences how and why?," PSE Working Papers halshs-00834203, HAL.
    20. CHADHA, Jagjit & SCHELLEKENS, Philip, "undated". "Monetary policy loss functions: two cheers for the quadratic," Working Papers 1999002, University of Antwerp, Faculty of Business and Economics.
    21. Söderlind, Paul, 1995. "Forward Interest Rates as Indicators of Inflation Expectations," CEPR Discussion Papers 1313, C.E.P.R. Discussion Papers.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0703-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.