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Improved likelihood inference in generalized linear models

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  • Vargas, Tiago M.
  • Ferrari, Silvia L.P.
  • Lemonte, Artur J.

Abstract

We address the issue of performing testing inference in generalized linear models when the sample size is small. This class of models provides a straightforward way of modeling normal and non-normal data and has been widely used in several practical situations. The likelihood ratio, Wald and score statistics, and the recently proposed gradient statistic provide the basis for testing inference on the parameters in these models. We focus on the small-sample case, where the reference chi-squared distribution gives a poor approximation to the true null distribution of these test statistics. We derive a general Bartlett-type correction factor in matrix notation for the gradient test which reduces the size distortion of the test, and numerically compare the proposed test with the usual likelihood ratio, Wald, score and gradient tests, and with the Bartlett-corrected likelihood ratio and score tests, and bootstrap-corrected tests. Our simulation results suggest that the corrected test we propose can be an interesting alternative to the other tests since it leads to very accurate inference even for very small samples. We also present an empirical application for illustrative purposes.11Supplementary Material presents derivation of Bartlett-type corrections to the gradient tests, and the computer code used in Section 6 (Appendix A).

Suggested Citation

  • Vargas, Tiago M. & Ferrari, Silvia L.P. & Lemonte, Artur J., 2014. "Improved likelihood inference in generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 110-124.
  • Handle: RePEc:eee:csdana:v:74:y:2014:i:c:p:110-124
    DOI: 10.1016/j.csda.2013.12.002
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    References listed on IDEAS

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    1. Bernardo M. Lagos & Pedro A. Morettin, 2004. "Improvement of the Likelihood Ratio Test Statistic in ARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(1), pages 83-101, January.
    2. Manor, Orly & Zucker, D.M.David M., 2004. "Small sample inference for the fixed effects in the mixed linear model," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 801-817, July.
    3. Lemonte, Artur J. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2010. "Improved likelihood inference in Birnbaum-Saunders regressions," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1307-1316, May.
    4. Bai, Peng, 2009. "Sphericity test in a GMANOVA-MANOVA model with normal error," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2305-2312, November.
    5. David M. Zucker & Offer Lieberman & Orly Manor, 2000. "Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 827-838.
    6. van Giersbergen, Noud P.A., 2009. "Bartlett Correction In The Stable Ar(1) Model With Intercept And Trend," Econometric Theory, Cambridge University Press, vol. 25(3), pages 857-872, June.
    7. Artur Lemonte & Silvia Ferrari, 2012. "The local power of the gradient test," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 373-381, April.
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    Cited by:

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