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Some restriction tests in a new class of regression models for proportions

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  • Melo, Tatiane F.N.
  • Vasconcellos, Klaus L.P.
  • Lemonte, Artur J.

Abstract

The main purpose of this work is to study the behaviour of Skovgaard's [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian Journal of Probability and Statistics 19, 13-31]. We show that, for our model, Skovgaard's adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed.

Suggested Citation

  • Melo, Tatiane F.N. & Vasconcellos, Klaus L.P. & Lemonte, Artur J., 2009. "Some restriction tests in a new class of regression models for proportions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3972-3979, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:3972-3979
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    References listed on IDEAS

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    1. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    2. Ib M. Skovgaard, 2001. "Likelihood Asymptotics," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 3-32, March.
    3. Wuyang Hu, 2004. "Trading off health, environmental and genetic modification attributes in food," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 31(3), pages 389-408, September.
    4. Gueorguieva, Ralitza & Rosenheck, Robert & Zelterman, Daniel, 2008. "Dirichlet component regression and its applications to psychiatric data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5344-5355, August.
    5. Ferrari, Silvia L.P. & Cysneiros, Audrey H.M.A., 2008. "Skovgaard's adjustment to likelihood ratio tests in exponential family nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3047-3055, December.
    6. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
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    Cited by:

    1. Souza Debora F. & Moura Fernando A. S., 2016. "Multivariate Beta Regression with Application in Small Area Estimation," Journal of Official Statistics, Sciendo, vol. 32(3), pages 747-768, September.

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