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Transformed goodness-of-fit statistics for a generalized linear model of binary data

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  • Taneichi, Nobuhiro
  • Sekiya, Yuri
  • Toyama, Jun

Abstract

In a generalized linear model of binary data, we consider models based on a general link function including a logistic regression model and a probit model as special cases. For testing the null hypothesis H0 that the considered model is correct, we consider a family of ϕ-divergence goodness-of-fit test statistics Cϕ that includes a power divergence family of statistics Ra. We propose a transformed Cϕ statistics that improves the speed of convergence to a chi-square limiting distribution and show numerically that the transformed Ra statistic performs well. We also give a real data example of the transformed Ra statistic being more reliable than the original Ra statistic for testing H0.

Suggested Citation

  • Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2014. "Transformed goodness-of-fit statistics for a generalized linear model of binary data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 311-329.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:311-329
    DOI: 10.1016/j.jmva.2013.09.014
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    References listed on IDEAS

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    1. Sekiya, Yuri & Taneichi, Nobuhiro, 2004. "Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 199-223, November.
    2. Taneichi, Nobuhiro & Sekiya, Yuri & Suzukawa, Akio, 2002. "Asymptotic Approximations for the Distributions of the Multinomial Goodness-of-Fit Statistics under Local Alternatives," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 335-359, May.
    3. Fujikoshi, Yasunori, 2000. "Transformations with Improved Chi-Squared Approximations," Journal of Multivariate Analysis, Elsevier, vol. 72(2), pages 249-263, February.
    4. Taneichi, Nobuhiro & Sekiya, Yuri & Toyama, Jun, 2011. "Improved transformed deviance statistic for testing a logistic regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(9), pages 1263-1279, October.
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