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Likelihood ratio tests for goodness-of-fit of a nonlinear regression model

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  • Crainiceanu, Ciprian M.
  • Ruppert, David

Abstract

We propose likelihood and restricted likelihood ratio tests for goodness-of-fit of nonlinear regression. The first-order Taylor approximation around the MLE of the regression parameters is used to approximate the null hypothesis and the alternative is modeled nonparametrically using penalized splines. The exact finite sample distribution of the test statistics is obtained for the linear model approximation and can be easily simulated. We recommend using the restricted likelihood instead of the likelihood ratio test because restricted maximum-likelihood estimates are not as severely biased as the maximum-likelihood estimates in the penalized splines framework.

Suggested Citation

  • Crainiceanu, Ciprian M. & Ruppert, David, 2004. "Likelihood ratio tests for goodness-of-fit of a nonlinear regression model," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 35-52, October.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:1:p:35-52
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    References listed on IDEAS

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    1. Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
    2. Diebolt, Jean & Zuber, Jacques, 1999. "Goodness-of-fit tests for nonlinear heteroscedastic regression models," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 53-60, March.
    3. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
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    Cited by:

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    2. Long Qu & Tobias Guennel & Scott L. Marshall, 2013. "Linear Score Tests for Variance Components in Linear Mixed Models and Applications to Genetic Association Studies," Biometrics, The International Biometric Society, vol. 69(4), pages 883-892, December.
    3. Sonja Greven & Fabian Scheipl, 2016. "Comment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1568-1573, October.
    4. Giles Hooker, 2009. "Forcing Function Diagnostics for Nonlinear Dynamics," Biometrics, The International Biometric Society, vol. 65(3), pages 928-936, September.
    5. Garrett M. Fitzmaurice & Stuart R. Lipsitz & Joseph G. Ibrahim, 2007. "A Note on Permutation Tests for Variance Components in Multilevel Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(3), pages 942-946, September.
    6. Zaixing Li & Lixing Zhu, 2010. "On Variance Components in Semiparametric Mixed Models for Longitudinal Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 442-457, September.

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