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Diagnostic Measures for Generalized Linear Models with Missing Covariates

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  • HONGTU ZHU
  • JOSEPH G. IBRAHIM
  • XIAOYAN SHI

Abstract

. In this paper, we carry out an in‐depth investigation of diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for generalized linear models. Our diagnostic measures include case‐deletion measures and conditional residuals. We use the conditional residuals to construct goodness‐of‐fit statistics for testing possible misspecifications in model assumptions, including the sampling distribution. We develop specific strategies for incorporating missing data into goodness‐of‐fit statistics in order to increase the power of detecting model misspecification. A resampling method is proposed to approximate the p‐value of the goodness‐of‐fit statistics. Simulation studies are conducted to evaluate our methods and a real data set is analysed to illustrate the use of our various diagnostic measures.

Suggested Citation

  • Hongtu Zhu & Joseph G. Ibrahim & Xiaoyan Shi, 2009. "Diagnostic Measures for Generalized Linear Models with Missing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 686-712, December.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:4:p:686-712
    DOI: 10.1111/j.1467-9469.2009.00644.x
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    References listed on IDEAS

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    1. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    2. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
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    5. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz, 1999. "Monte Carlo EM for Missing Covariates in Parametric Regression Models," Biometrics, The International Biometric Society, vol. 55(2), pages 591-596, June.
    6. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    7. 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.
    8. Winfried Stute & Li‐Xing Zhu, 2002. "Model Checks for Generalized Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 535-545, September.
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    Cited by:

    1. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    2. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.

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