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Likelihood inference in generalized linear mixed measurement error models

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  • Torabi, Mahmoud

Abstract

The generalized linear mixed models (GLMMs) for clustered data are studied when covariates are measured with error. The most conventional measurement error models are based on either linear mixed models (LMMs) or GLMMs. Even without the measurement error, the frequentist analysis of LMM, and particularly of GLMM, is computationally difficult. On the other hand, Bayesian analysis of LMM and GLMM is computationally convenient in both cases without and with the measurement error. Recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. As an application of data cloning, we conduct a frequentist analysis of GLMM with covariates subject to the measurement error model. The performance of the proposed approach which yields the maximum likelihood estimation is evaluated by two important real data types, Normal and logistic linear mixed measurement error models, and also through simulation studies.

Suggested Citation

  • Torabi, Mahmoud, 2013. "Likelihood inference in generalized linear mixed measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 549-557.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:549-557
    DOI: 10.1016/j.csda.2012.07.018
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    References listed on IDEAS

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    1. Torabi, Mahmoud, 2012. "Small area estimation using survey weights under a nested error linear regression model with structural measurement error," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 52-60.
    2. Torabi, Mahmoud & Shokoohi, Farhad, 2012. "Likelihood inference in small area estimation by combining time-series and cross-sectional data," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 213-221.
    3. A. Guolo, 2008. "A Flexible Approach to Measurement Error Correction in Case–Control Studies," Biometrics, The International Biometric Society, vol. 64(4), pages 1207-1214, December.
    4. Hamilton, James D., 1986. "A standard error for the estimated state vector of a state-space model," Journal of Econometrics, Elsevier, vol. 33(3), pages 387-397, December.
    5. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
    6. Raymond J. Carroll & Kathryn Roeder & Larry Wasserman, 1999. "Flexible Parametric Measurement Error Models," Biometrics, The International Biometric Society, vol. 55(1), pages 44-54, March.
    7. Mahmoud Torabi & Gauri S. Datta & J. N. K. Rao, 2009. "Empirical Bayes Estimation of Small Area Means under a Nested Error Linear Regression Model with Measurement Errors in the Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 355-369, June.
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    Cited by:

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    3. Gul Inan & Ozlem Ilk, 2019. "A marginalized multilevel model for bivariate longitudinal binary data," Statistical Papers, Springer, vol. 60(3), pages 601-628, June.

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