Abstract
The independent variables of linear mixed models are subject to measurement errors in practice. In this paper, we present a unified method for the estimation in linear mixed models with errors-in-variables, based upon the corrected score function of Nakamura (1990, Biometrika, 77, 127–137). Asymptotic normality properties of the estimators are obtained. The estimators are shown to be consistent and convergent at the order of n −1/2. The performance of the proposed method is studied via simulation and the analysis of a data set on hedonic housing prices.
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References
Armstrong, B. (1985). Measurement error in the generalized linear model, Comm. Statist. Simulation Comput., 14, 529–544.
Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, J. Amer. Statist. Assoc., 88, 9–25.
Buzas, J. S. and Stefanski, L. A. (1996). A note on corrected-score estimation, Statist. Probab. Lett., 28, 1–8.
Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement Error in Nonlinear Models, Chapman and Hall, London.
Davidian, M. and Giltinan, D. M. (1995). Nonlinear Models for Repeated Measurement Data, Chapman and Hall, London.
Diggle, P. J., Liang, K. Y. and Zeger, S. L. (1994). Analysis of Longitudinal Data, Clarendon Press, Oxford.
Fellner, W. H. (1986). Robust estimation of variance components, Technometrics, 28, 51–60.
Fuller, W. A. (1987). Measurement Error Models, Wiley, New York.
Gimenz, P. and Bolfarine, H. (1997). Corrected score functions in classical error-in-variables and incidental parameter models, Austral. J. Statist., 39, 325–344.
Hanfelt, J. J. and Liang K. Y. (1997). Approximate likelihood for generalized linear errors-in-variables models, J. Roy. Statist. Soc. Ser. B, 59, 627–637.
Harrison, D. and Rubinfeld, D. L. (1978). Hedonic housing prices and the demand for clean air, Journal of Environmental Economics and Management, 5, 81–102.
Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and related problems (with discussion), J. Amer. Statist. Assoc., 72, 320–340.
Lee, Y. and Nelder, N. A. (1996). Hierarchical generalized linear models (with discussion), J. Roy. Statist. Soc. Ser. B, 58, 619–678.
Lin, X. and Breslow, N. E. (1996). Bias correction in generalized linear models with multiple components of dispersion, J. Amer. Statist. Assoc., 91, 1007–1016.
Lin, X. and Carroll, R. J. (1999). SIMEX variance component tests in generalized linear mixed measurement error models, Biometrics, 55, 613–619.
Liu, Q. and Pierce, D. A. (1993). Heterogeneity in Mantel-Haenzel-Type models, Biometrika, 80, 543–556.
Nakamura, T. (1990). Corrected score function for errors-in-variables models: Methodology and application to generalized linear models, Biometrika, 77, 127–137.
Nakamura, T. (1992). Proportional hazards model with covariates subject to measurement error, Biometrics, 48, 829–838.
Palta, M. and Lin, C.-Y. (1996). Latent variables, measurement error and method for analyzing longitudinal ordinal data, Proceedings of American Statistical Association in Biometrics, 340–345.
Robinson, G. K. (1991). That BLUP is a good thing: The estimation of random effects (with discussion), Statist. Sci., 6, 15–51.
Schall, R. (1991). Estimation in generalized linear models with random effects, Biometrika, 78, 719–727.
Stefanski, L. A. and Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement error models, Biometrika, 74, 703–716.
Stefanski, L. A. and Carroll, R. J. (1990). Score tests in generalized linear measurement error models, J. Roy. Statist. Soc. Ser. B, 52, 345–359.
Wang, N., Lin, X., Gutierrez, R. G. and Carroll, R. J. (1998). Bias analysis and SIMEX approach in generalized linear mixed measurement error models, J. Amer. Statist. Assoc., 93, 249–261.
Zhong, X. P., Wei, B. C. and Fung, W. K. (2000). Influence analysis for linear measurement error models, Ann. Inst. Statist. Math., 52, 367–379.
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Zhong, XP., Fung, WK. & Wei, BC. Estimation in Linear Models with Random Effects and Errors-in-Variables. Annals of the Institute of Statistical Mathematics 54, 595–606 (2002). https://doi.org/10.1023/A:1022467212133
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DOI: https://doi.org/10.1023/A:1022467212133