Abstract
In this paper, we consider a linear mixed model with measurement errors in fixed effects. We find the corrected score function estimators for the variance components. An iterative algorithm is proposed for estimating the parameters. The computations on each iteration of this algorithm are those associated with computing estimates of fixed and random effects for given values of the variance components. We also derive the consistency of the estimators under regularity conditions. The simulation study shows that for relatively small sample size the corrected estimators perform very well. Finally, an example of real data is given for illustration.
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References
Anderson TW (1984) Estimating linear statistical relationships. Ann Stat 12: 1–45
Armstrong B (1985) Measurement error in the generalized linear model. Commun Stat Simul Comput 14: 529–544
Belsley DA, Kuh E, Welsch RE (1980) Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York
Carroll RJ, Stefanski LA (1997) Asymptotic theory for the SIMEX estimator in measurement error models. In: Balakrishnan N, Panchapekesan S (eds) Advances in statistical decision theory and methodology, 2nd edn. Birkholder, Berlin
Carroll RJ, Ruppert D, Stefanski LA, Crainiceanu CM (2006) Measurement error in nonlinear models. Monographs on statistics and applied probability. Chapman and Hall, London
Cheng CL, Van Ness JW (1999) Statistical regression with measurement error. Arnold, London
Cui H, Kai WN, Zhu LX (2004) Estimation in mixed effects model with errors in variables. J Multivar Anal 91: 53–73
Davidian M, Giltinan DM (1993) Some general estimation methods for nonlinear mixed-effects models. J Biopharm Stat 3: 23–55
Davidian M, Giltinan DM (1995) Nonlinear models for repeated measurements data. Chapman and Hall, London
Demidenko E, Stukel TA (2002) Efficient estimation of general linear mixed effects models. J Stat Plan Inference 104: 197–219
Diggle PJ, Liang KY, Zeger SL (1994) Analysis of longitudinal data. Clarendon Press, Oxford
Fellner WH (1986) Robust estimation of variance components. Technometrics 28: 51–60
Fuller WA (1987) Measurement error models. Wiley, New York
Gimenz P, Bolfarine H (1997) Corrected score functions in classical errors-in-variables and incidental parameter models. Austral J Stat 39: 325–344
Hanfelt JJ, Liang KY (1997) Approximate likelihood for generalized linear errors-in-variables models. J R Stat Soc Ser B 59: 627–637
Harrison D, Rubinfeld DL (1978) Hedonic housing prices and the demand for clean air. J Environ Econ Manag 5: 81–102
Harvill DA (1977) Maximum likelihood approaches to variance component estimation and related problems (with discussion). J Am Stat Assoc 72: 320–340
Johnson DL, Thompson R (1995) Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information. J Dairy Sci 78: 449–456
Karcher P, Wang Y (2001) Generalized nonparametric mixed effects models. J Comput Graph Stat 10: 641–655
Lee Y, Nelder NA (1996) Hierarchical generalized linear models (with discussion). J R Stat Soc Ser B 58: 619–678
McCulloch CE, Searle SR, Neuhaus JM (2008) Generalized, linear and mixed models. Wiley, New York
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
Schall R (1991) Estimation in generalized linear models with random effects. Biometrika 78: 719–727
Stefanski LA, Carroll RJ (1987) Conditional scores and optimal scores for generalized linear measurement error models. Biometrika 74: 703–716
Stefanski LA, Carroll RJ (1991) Deconvolution-based score tests in measurement error models. Ann Stat 19: 249–259
Vonesh EF, Wang H, Nie L, Majumdar D (2002) Conditional second-order generalized estimation equations for generalized linear and nonlinear mixed-effects models. J Am Stat Assoc 97: 271–291
Wang N, Lin X, Gutierrez RG, Carroll RJ (1998) Bias analysis and SIMEX approach in generalized linear mixed measurement error models. J Am Stat Assoc 93: 249–261
Zhong XP, Fung WK, Wei BC (2002) Estimation in linear models with random effects and errors-in-variables. Ann Inst Math Stat 54: 595–606
Zhong XP, Wei BC, Fung WK (2000) Influence analysis for linear measurement error models. Ann Inst Stat Math 52: 367–379
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Zare, K., Rasekh, A. & Rasekhi, A.A. Estimation of variance components in linear mixed measurement error models. Stat Papers 53, 849–863 (2012). https://doi.org/10.1007/s00362-011-0387-0
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DOI: https://doi.org/10.1007/s00362-011-0387-0