Far East Journal of Theoretical Statistics
Volume 13, Issue 2, Pages 189 - 213
(July 2004)
|
|
LINEAR REGRESSION AND LINEAR MIXED MODELS WITH CONTAMINATED COVARIATES
Yi Li (U. S. A.)
|
Abstract: This article studies several commonly adopted approaches, namely, maximal likelihood estimation (MLE), simulation extrapolation (SIMEX) and regression calibration (RC), to correcting estimation biases caused by covariate measurement errors in the linear regression models. We study these methods from the perspective of estimating equations and focus on their inter-relationships. Specifically, we show that, for simple linear regression models, these three methods yield the same estimators, while for general linear regression models, both the SIMEX and the RC are essentially the method-of-moments bias-correcting techniques, and, hence, generate the same estimators. We further discuss their applications in linear mixed models. We study robustness of the MLE and show a desirable fact that the maximal likelihood estimates are consistent as long as the covariance structures of the error-prone covariates are correctly specified. We compare via extensive simulations the finite sample performance of these methods in terms of efficiency and robustness and apply them to a beta-carotene study. |
Keywords and phrases: linear regression, linear mixed models, covariate measurement error, maximal likelihood estimation, simulation extrapolation, regression calibration, estimating equations. |
|
Number of Downloads: 266 | Number of Views: 861 |
|