Simulation-based estimation methods for regression models with covariate measurement error

Kuha, Jouni Tapio (1995) Simulation-based estimation methods for regression models with covariate measurement error. University of Southampton, Doctoral Thesis.

Abstract

Estimation methods for generalized linear models with some covariates measured with error are considered. It is assumed that a response variable Y depends on a set of covariates, of which U are measured accurately but X are subject to measurement error so that surrogate variables Z are observed instead of X. The vector X may be mixed, that is it may contain both continuous and categorical variables. Two data sets are assumed to be available, a primary data set of observations (Y_i, U_i, Z_i) and a validation data set of observations (X_i, Z_i, U_i). Two types of validation data are considered, internal data sets where the distribution of X given U is the same as in the primary data, and external validation data sets where the distribution is not the same in the two data sets.

Measurement error causes bias in the estimated coefficients of the model of interest. Information on the error obtained from the validation data are utilized to take the effects of measurement error into account and compute adjusted estimates which are less biased. The estimation methods considered here are structural modelling methods where all the distributions of the observed variables are specified parametrically. Distributions for X given U and for Z given X and U are defined for mixed covariates using models based on homogenous conditional Gaussian distributions. A rejection sampling method for generating variates from the distribution of X given U, Z and Y under these models is developed.

Four simulation-based estimation methods are described: (i) data augmentation, which is a Bayesian approach and a version of the Gibbs sampling algorithm; (ii) Monte Carlo EM, a modification of the standard EM algorithm with simulation-based Monte Carlo integration used at the E-step; (iii) a method based on using Monte Carlo integration to evaluate the density function of Y given the observed data; (iv) Monte Carlo regression calibration, a first-order approximation of method (iii). The estimators are based on general computational techniques developed for missing data problems, and they are thus applicable also to other measurement error models than the ones considered here.

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