Generalized Linear Measurement-Error Models with Multivariate t-Measurement Error

Abstract

We consider a generalized linear model with canonical link when some of the covariates are subject to measurement error. In this article we propose a likelihood based method of adjusting the estimate of the regression parameter β by replacing normal measurment error distribution with a larger and flexible class of parametric distributions in order to get obust estimates of the regression parameter. We replace the normal measurement error model with the multivariate measurement error model. We also investigate the robustness of normal measurement error model against nonnormality. We show by conducting a simulation study that the maximum likelihood estimator of the regression parameter β in a logistic regression obtained under the assumption of normal measurement error performs poorly compared to the estimator obtained by assuming t measurement error when the true measurement error model is a t-distribution with known kurtosis parameter. The likelihood estimates are obtained by applying EM alogrithm instead of directly maximizing the likelihood function which involves evaluation of a high dimensional integral and in most situations it is unmanageable.