Covariance analysis in generalized linear measurement error models

Abstract

We summarize some of the recent work on the errors-in-variables problem in generalized linear models. The focus is on covariance analysis, and in particular testing for and estimation of treatment effects. There is a considerable difference between the randomized and non-randomized models when testing for an effect. In randomized studies, simple techniques exist for testing for a treatment effect. In some instances, such as linear and multiplicative regression, simple methods exist for estimating the treatment effect. In other examples such as logistic regression, estimating a treatment effect requires careful attention to measurement error. In non-randomized studies, there is no recourse to understanding and modelling measurement error. In particular ignoring measurement error can lead to the wrong conclusions, for example the true but unobserved data may indicate a positive effect for treatment, while the observed data indicate the opposite. Some of the possible methods are outlined and compared.