Theoretical Analysis of Mixed-Effects Models with Minimized Measurement Error

Abstract

The prevalence of binary outcomes in some areas of studies like Genetics, Environmental and Behaviorial sciences serves is very interesting to many researches in modelling. In such areas, the use of error-prone variables instead of unobserved variables, is very common and that often leads to bias in naive estimators. In this paper we describe how changes in each of the parameters in our model affect the bias in the naive estimators, in the situation where the others are held constant. The model we considered in the study has several advantages. First, it is a contribution to statistical modelling and analysis involving categorical responses. We analyzed the bias patterns, first, for a model with measurement error in covariate; then we did the same for model with Misclassification in covariate, and finally, for a model with both measurement error and misclassification in covariates. For the model with measurement error, we confirmed that the bias in naive estimators increase as the variance of measurement error increases. Most of the well known measurement error has drawn similar conclusion.