Adjusting for the Incidence of Measurement Errors in Multilevel Models Using Bootstrapping and Gibbs Sampling Techniques

Abstract

In the face of seeming dearth of objective methods of estimating measurement error variance and realistically adjusting for the incidence of measurement errors in multilevel models, researchers often indulge in the traditional approach of arbitrary choice of measurement error variance and this has the potential of giving misleading inferences. This paper employs bootstrapping and Gibbs Sampling techniques to systematically estimate measurement error variance of selected error-prone predictor variables and adjusts for measurement errors in 2 and 4 level model frameworks. Five illustrative data sets, partly supplemented through simulation, were drawn from an educational environment giving rise to the multilevel structures needed. Adjusting for the incidence of measurement errors using these techniques generally revealed coefficient estimates of error-prone predictors to have increased numerical value, increased standard error, reduced overall model deviance and reduced coefficient of variation. The techniques, however,
performed better for error-prone predictor(s) having random coefficients. It is opined that the bootstrapping and Gibbs Sampling techniques for adjusting for the incidence of measurement errors in multilevel models is systematic and realistic enough to employ in respect of error-prone predictors that have random coefficients and adjustments that are meaningful should be appraised taking into cognizance changes in the coefficient of variation alongside other traditionally expected changes that should follow measurement error djustments.
Key words: Multilevel models, Measurement error adjustment, Coefficient of variation, Predictor variables, Bootstrapping, Gibbs sampling