Adjustment for measurement error in multilevel analysis
Measurements in educational research are often subject to error. Where it is desired to base conclusions on underlying characteristics rather than on the raw measurements of them, it is necessary to adjust for measurement error in the modelling process. In this thesis it is shown how the classical model for measurement error may be extended to model the more complex structures of error variance and covariance that typically occur in multilevel models, particularly multivariate multilevel models, with continuous response. For these models parameter estimators are derived, with adjustment based on prior values of the measurement error variances and covariances among the response and explanatory variables. A straightforward method of specifring these prior values is presented. In simulations using data with known characteristics the new procedure is shown to be effective in reducing the biases in parameter estimates that result from unadjusted estimation. Improved estimates of the standard errors also are demonstrated. In particular, random coefficients of variables with error are successfully estimated. The estimation procedure is then used in a two-level analysis of an educational data set. It is shown how estimates and conclusions can vary, depending on the degree of measurement error that is assumed to exist in explanatory variables at level 1 and level 2. The importance of obtaining satisfactory prior estimates of measurement error variances and covariances, and of correctly adjusting for them during analysis, is demonstrated.