Consistent Parameter Estimation for Lagged Multilevel Models

Abstract

The estimation of parameters of lagged multilevel models is considered. This type of model is used in many application areas, including psychology and education, where changes in test results over time can be modelled. Standard estimation techniques are shown to give inconsistent results for this formulation of the multilevel model. For two simple assumptions concerning the nature of the model covariate a first and second difference instrument methods for consistent estimation are developed. Simulations are used to demonstrate their success in obtaining consistent parameter estimates. Use of the instrument methods with more complex multilevel models is considered.