Fitting Multivariate Multilevel Models under Informative Sampling

Abstract

A model-dependent approach for multivariate multilevel normal modelling that accounts for informative sampling of group and unit level population elements is developed. The approach involves extracting the multilevel model holding for the sample data, given the selected sample, as a function of the corresponding population model and the sample selection probabilities, and then fitting the resulting sample model using Bayesian methods. A model-based simulation study is carried out to study the performance of our approach under one scenario motivated by a Brazilian nationwide proficiency assessment exercise. Results indicate that our approach enables improved inference under the informative sampling considered.