Title: Modelling multilevel data under complex sampling designs: An empirical likelihood approach
Authors: Yves Berger - University of Southampton (United Kingdom) [presenting]
Melike Oguz-Alper - Statistics Norway (Norway)
Abstract: Data used in social, behavioural, health or biological sciences may have a hierarchical structure due to the population of interest or the sampling design. Multilevel are often used to analyse such hierarchical data, or to estimate small domains means. These data are often selected with unequal probabilities from a clustered and stratified population. Inference may be invalid when the sampling design is informative. We propose a design-based empirical likelihood approach for the regression parameters of a multilevel model. It has the advantage of taking into account of the informative effect of the sampling design. This approach can be used for point estimation, hypothesis testing and confidence intervals for the sub-vector of parameters. It can be also used for estimation of small domains means. It provides asymptotically valid inference for the finite population parameters. The simulation study shows the advantages of the empirical likelihood approach over alternative approaches used for multilevel models. We applied our approach to the Programme for International Student Assessment (PISA) survey data. We show that the proposed approach can give more accurate and different p-values than the naive restricted maximum likelihood approach, which ignores the survey weights.