Multi-level modelling under informative sampling
1 Department of Statistics, Hebrew University of Jerusalem, Jerusalem, 91905, Israel msdanny{at}huji.ac.il, 2 Department of Statistical Methods, Federal University of Rio de Janeiro, Rio de Janeiro 21945-970, Brazil fmoura{at}im.ufrj.br, 3 Escola Nacional de Ciencias Estatisticas—IBGE, Rio de Janeiro, 20231-050, Brazil pedrosilva{at}ibge.gov.br
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Abstract |
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We consider a model-dependent approach for multi-level modelling that accounts for informative probability sampling of first- and lower-level population units. The proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample, as a function of the corresponding population model and the first- and lower-level sample selection probabilities, and then fitting the resulting sample model using Bayesian methods. An important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators. A simulation experiment is carried out in order to study the performance of this approach and compare it to the use of ‘design-based’ methods. The simulation study indicates that both approaches perform in general equally well in terms of point estimation, but the model-dependent approach yields confidence/credibility intervals with better coverage properties. Another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities. The use of maximum likelihood estimation is also considered.
Key Words: Confidence interval; Credibility interval; Full likelihood; Markov chain Monte Carlo; Maximum likelihood estimation; Probability weighting; Small area estimation.
Received May 2004. Revised March 2006.