Multi-level modelling under informative sampling

Danny Pfeffermann*, Fernando Antonio Da Silva Moura, Pedro Luis Do Nascimento Silva

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)943-959
Number of pages17
JournalBiometrika
Volume93
Issue number4
DOIs
StatePublished - Dec 2006

Keywords

  • Confidence interval
  • Credibility interval
  • Full likelihood
  • Markov chain Monte Carlo
  • Maximum likelihood estimation
  • Probability weighting
  • Small area estimation

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