Multi-level modelling under informative sampling

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 functi...

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Bibliographic Details
Published in:Biometrika 2006-12, Vol.93 (4), p.943-959
Main Authors: Pfeffermann, Danny, Da Silva Moura, Fernando Antonio, Do Nascimento Silva, Pedro Luis
Format: Article
Language:English
Subjects:
Applications
Bayesian analysis
Biology, psychology, social sciences
Confidence interval
Credibility
Credibility interval
Estimation bias
Estimators
Exact sciences and technology
Experimental design
Experiments
Full likelihood
Markov analysis
Markov chain Monte Carlo
Mathematics
Maximum likelihood estimation
Modeling
Multilevel models
Musical intervals
Parametric models
Population
Probability
Probability and statistics
Probability weighting
Proposals
Sampling
Sampling bias
Sampling methods
Sampling theory, sample surveys
Schools
Sciences and techniques of general use
Simulation
Small area estimation
Statistics
Studies
Term weighting
Test data
Variables
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Summary: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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/93.4.943