TY - JOUR
T1 - Multi-level modelling under informative sampling
AU - Pfeffermann, Danny
AU - Da Silva Moura, Fernando Antonio
AU - Do Nascimento Silva, Pedro Luis
PY - 2006/12
Y1 - 2006/12
N2 - 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.
AB - 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.
KW - Confidence interval
KW - Credibility interval
KW - Full likelihood
KW - Markov chain Monte Carlo
KW - Maximum likelihood estimation
KW - Probability weighting
KW - Small area estimation
UR - http://www.scopus.com/inward/record.url?scp=33845784701&partnerID=8YFLogxK
U2 - 10.1093/biomet/93.4.943
DO - 10.1093/biomet/93.4.943
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AN - SCOPUS:33845784701
SN - 0006-3444
VL - 93
SP - 943
EP - 959
JO - Biometrika
JF - Biometrika
IS - 4
ER -