The DOI matches its Crossref record; 9 of the 9 references it cites were found in a registry or an index.
Weighting for Unequal Selection Probabilities in Multilevel Models
Abstract
Summary: When multilevel models are estimated from survey data derived using multistage sampling, unequal selection probabilities at any stage of sampling may induce bias in standard estimators, unless the sources of the unequal probabilities are fully controlled for in the covariates. This paper proposes alternative ways of weighting the estimation of a two-level model by using the reciprocals of the selection probabilities at each stage of sampling. Consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase. Scaling of the weights is proposed to improve the properties of the estimators and to simplify computation. Variance estimators are also proposed. In a limited simulation study the scaled weighted estimators are found to perform well, although non-negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small. The variance estimators perform extremely well. The procedures are illustrated using data from the survey of psychiatric morbidity.
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Cites
RUBIN, D. B. (1976) · Biometrika · doi:10.1093/biomet/63.3.581 · Cited by 9,925
On the Variances of Asymptotically Normal Estimators from Complex Surveys
Binder, D. A. (1983) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1402588 · Cited by 982
Multilevel mixed linear model analysis using iterative generalized least squares
GOLDSTEIN, H. (1986) · Biometrika · doi:10.1093/biomet/73.1.43 · Cited by 802
Self-citationThe Role of Sampling Weights When Modeling Survey Data
Pfeffermann, D. (1993) · International Statistical Review / Revue Internationale de Statistique · doi:10.2307/1403631 · Cited by 591
Self-citationSurvey Design under the Regression Superpopulation Model
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Asymptotically Efficient Estimation of Covariance Matrices with Linear Structure
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The prevalence of psychiatric morbidity among adults living in private households
Meltzer, H. (1995) · OpenGrey (Institut de l'Information Scientifique et Technique) · Cited by 200
Psychiatric morbidity: a multilevel approach to regional variations in the UK.
Duncan, C., Jones, K., & Moon, G. (1995) · Journal of Epidemiology & Community Health · doi:10.1136/jech.49.3.290 · Cited by 110
Modelling the sampling design in the analysis of health surveys
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Cited by
Improving predictive inference under covariate shift by weighting the log-likelihood function
Shimodaira, H. (2000) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(00)00115-4 · Cited by 1,678
Dataset Shift in Machine Learning
(2008) · doi:10.7551/mitpress/9780262170055.001.0001 · Cited by 1,553
Advances in Analysis of Longitudinal Data
Gibbons, R. D., Hedeker, D., & DuToit, S. (2010) · Annual Review of Clinical Psychology · doi:10.1146/annurev.clinpsy.032408.153550 · Cited by 452
Liu, S., Wu, X., Lopez, A. D., Wang, L., Cai, Y., Page, A., Yin, P., Liu, Y., Li, Y., Liu, J., et al. (2016) · Bulletin of the World Health Organization · doi:10.2471/blt.15.153148 · Cited by 395
General Multi-Level Modeling with Sampling Weights
Asparouhov, T. (2006) · Communications in Statistics - Theory and Methods · doi:10.1080/03610920500476598 · Cited by 296
Metadata
- Authors
- Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., & Rasbash, J.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1998-01-01
- Volume
- 60
- Issue
- 1
- Pages
- 23-40
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2121909644
- Cited by
- 438
- References
- 9
- FWCI
- 3.50
- Type
- journal article
- Language
- en
- Open access
- closed
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- Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., & Rasbash, J. (1998). Weighting for Unequal Selection Probabilities in Multilevel Models. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/1467-9868.00106
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
