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Weighting for unequal selection probabilities in multilevel models

Pfeffermann, D., Skinner, C.J., Holmes, D.J., Goldstein, H. and Rasbash, J. (1998) Weighting for unequal selection probabilities in multilevel models Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60, (1), pp. 23-40. (doi:10.1111/1467-9868.00106).

Record type: Article

Abstract

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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Published date: 1998

Identifiers

Local EPrints ID: 34236
URI: http://eprints.soton.ac.uk/id/eprint/34236
ISSN: 1369-7412
PURE UUID: 28263fa8-a8eb-4709-93f4-f8d1abcbc643

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Date deposited: 11 Feb 2008
Last modified: 17 Jul 2017 15:50

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Contributors

Author: D. Pfeffermann
Author: C.J. Skinner
Author: D.J. Holmes
Author: H. Goldstein
Author: J. Rasbash

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