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), 23-40. (doi:10.1111/1467-9868.00106).

Download

Full text not available from this repository.

Original Publication URL: http://dx.doi.org/10.1111/1467-9868.00106

Description/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.

Item Type: Article
ISSNs: 1369-7412 (print)
Related URLs:
Subjects: H Social Sciences > HA Statistics
Divisions: University Structure - Pre August 2011 > School of Social Sciences > Social Statistics
ePrint ID: 34236
Date Deposited: 11 Feb 2008
Last Modified: 27 Mar 2014 18:21
URI: http://eprints.soton.ac.uk/id/eprint/34236

Actions (login required)

View Item View Item