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Limited information likelihood analysis of survey data

Limited information likelihood analysis of survey data
Limited information likelihood analysis of survey data
Analysts of survey data are often interested in modelling the population process, or superpopulation, that gave rise to a 'target' set of survey variables. An important tool for this is maximum likelihood estimation. A survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which needs to be incorporated into the analysis. We consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables, and only sample values of these are available. Strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case, but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator. In a simulation study, this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature.
1369-7412
397-411
Chambers, R.L.
df4b494f-3260-4198-8137-3bf1d9c60fa2
Dorfman, A.H.
ee24f795-5a10-4cd5-9457-e74db8fbbccc
Wang, S.
8bce5bdb-420c-4b22-b009-8f4ce1febaa8
Chambers, R.L.
df4b494f-3260-4198-8137-3bf1d9c60fa2
Dorfman, A.H.
ee24f795-5a10-4cd5-9457-e74db8fbbccc
Wang, S.
8bce5bdb-420c-4b22-b009-8f4ce1febaa8

Chambers, R.L., Dorfman, A.H. and Wang, S. (1998) Limited information likelihood analysis of survey data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60 (2), 397-411. (doi:10.1111/1467-9868.00132).

Record type: Article

Abstract

Analysts of survey data are often interested in modelling the population process, or superpopulation, that gave rise to a 'target' set of survey variables. An important tool for this is maximum likelihood estimation. A survey is said to provide limited information for such inference if data used in the design of the survey are unavailable to the analyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which needs to be incorporated into the analysis. We consider the case where these inclusion probabilities can be modelled in terms of a linear combination of the design and target variables, and only sample values of these are available. Strict maximum likelihood estimation of the underlying superpopulation means of these variables appears to be analytically impossible in this case, but an analysis based on approximations to the inclusion probabilities leads to a simple estimator which is a close approximation to the maximum likelihood estimator. In a simulation study, this estimator outperformed several other estimators that are based on approaches suggested in the sampling literature.

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Published date: 1998

Identifiers

Local EPrints ID: 34169
URI: http://eprints.soton.ac.uk/id/eprint/34169
ISSN: 1369-7412
PURE UUID: 96d7cc84-38c8-42b0-a797-4656cfaeb2c6

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Date deposited: 11 Jan 2008
Last modified: 15 Mar 2024 07:46

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Contributors

Author: R.L. Chambers
Author: A.H. Dorfman
Author: S. Wang

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