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Maximum Likelihood Under Response Biased Sampling

Maximum Likelihood Under Response Biased Sampling
Maximum Likelihood Under Response Biased Sampling
Informative sampling occurs when the probability of inclusion in sample depends on the value of the survey response variable. Response or size biased sampling is a particular case of informative sampling where the inclusion probability is proportional to the value of this variable. In this paper we describe a general model for response biased sampling, which we call array sampling, and develop maximum likelihood and estimating equation theory appropriate to this situation. The Missing Information Principle (MIP) (Orchard and Woodbury, 1972) yields one (indirect) approach to likelihood based survey inference (Breckling et al 1994). Some have questioned its applicability in the case of informative sampling, because of the way it conditions on the given sample. In this paper we describe a direct approach and show that it and the MIP-based approach lead to identical results under array sampling. Comparison is made to the weighted likelihood based approach described in Krieger and Pfeffermann (1992). Extensions to the theory are also explored.
M03/18
Southampton Statistical Sciences Research Institute
Chambers, Raymond
68685a02-e1d0-4143-b5d4-0e91ff0e3d02
Dorfman, Alan
1ed85e51-d32c-4e29-a759-f35b6388006a
Wang, Suojin
87b7d7d7-ce66-4870-8f0b-d0f809542122
Chambers, Raymond
68685a02-e1d0-4143-b5d4-0e91ff0e3d02
Dorfman, Alan
1ed85e51-d32c-4e29-a759-f35b6388006a
Wang, Suojin
87b7d7d7-ce66-4870-8f0b-d0f809542122

Chambers, Raymond, Dorfman, Alan and Wang, Suojin (2003) Maximum Likelihood Under Response Biased Sampling (S3RI Methodology Working Papers, M03/18) Southampton, UK. Southampton Statistical Sciences Research Institute 21pp.

Record type: Monograph (Project Report)

Abstract

Informative sampling occurs when the probability of inclusion in sample depends on the value of the survey response variable. Response or size biased sampling is a particular case of informative sampling where the inclusion probability is proportional to the value of this variable. In this paper we describe a general model for response biased sampling, which we call array sampling, and develop maximum likelihood and estimating equation theory appropriate to this situation. The Missing Information Principle (MIP) (Orchard and Woodbury, 1972) yields one (indirect) approach to likelihood based survey inference (Breckling et al 1994). Some have questioned its applicability in the case of informative sampling, because of the way it conditions on the given sample. In this paper we describe a direct approach and show that it and the MIP-based approach lead to identical results under array sampling. Comparison is made to the weighted likelihood based approach described in Krieger and Pfeffermann (1992). Extensions to the theory are also explored.

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Published date: 2003

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Local EPrints ID: 8168
URI: http://eprints.soton.ac.uk/id/eprint/8168
PURE UUID: afe14be2-b4c4-451d-b87f-9fc8deb71472

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Date deposited: 11 Jul 2004
Last modified: 11 Dec 2021 13:25

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Contributors

Author: Raymond Chambers
Author: Alan Dorfman
Author: Suojin Wang

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