Results on point and interval estimation for log-linear models with non-ignorable non-response
Results on point and interval estimation for log-linear models with non-ignorable non-response
It is common that log-linear models for multi-way contingency tables with one variable subject to non-ignorable non-response will yield non-response boundary solutions, where the probability of non-respondents being classified in certain cells of the table is estimated to be zero, resulting in infinite estimates for some of the log-linear parameters. This paper investigates the effect of such non-standard behaviour on the maximum likelihood estimator. Provided that the model parameters are identifiable from infinite samples, it is demonstrated that: 1) existence and uniqueness of the maximum likelihood estimates is assured under weak conditions; and 2) the maximum likelihood estimator is consistent and asymptotically normal. However, boundary solutions do result in a singular information matrix, which prevents calculating confidence intervals based on a normal approximation to the maximum likelihood estimator; it is shown that these singularities can be removed by a simple transformation of the log-linear parameters.
Southampton Statistical Sciences Research Institute, University of Southampton
Clarke, Paul S.
7f5256f9-da31-4af8-8c93-ebb6cdb0037e
Smith, Peter
961a01a3-bf4c-43ca-9599-5be4fd5d3940
2003
Clarke, Paul S.
7f5256f9-da31-4af8-8c93-ebb6cdb0037e
Smith, Peter
961a01a3-bf4c-43ca-9599-5be4fd5d3940
Clarke, Paul S. and Smith, Peter
(2003)
Results on point and interval estimation for log-linear models with non-ignorable non-response
(S3RI Methodology Working Papers, M03/23)
Southampton, UK.
Southampton Statistical Sciences Research Institute, University of Southampton
16pp.
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Monograph
(Project Report)
Abstract
It is common that log-linear models for multi-way contingency tables with one variable subject to non-ignorable non-response will yield non-response boundary solutions, where the probability of non-respondents being classified in certain cells of the table is estimated to be zero, resulting in infinite estimates for some of the log-linear parameters. This paper investigates the effect of such non-standard behaviour on the maximum likelihood estimator. Provided that the model parameters are identifiable from infinite samples, it is demonstrated that: 1) existence and uniqueness of the maximum likelihood estimates is assured under weak conditions; and 2) the maximum likelihood estimator is consistent and asymptotically normal. However, boundary solutions do result in a singular information matrix, which prevents calculating confidence intervals based on a normal approximation to the maximum likelihood estimator; it is shown that these singularities can be removed by a simple transformation of the log-linear parameters.
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Published date: 2003
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Local EPrints ID: 8173
URI: http://eprints.soton.ac.uk/id/eprint/8173
PURE UUID: d515a252-3ab8-4d08-b5b0-6a91b94282e8
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Date deposited: 11 Jul 2004
Last modified: 16 Mar 2024 02:41
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Author:
Paul S. Clarke
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