The University of Southampton
University of Southampton Institutional Repository

Interval estimation for log-linear models with one variable subject to non-ignorable non-response

Interval estimation for log-linear models with one variable subject to non-ignorable non-response
Interval estimation for log-linear models with one variable subject to non-ignorable non-response
Log-linear models for multiway contingency tables where one variable is subject to non-ignorable non-response will often yield boundary solutions, with the probability of non-respondents being classified in some cells of the table estimated as 0. The paper considers the effect of this non-standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator. The first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix. It is shown that the information matrix is singular for boundary solutions, but intervals can be calculated after a simple transformation. For the second method, based on the bootstrap, asymptotic results suggest that the coverage properties may be poor for boundary solutions. Both methods are compared with profile likelihood intervals in a simulation study based on data from the British General Election Panel Study. The results of this study indicate that all three methods perform poorly for a parameter of the non-response model, whereas they all perform well for a parameter of the margin model, irrespective of whether or not there is a boundary solution.
bootstrap, boundary solutions, categorical data, confidence intervals, informative non-response, profile likelihood
1369-7412
357-368
Clarke, P. S.
d262b147-f175-4c40-820b-fdb3940117cf
Smith, P. W. F.
961a01a3-bf4c-43ca-9599-5be4fd5d3940
Clarke, P. S.
d262b147-f175-4c40-820b-fdb3940117cf
Smith, P. W. F.
961a01a3-bf4c-43ca-9599-5be4fd5d3940

Clarke, P. S. and Smith, P. W. F. (2004) Interval estimation for log-linear models with one variable subject to non-ignorable non-response. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66 (2), 357-368. (doi:10.1111/j.1369-7412.2003.04973.x).

Record type: Article

Abstract

Log-linear models for multiway contingency tables where one variable is subject to non-ignorable non-response will often yield boundary solutions, with the probability of non-respondents being classified in some cells of the table estimated as 0. The paper considers the effect of this non-standard behaviour on two methods of interval estimation based on the distribution of the maximum likelihood estimator. The first method relies on the estimator being approximately normally distributed with variance equal to the inverse of the information matrix. It is shown that the information matrix is singular for boundary solutions, but intervals can be calculated after a simple transformation. For the second method, based on the bootstrap, asymptotic results suggest that the coverage properties may be poor for boundary solutions. Both methods are compared with profile likelihood intervals in a simulation study based on data from the British General Election Panel Study. The results of this study indicate that all three methods perform poorly for a parameter of the non-response model, whereas they all perform well for a parameter of the margin model, irrespective of whether or not there is a boundary solution.

This record has no associated files available for download.

More information

Published date: 2004
Additional Information: (Statistical Methodology)
Keywords: bootstrap, boundary solutions, categorical data, confidence intervals, informative non-response, profile likelihood

Identifiers

Local EPrints ID: 34762
URI: http://eprints.soton.ac.uk/id/eprint/34762
ISSN: 1369-7412
PURE UUID: 3c8dffaa-b770-4301-979e-2c54d423a53a
ORCID for P. W. F. Smith: ORCID iD orcid.org/0000-0003-4423-5410

Catalogue record

Date deposited: 16 May 2006
Last modified: 16 Mar 2024 02:42

Export record

Altmetrics

Contributors

Author: P. S. Clarke
Author: P. W. F. Smith ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×