Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 42030, 13 pages
Estimating from cross-sectional categorical data subject to misclassification and double sampling: Moment-based, maximum likelihood and quasi-likelihood approaches
1 Centre for Longitudinal Studies (CLS), Institute of Education, University of London, 20 Bedford Way, London WC1H 0AL, United Kingdom
2Southampton Statistical Sciences Research Institute, University of Southampton, United Kingdom
3School of Mathematics and Applied Statistics, University of Wollongong, Northfields Ave, Wollongong 2500, NSW, Australia
Received 1 October 2004; Revised 6 May 2005; Accepted 21 July 2005
Copyright © 2006 Nikos Tzavidis and Yan-Xia Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We discuss alternative approaches for estimating from cross-sectional categorical data in the presence of
misclassification. Two parameterisations of the misclassification model are reviewed. The first employs misclassification
probabilities and leads to moment-based inference. The second employs calibration probabilities and leads to maximum likelihood inference. We show that maximum likelihood estimation can be alternatively performed by employing misclassification probabilities and a missing data specification. As an alternative to maximum likelihood estimation we propose a quasi-likelihood parameterisation of the misclassification model. In this context an explicit definition of the likelihood function is avoided and a different way of resolving a missing data problem is provided.
Variance estimation for the alternative point estimators is considered. The different approaches are illustrated using real data from the UK Labour Force Survey and simulated data.