Journal of Applied Mathematics and Decision Sciences 
Volume 2006 (2006), Article ID 42030, 13 pages
doi:10.1155/JAMDS/2006/42030

Estimating from cross-sectional categorical data subject to misclassification and double sampling: Moment-based, maximum likelihood and quasi-likelihood approaches

Nikos Tzavidis1,2 and Yan-Xia Lin3

 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

Abstract

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.