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

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 tomoment-based inference. The second employs calibration probabilities and leads tomaximum 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.