Domain estimation under informative linkage

A standard assumption when modelling linked sample data is that the stochastic properties of the linking process and process underpinning the population values of the response variable are independent of one another. This is often referred to as non-informative linkage. But what if linkage errors are informative? In this paper, we provide results from two simulation experiments that explore two potential informative linking scenarios. The first is where the choice of sample record to link is dependent on the response; and the second is where the probability of correct linkage is dependent on the response. We focus on the important and widely applicable problem of estimation of domain means given linked data, and provide empirical evidence that while standard domain estimation methods can be substantially biased in the presence of informative linkage errors, an alternative estimation method, based on a Gaussian approximation to a maximum likelihood estimator that allows for non-informative linkage error, performs well.