Domain estimation under informative linkage

ABSTRACT

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.

KEYWORDS:

• Non-deterministic data linkage
• exchangeable linkage errors
• informative sampling
• auxiliary information
• domain estimation
• maximum likelihood

ORCID

Nicola Salvati http://orcid.org/0000-0002-4160-9387

Enrico Fabrizi http://orcid.org/0000-0003-2504-7043

Additional information

Notes on contributors

Ray Chambers

Ray Chambers is Honorary Professorial Fellow at the National Institute for Applied Statistics Research Australia. His research is focused on robust model–based methods for inference from complex data, and particularly where this complexity arises through integration of data from multiple sources.

Nicola Salvati

Nicola Salvati is associate professor in Statistics at the University of Pisa, Pisa, Italy. He holds a PhD in Applied Statistics from the Department of Statistics ‘G. Parenti’, University of Florence. His research interests cover robust statistics, small area estimation, survey sampling methodology, quantile and M-quantile regression, multilevel models and spatial statistics.

Enrico Fabrizi

Enrico Fabrizi is associate professor in Statistics at the University Cattolica del Sacro Cuore (Catholic University of the Sacred Heart), Milan, Italy. He holds a PhD in Statistics from the Department of Statistics, University of Bologna. His research interests cover survey sampling methodology, Bayesian inference applied to the analysis of complex survey data and small area estimation.

Andrea Diniz da Silva

Andrea Diniz da Silva is a Professor in the National School of Statistical Science, Rio de Janeiro, Brazil and holds a PhD in Public Statistics from the same institution. She is also a senior statistician in the Methodology Department of the Brazilian Institute of Geography and Statistics.