Most probability-based methods used to link records from two distinct data sets
corresponding to the same target population do not lead to perfect linkage, i.e. there are
linkage errors in the merged data. Further, the linkage is often incomplete, in the sense
that many records in the two data sets remain unmatched at the completion of the linkage
process. This paper introduces methods that correct for the biases due to linkage errors and
incomplete linkage when carrying out regression analysis using linked data. In particular, it
focuses on the case where one of the linked data sets is a sample from the target population
and the other is a register, i.e. it covers the entire target population.