Regression analysis under incomplete linkage

Most probability-based methods used to link records from two distinct data sets correspond- ing to the same target population do not lead to perfect linkage, i.e. there are linkage errors in the merged data. Chambers (2008) describes modi¯cations to standard methods of regression analysis that can be used with such imperfectly linked data. However, these methods assume that the linkage process is complete, i.e. all records on the two data sets are linked. This paper extends these ideas to regression analysis using data that have been incompletely linked, and in particular to the situation where one of the data sets being linked is a sample from the target population and the other is a register, i.e. it covers the entire target population.