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Data sets obtained from linking multiple files are frequently affected bymismatch error, as a result of non-unique or noisy identifiers used duringrecord linkage. Accounting for such mismatch error in downstream analysisperformed on the linked file is critical to ensure valid statistical inference.In this paper, we present a general framework to enable valid post-linkageinference in the challenging secondary analysis setting in which only thelinked file is given. The proposed framework covers a wide selection ofstatistical models and can flexibly incorporate additional information aboutthe underlying record linkage process. Specifically, we propose a mixture modelfor pairs of linked records whose two components reflect distributionsconditional on match status, i.e., correct match or mismatch. Regardinginference, we develop a method based on composite likelihood and the EMalgorithm as well as an extension towards a fully Bayesian approach. Extensivesimulations and several case studies involving contemporary record linkageapplications corroborate the effectiveness of our framework.

A General Framework for Regression with Mismatched Data Based on Mixture Modeling