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Abstract The advent of the information age has revolutionized data collection and has led to a rapid expansion of available data sources. Methods of data integration are indispensable when a question of interest cannot be addressed using a single data source. Record linkage (RL) is at the forefront of such data integration efforts. Incentives for sharing linked data for secondary analysis have prompted the need for methodology accounting for possible errors at the RL stage. Mismatch error is a common consequence resulting from the use of nonunique or noisy identifiers at that stage. In this paper, we present a framework to enable valid postlinkage inference in the secondary analysis setting in which only the linked file is given. The proposed framework covers a variety of statistical models and can flexibly incorporate information about the underlying RL process. We propose a mixture model for linked records whose two components reflect distributions conditional on match status, i.e. correct or false match. Regarding inference, we develop a method based on composite likelihood and the expectation-maximization algorithm that is implemented in the R package pldamixture. Extensive simulations and case studies involving contemporary RL applications corroborate the effectiveness of our framework. 

In the analysis of data sets consisting of (X, Y)-pairs, a tacit assumption is that each pair corresponds to the same observational unit. If, however, such pairs are obtained via record linkage of two files, this assumption can be violated as a result of mismatch error rooting, for example, in the lack of reliable identifiers in the two files. Recently, there has been a surge of interest in this setting under the term “Shuffled Data” in which the underlying correct pairing of (X, Y)-pairs is represented via an unknown permutation. Explicit modeling of the permutation tends to be associated with overfitting, prompting the need for suitable methods of regularization. In this paper, we propose an exponential family prior on the permutation group for this purpose that can be used to integrate various structures such as sparse and local shuffling. This prior turns out to be conjugate for canonical shuffled data problems in which the likelihood conditional on a fixed permutation can be expressed as product over the corresponding (X,Y)-pairs. Inference can be based on the EM algorithm in which the E-step is approximated by sampling, e.g., via the Fisher-Yates algorithm. The M-step is shown to admit a reduction from n^2 to n terms if the likelihood of (X,Y)-pairs has exponential family form. Comparisons on synthetic and real data show that the proposed approach compares favorably to competing methods.