In official statistics record linkage is an important activity, which consists in identifying records from the same individual in one or many files. It is used to combine data sources including administrative, survey or big data sources. In practice, record link- age is subject to linkage errors when it relies on quasi-identifiers, such as names and demographic variables, which are non-unique and recorded with errors. Accounting for these errors is an important but challenging problem. In this work, two methods are described for the primary analysis of such data, i.e. an analysis by someone with unfettered access to all the related micro-data and project information. Both solutions are estimating equation methods, which explicitly account for the uncertainty about the match status of record pairs and require the marginal distribution of a pair agreement vector. The fifirst methodology is model-based and operates under the assumption of conditional independence between the pairs agreement vectors and the responses given the covariates. The second methodology uses a model-assisted estimating equation, which dispenses with the above assumption but requires reliable clerical-reviews.