This paper considers logistic regression analysis with linked data. It is shown that, in logistic regression analysis with linked data, a finite mixture of Bernoulli distributions can be used for modeling the response variables. We proposed an iterative maximum likelihood estimator for the regression coefficients that takes the matching probabilities into account. Next, the Bayesian counterpart of the frequentist model is developed. Then, a simulation study is performed to check the applicability and performance of the proposed frequentist and Bayesian methodologies encountering mismatch.