Bayesian regression analysis with linked data using mixture normal distributions

The probabilistic uncertainty in record linkage affects statistical analysis such as regression analysis of linked data. This paper considers Bayesian regression analysis with linked data and shows that despite using the usual normal regression analysis, the least squares type estimators of regression coefficients are not always adequate. A method is proposed in which the distribution of the response variable is used. This method is related to finite mixture analysis and leads to more accurate estimations. A simple approach has been proposed to increase the tractability and reduce the number of mixture components. A Monte Carlo simulation study is also performed to assess the proposed approach.