How to Borrow Information across Unlinked Data? A Relative Density Approach for Predicting Unobserved Distributions

• In Event: 4464 - Regular Session on Methodology: Progress and New Approaches

Abstract

One of the most important developments in the current era of social sciences is the growing availability and diversity of data, big and small. Social scientists increasingly combine information from multiple datasets in their research. While conducting statistical analyses with linked data is usually not much different from the analyzing a single dataset as the unique identifiers allow the researcher to directly merge two or more data matrices, borrowing information across unlinked data can be much more challenging. This paper proposes a new methodological approach for borrowing information across unlinked surveys to predict unobserved distributions. The gist of the proposed approach lies in the idea of using the relative density between the observed and unobserved distributions in the reference data to characterize the relationship between the two distributions and borrow that information to the base data. The key benefit of this approach over prior approaches is that it relaxes the conditions of comparable representativeness and comparable measurement across datasets, and instead relies on the assumption that the relative density between the observed and unobserved distributions is the same or very similar between datasets. It also has the additional advantage of allowing the researcher to borrow information about the entire distribution, rather than a limited number of summary statistics. The approach also comes with a method for incorporating and quantifying the uncertainty in its output. We illustrate the formulation of this relative density approach, demonstrate with simulation studies, and then apply it to address the problem of employment selection in wage inequality research.

Author

• Siwei Cheng, New York University