Accurate estimation of structural equation models with remote partitioned data

This paper focuses on a privacy paradigm centered around providing access to researchers to remotely carry out analyses on sensitive data stored behind firewalls. We develop and demonstrate a method for accurate estimation of structural equation models (SEMs) for arbitrarily partitioned data. We show that under a certain set of assumptions our method for estimation across these partitions achieves identical results as estimation with the full data. We consider two situations: (i) a standard setting with a trusted central server and (ii) a round-robin setting in which none of the parties are fully trusted, and extend them in two specific ways. First, we formulate our methods specifically for SEMs, which have become increasingly common models in psychology, human development, and the behavioral sciences. Secondly, our methods work for horizontal, vertical, and complex partitions without needing different routines. In application, this method will serve to increase opportunities for research by allowing SEM estimation without transfer or combination of data. We demonstrate our methods with both simulated and real data examples.