We propose a novel approach for automatic model selection for hierarchical models using Wasserstein Generative Adversarial Networks (WGANs).

Model checking and selection can be performed by graphically comparing fake data generated by the proposed model to the actual data. The aim is to select a model that generates fake data with a similar distribution to that of the actual data.

The critic component of a WGAN is trained to discriminate data generated by the generator component from the real data.

We propose using the critic components of WGANs trained on data simulated from candidate models. If the critic component of a WGAN for a candidate model cannot successfully discriminate between synthetic data generated from that model and the real data, that indicates better model fit. We describe an algorithm for model selection using this intuition.

We demonstrate that our approach can be used to select appropriate models for synthetic and real social science datasets.