Latent Factor Regressions for the Social Sciences∗

In this paper I present a general framework for regression in the presence of complex dependence structures between units such as in time-series cross-sectional data, relational/network data, and spatial data. These types of data are challenging for standard multilevel models because they involve multiple types of structure (e.g. temporal effects and cross-sectional effects) which are interactive. I show that interactive latent factor models provide a powerful modeling alternative that can address a wide range of data types. Although related models have previously been proposed in several different fields, inference is typically cumbersome and slow. I introduce a class of fast variational inference algorithms that allows for models to be fit quickly and accurately. ∗For comments and discussions on various portions of this material I thank Michael Gill, Adam Glynn, Justin Grimmer, Gary King, Horacio Larreguy, Chris Lucas, John Marshall, Helen Milner, Brendan O’Connor, Marc Ratkovic, Beth Simmons, and Alex Volfovsky. Molly Roberts provided both enlightening discussions and code from her paper on robust standard errors. Special thanks to Dustin Tingley without whom this paper would not have been possible. An appendix containing additional details is available on my website: scholar.harvard.edu/bstewart †Graduate Student. Department of Government Harvard University. [email protected]