Hamiltonian Monte Carlo for Regression with High-Dimensional Categorical Data

Latent variable models are increasingly used in economics for high-dimensional categorical data like text and surveys. We demonstrate the effectiveness of Hamiltonian Monte Carlo (HMC) with parallelized automatic differentiation for analyzing such data in a computationally efficient and methodologically sound manner. Our new model, Supervised Topic Model with Covariates, shows that carefully modeling this type of data can have significant implications on conclusions compared to a simpler, frequently used, yet methodologically problematic, two-step approach. A simulation study and revisiting Bandiera et al. (2020)'s study of executive time use demonstrate these results. The approach accommodates thousands of parameters and doesn't require custom algorithms specific to each model, making it accessible for applied researchers