  Topic models such as the Structural Topic Model (STM) estimate latent topical
clusters within text. An important step in many topic modeling applications is
to explore relationships between the discovered topical structure and metadata
associated with the text documents. Methods used to estimate such relationships
must take into account that the topical structure is not directly observed, but
instead being estimated itself. The authors of the STM, for instance, perform
repeated OLS regressions of sampled topic proportions on metadata covariates by
using a Monte Carlo sampling technique known as the method of composition. In
this paper, we propose two improvements: first, we replace OLS with more
appropriate Beta regression. Second, we suggest a fully Bayesian approach
instead of the current blending of frequentist and Bayesian methods. We
demonstrate our improved methodology by exploring relationships between Twitter
posts by German members of parliament (MPs) and different metadata covariates.
