  Analysis of short text, such as social media posts, is extremely difficult
because of their inherent brevity. In addition to classifying topics of such
posts, a common downstream task is grouping the authors of these documents for
subsequent analyses. We propose a novel model that expands on the Latent
Dirichlet Allocation by modeling strong dependence among the words in the same
document, with user-level topic distributions. We also simultaneously cluster
users, removing the need for post-hoc cluster estimation and improving topic
estimation by shrinking noisy user-level topic distributions towards typical
values. Our method performs as well as -- or better -- than traditional
approaches, and we demonstrate its usefulness on a dataset of tweets from
United States Senators, recovering both meaningful topics and clusters that
reflect partisan ideology. We also develop a novel measure of echo chambers
among these politicians by characterizing insularity of topics discussed by
groups of Senators and provide uncertainty quantification.
