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.