Distributed Multinomial Regression

faculty.chicagobooth.edu/matt.taddy This article introduces a model-based approach to distributed computing for multinomial logis-tic regression. We treat counts for each response category as independent Poisson regressions via plug-in estimates for fixed effects shared across categories. The work is driven by the high-dimensional-response multinomial models that arise in analysis of a large number of random counts. Our archetypal applications are in text analysis, where documents are tokenized and the token counts are modeled as arising from a multinomial dependent upon document attributes. We estimate such models for a publicly available dataset of reviews from Yelp, with text re-gressed onto a large set of explanatory variables (user, business, and rating information). The fitted models serve as a basis for exploring the connection between words and variables of inter-est (e.g., star rating), for reducing dimension into supervised factor scores, and for prediction. ar