Poisson reduced rank models with an application to political text data

Résumé

In the talk we will discuss Poisson reduced rank models for low-dimensional summaries of high-dimensional Poisson vectors that allow for inference on the location of individuals in a low-dimensional space. We show that under weak dependence assumptions, the locations can be consistently estimated by Poisson maximum likelihood estimation. Our theory allows us to develop a rule to determine the proper dimension of the locations. Our main motivation for studying Poisson reduced rank models comes from applications to political text data, where word counts in a political document are modeled as Poisson random variables. We apply our approach to party manifesto data from German parties over seven federal elections after German reunification to do statistical inference on the evolution of multi-dimensional party positions. The talk reports on joint work with Carsten Jentsch, Dortmund and Eun Ryung Lee, Seoul.