Poisson reduced-rank models with an application to political text data. (31st July 2020)

• Record Type: Journal Article
• Authors: Jentsch, Carsten; Lee, Eun Ryung; Mammen, Enno
• Is Part Of: Biometrika. Volume 108:Number 2(2021)
• Page Start: 455
• Page End: 468
• Publication Date: 2020-07-31
• Subjects: Dimension selection -- Large-dimensional data matrix -- Multi-dimensional party position -- Party manifesto data -- Poisson reduced-rank model -- Wordfish; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asaa063
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: We discuss Poisson reduced-rank models for low-dimensional summaries of high-dimensional Poisson vectors that allow inference on the location of individuals in a low-dimensional space. We show that under weak dependence conditions, which allow for certain correlations between the Poisson random variables, the locations can be consistently estimated using Poisson maximum likelihood estimation. Moreover, we develop consistent rules for determining the dimension of the location from the discrete data. Our main motivation for studying Poisson reduced-rank models arises from applications to political text data, where word counts in a political document are modelled by Poisson random variables. We apply our method to party manifesto data taken from German political parties across seven federal elections following German reunification, to make statistical inferences on the multi-dimensional evolution of party positions.