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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.<\/jats:p>","DOI":"10.1093\/biomet\/asaa063","type":"journal-article","created":{"date-parts":[[2020,7,24]],"date-time":"2020-07-24T11:25:03Z","timestamp":1595589903000},"page":"455-468","source":"Crossref","is-referenced-by-count":10,"title":["Poisson reduced-rank models with an application to political text data"],"prefix":"10.1093","volume":"108","author":[{"given":"Carsten","family":"Jentsch","sequence":"first","affiliation":[{"name":"Department of Statistics, TU Dortmund University, 44221 Dortmund, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eun Ryung","family":"Lee","sequence":"additional","affiliation":[{"name":"Department of Statistics, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul 03063, South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enno","family":"Mammen","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,7,31]]},"reference":[{"key":"2021051519493513300_B1","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.3982\/ECTA8968","article-title":"Eigenvalue ratio test for the number of factors","volume":"81","author":"Ahn,","year":"2013","journal-title":"Econometrica"},{"key":"2021051519493513300_B2","first-page":"917","article-title":"A spectral algorithm for latent Dirichlet allocation","author":"Anandkumar,","year":"2012","journal-title":"Advances in Neural Information Processing Systems 25 (NIPS 2012)"},{"key":"2021051519493513300_B3","first-page":"2773","article-title":"Tensor decompositions for learning latent variable models","volume":"15","author":"Anandkumar,","year":"2014","journal-title":"J. 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