We 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 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 via Poisson random variables. We apply our approach 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.

中文翻译：

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泊松降级模型在政治文本数据中的应用

我们讨论了高维泊松向量的低维摘要的泊松降秩模型，该模型允许推断低维空间中个体的位置。我们表明，在弱依赖条件下（允许泊松随机变量之间存在一定的相关性），可以使用泊松最大似然估计来一致地估计位置。此外，我们制定了一致的规则，用于根据离散数据确定位置的维度。我们研究Poisson降级模型的主要动机来自于对政治文本数据的应用，其中政治文件中的字数通过Poisson随机变量建模。我们将我们的方法应用于政党宣言数据，这些数据来自德国统一后七次联邦选举中的德国政党，