As a generalization of the classical linear factor model, generalized latent factor models are useful for analyzing multivariate data of different types, including binary choices and counts. This paper proposes an information criterion to determine the number of factors in generalized latent factor models. The consistency of the proposed information criterion is established under a high-dimensional setting where both the sample size and the number of manifest variables grow to infinity, and data may have many missing values. An error bound is established for the parameter estimates, which plays an important role in establishing the consistency of the proposed information criterion. This error bound improves several existing results and may be of independent theoretical interest. We evaluate the proposed method by a simulation study and an application to Eysenck's personality questionnaire.

翻译：作为古典线性要素模型的概括,通用潜伏系数模型有助于分析不同类型、包括二进制选择和计数的多变量数据。本文件提出一个信息标准,用以确定普遍潜伏系数模型中的因素数量。拟议信息标准的一致性是在高维设置下确定的,在高空设置下,样本大小和表列变量数量都逐渐扩大至无限,数据可能有许多缺失值。参数估计有误,在确定拟议信息标准的一致性方面起重要作用。这一误差将改进若干现有结果,并可能具有独立的理论意义。我们通过模拟研究和对Eysenck的人格问卷的应用,对拟议方法进行评估。