论文标题
确定高维广义潜在因子模型中的因素数量
Determining the Number of Factors in High-dimensional Generalized Latent Factor Models
论文作者
论文摘要
作为经典线性因子模型的概括，广义潜在因子模型可用于分析不同类型的多元数据，包括二进制选择和计数。本文提出了一个信息标准，以确定广义潜在因子模型中的因素数量。提出的信息标准的一致性是在高维设置下建立的，在该设置中，样本量和明显变量的数量都会生长到无穷大，并且数据可能具有许多缺失值。为参数估计建立了误差绑定，该估计在建立建议的信息标准的一致性中起着重要作用。此错误绑定可改善几种现有结果，并且可能具有独立的理论利益。我们通过模拟研究评估了提出的方法，并应用了Eysenck的个性问卷。
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.
