Determining the number of factors in high-dimensional generalized latent factor models
Determining the number of factors in high-dimensional generalized latent factor models
复制标题
DOI：
10.1093/biomet/asab044
复制
发表时间：
2021-12-28
期刊：
影响因子：
2.7
通讯作者：
Li, X.
中科院分区：
文献类型：
--
作者：
Chen, Y.;Li, X.
作为经典线性因子模型的推广，广义潜在因子模型可用于分析不同类型的多元数据，包括二元选择和计数。本文提出了一种信息准则来确定广义潜在因子模型中的因子数量。所提出的信息标准的一致性是在高维设置下建立的，其中样本量和明显变量的数量都增长到无穷大，并且数据可能有许多缺失值。为参数估计建立误差界限，这对于建立所提出的信息标准的一致性起着重要作用。这个误差界限改进了几个现有的结果，并且可能具有独立的理论意义。我们通过模拟研究和艾森克人格问卷的应用来评估所提出的方法。
As a generalization of the classical linear factor model, generalized latent factor models are useful for analysing 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.