Determining the number of factors in high-dimensional generalized latent factor models
提出一种信息准则来确定广义潜变量模型中的因子数量，适用于高维数据（样本量和变量数都很大）以及存在缺失值的情况，并通过模拟和人格问卷数据验证了方法。
Summary 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.