Determining the Number of Factors in High-dimensional Generalized Latent Factor Models

TL;DR

This paper introduces an information criterion for accurately determining the number of factors in high-dimensional generalized latent factor models, accommodating various data types and missing values, with proven consistency and improved error bounds.

Contribution

It proposes a new consistent information criterion for high-dimensional generalized latent factor models, extending factor analysis to diverse data types with missing data.

Findings

The criterion is consistent in high-dimensional settings.

Error bounds for parameter estimates are improved.

Method performs well in simulations and real data application.

Abstract

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.