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

arXiv: https://arxiv.org/abs/2010.02326 · HTML: https://mlsanity.com/paper/2010.02326/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [A Latent Variable Framework for Scaling Laws in Large Language Models](https://mlsanity.com/paper/2512.06553/) (2025)
- [A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistency](https://mlsanity.com/paper/2211.09272/) (2022)
- [Inference on covariance structure in high-dimensional multi-view data](https://mlsanity.com/paper/2509.02772/) (2025)
- [Overfitted high-dimensional matrix factorizations via adaptive spectral shrinkage](https://mlsanity.com/paper/2606.19540/) (2026)
- [Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications](https://mlsanity.com/paper/2501.07437/) (2025)

## Abstract (arXiv)

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.