# Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications

arXiv: https://arxiv.org/abs/1712.08966 · HTML: https://mlsanity.com/paper/1712.08966/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2017.

## Built on by (most cited first, 8 of 8)

- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Sparse Bayesian Multidimensional Item Response Theory](https://mlsanity.com/paper/2310.17820/) (2023)
- [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)
- [Multidimensional Item Response Theory in the Style of Collaborative Filtering](https://mlsanity.com/paper/2301.00909/) (2023)
- [Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes](https://mlsanity.com/paper/2410.04996/) (2024)
- [Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications](https://mlsanity.com/paper/2501.07437/) (2025)

## Abstract (arXiv)

Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated, yielding structured (confirmatory) latent factor models. Motivated by the applications of latent factor models to large-scale measurements which consist of many manifest variables (e.g. test items) and a large sample size, we study the properties of structured latent factor models under an asymptotic setting where both the number of manifest variables and the sample size grow to infinity. Specifically, under such an asymptotic regime, we provide a definition of the structural identifiability of the latent factors and establish necessary and sufficient conditions on the measurement design that ensure the structural identifiability under a general family of structured latent factor models. In addition, we propose an estimator that can consistently recover the latent factors under mild conditions. This estimator can be efficiently computed through parallel computing. Our results shed lights on the design of large-scale measurement and have important implications on measurement validity. The properties of the proposed estimator are verified through simulation studies.