# Latent class analysis for multi-layer categorical data

arXiv: https://arxiv.org/abs/2408.05535 · HTML: https://mlsanity.com/paper/2408.05535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 27 references that are in the map.
- First posted on arXiv 10 Aug 2024.

## Builds on (most cited first, 8 of 8)

- [Spectral and matrix factorization methods for consistent community detection in multi-layer networks](https://mlsanity.com/paper/1704.07353/) (2017)
- [Impact of regularization on Spectral Clustering](https://mlsanity.com/paper/1312.1733/) (2013)
- [Analysis of spectral clustering algorithms for community detection: the general bipartite setting](https://mlsanity.com/paper/1803.04547/) (2018)
- [Community detection for weighted bipartite networks](https://mlsanity.com/paper/2109.10319/) (2021)
- [Beyond the EM Algorithm: Constrained Optimization Methods for Latent Class Model](https://mlsanity.com/paper/1901.02928/) (2019)
- [A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses](https://mlsanity.com/paper/2103.16036/) (2021)
- [Partial-Mastery Cognitive Diagnosis Models](https://mlsanity.com/paper/2208.03252/) (2022)
- [Latent class analysis by regularized spectral clustering](https://mlsanity.com/paper/2310.18727/) (2023)

## Abstract (arXiv)

Traditional categorical data, often collected in psychological tests and educational assessments, are typically single-layer and gathered only once.This paper considers a more general case, multi-layer categorical data with polytomous responses. To model such data, we present a novel statistical model, the multi-layer latent class model (multi-layer LCM). This model assumes that all layers share common subjects and items. To discover subjects' latent classes and other model parameters under this model, we develop three efficient spectral methods based on the sum of response matrices, the sum of Gram matrices, and the debiased sum of Gram matrices, respectively. Within the framework of multi-layer LCM, we demonstrate the estimation consistency of these methods under mild conditions regarding data sparsity. Our theoretical findings reveal two key insights: (1) increasing the number of layers can enhance the performance of the proposed methods, highlighting the advantages of considering multiple layers in latent class analysis; (2) we theoretically show that the algorithm based on the debiased sum of Gram matrices usually performs best. Additionally, we propose an approach that combines the averaged modularity metric with our methods to determine the number of latent classes. Extensive experiments are conducted to support our theoretical results and show the powerfulness of our methods in the task of learning latent classes and estimating the number of latent classes in multi-layer categorical data with polytomous responses.