Sparse Latent Class Analysis For Dichotomous Responses: Post-Estimation Refinement via Item-level Pseudo-Likelihood
Abstract
Latent Class Analysis (LCA) is widely used to identify unobserved subgroups in social and behavioural sciences. A long-standing challenge for LCA is the interpretability of the latent classes, due to the high complexity of the estimated item response probability matrix. To address this, we propose a computationally efficient post-estimation refinement procedure that enhances model interpretability by a sparse model estimate. The method begins by estimating a classical, unrestricted, latent class model and determining the number of classes using the Bayesian information criterion (BIC). It is followed by a refinement step that further performs model selection on the item-specific response probabilities based on the initial estimate. This refinement penalises the number of distinct response probability levels per item, collapsing redundant levels to yield a sparse matrix that is significantly easier to interpret than those produced by classical LCA. We provide asymptotic theory showing that the proposed procedure consistently recovers the sparse pattern of the item response probabilities for each item, and further validate its performance through extensive simulations. The practical power of the proposed method is further illustrated via an application to survey data on social role performance, where it provides a parsimonious and clear characterisation of the resulting latent classes. The code for implementing the proposed method is publicly available at https://github.com/florence07/Sparse-LCA-Refinement.
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BibTeX
@misc{xu2026sparse,
title = {{Sparse Latent Class Analysis For Dichotomous Responses: Post-Estimation Refinement via Item-level Pseudo-Likelihood}},
author = {Yuxuan Xu and Lea Kaufmann and Yunxiao Chen and Maria Kateri and Irini Moustaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.19034},
eprint = {2605.19034},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.19034},
}
RIS
TY - UNPB
TI - Sparse Latent Class Analysis For Dichotomous Responses: Post-Estimation Refinement via Item-level Pseudo-Likelihood
AU - Yuxuan Xu
AU - Lea Kaufmann
AU - Yunxiao Chen
AU - Maria Kateri
AU - Irini Moustaki
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.19034
UR - https://arxiv.org/abs/2605.19034
AB - Latent Class Analysis (LCA) is widely used to identify unobserved subgroups in social and behavioural sciences. A long-standing challenge for LCA is the interpretability of the latent classes, due to the high complexity of the estimated item response probability matrix. To address this, we propose a computationally efficient post-estimation refinement procedure that enhances model interpretability by a sparse model estimate. The method begins by estimating a classical, unrestricted, latent class model and determining the number of classes using the Bayesian information criterion (BIC). It is followed by a refinement step that further performs model selection on the item-specific response probabilities based on the initial estimate. This refinement penalises the number of distinct response probability levels per item, collapsing redundant levels to yield a sparse matrix that is significantly easier to interpret than those produced by classical LCA. We provide asymptotic theory showing that the proposed procedure consistently recovers the sparse pattern of the item response probabilities for each item, and further validate its performance through extensive simulations. The practical power of the proposed method is further illustrated via an application to survey data on social role performance, where it provides a parsimonious and clear characterisation of the resulting latent classes. The code for implementing the proposed method is publicly available at https://github.com/florence07/Sparse-LCA-Refinement.
ER -