Sparse Latent Class Analysis: Post-Estimation Refinement via Item-level Pseudo-Likelihood

TL;DR

This paper introduces a post-estimation refinement method for Latent Class Analysis that produces sparse, interpretable item response probability matrices, validated through theory, simulations, and real data application.

Contribution

It proposes a novel, computationally efficient procedure to enhance LCA interpretability by inducing sparsity in response probabilities, improving clarity over classical methods.

Findings

The method consistently recovers sparse response patterns asymptotically.

Simulations demonstrate improved interpretability without sacrificing accuracy.

Application to survey data yields clearer latent class characterization.

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.