Latent class analysis by regularized spectral clustering
This work addresses latent class analysis for categorical data in social, psychological, and behavioral sciences, representing an incremental improvement with new algorithms and theoretical guarantees.
The authors tackled the problem of identifying latent classes in categorical data by proposing two new algorithms based on a regularized Laplacian matrix, achieving consistent results under mild conditions and verifying efficiency and accuracy through simulations and real-world applications.
The latent class model is a powerful tool for identifying latent classes within populations that share common characteristics for categorical data in social, psychological, and behavioral sciences. In this article, we propose two new algorithms to estimate a latent class model for categorical data. Our algorithms are developed by using a newly defined regularized Laplacian matrix calculated from the response matrix. We provide theoretical convergence rates of our algorithms by considering a sparsity parameter and show that our algorithms stably yield consistent latent class analysis under mild conditions. Additionally, we propose a metric to capture the strength of latent class analysis and several procedures designed based on this metric to infer how many latent classes one should use for real-world categorical data. The efficiency and accuracy of our algorithms are verified by extensive simulated experiments, and we further apply our algorithms to real-world categorical data with promising results.