  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.
