# Beyond the EM Algorithm: Constrained Optimization Methods for Latent Class Model

## TL;DR

This paper introduces constrained optimization methods, specifically quasi-Newton techniques, as efficient alternatives to the EM algorithm for latent class models, achieving faster convergence and more accurate estimators.

## Contribution

It proposes and evaluates quasi-Newton constrained optimization methods for latent class models, improving convergence speed and estimator accuracy over traditional EM algorithms.

## Key findings

- Faster convergence than EM algorithm.
- More accurate model estimators.
- Effective in simulation studies.

## Abstract

Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape, researchers in practice areas such as marketing and social sciences also frequently use LCM to gain insights from their data. One likelihood-based method, the Expectation-Maximization (EM) algorithm, is often used to obtain the model estimators. However, the EM algorithm is well-known for its notoriously slow convergence. In this research, we explore alternative likelihood-based methods that can potential remedy the slow convergence of the EM algorithm. More specifically, we regard likelihood-based approach as a constrained nonlinear optimization problem, and apply quasi-Newton type methods to solve them. We examine two different constrained optimization methods to maximize the log likelihood function. We present simulation study results to show that the proposed methods not only converge in less iterations than the EM algorithm but also produce more accurate model estimators.