Beyond the EM algorithm: constrained optimization methods for latent class model. Issue 9 (27th September 2022)

• Record Type: Journal Article
• Authors: Chen, Hao; Han, Lanshan; Lim, Alvin
• Is Part Of: Communications in statistics. Volume 51:Issue 9(2022)
• Page Start: 5222
• Page End: 5244
• Publication Date: 2022-09-27
• Subjects: Constrained optimization -- EM algorithm -- Finite mixture model -- Latent class model -- Quasi-Newton's method -- Quadratic programing; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2020.1764034
• Languages: English
• ISSNs: 0361-0918

Abstract

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 noncontinuous nature and flexibility in shape, researchers in 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.