  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.
