Maximum Likelihood Estimation of the Latent Class Model through Model Boundary Decomposition
Special Volume in honor of memory of S.E.Fienberg
Elizabeth S. Allman
Creator
Faculty
jarhodes2@alaska.edu
BaĆ±os Cervantes, Hector
Creator
Evans, Robin
Creator
Hosten, Serkan
Creator
Kubjas, Kaie
Creator
Lemke, Daniel
Creator
Rhodes, John
Creator
Zwiernik, Piotr
Creator
MATH / Applied Mathematics
Illinois Institute of Technology
Affiliated department
Maximum likelihood estimation
Expectation Maximization
latent
2019
2019-04-12
The Expectation-Maximization (EM) algorithm is routinely used for maximum likelihood estimation in latent class analysis. However, the EM algorithm comes with no global guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata and performance of the EM algorithm. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.
Article