Two-Stage maximum likelihood estimation in the misspecified restricted latent class model

2017 ◽  
Vol 71 (2) ◽  
pp. 300-333 ◽  
Author(s):  
Shiyu Wang
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Latent Class ◽  
Latent Class Model ◽  
Likelihood Estimation ◽  
Class Model ◽  
Two Stage

scholarly journals Maximum likelihood estimation of the Latent Class Model through model boundary decomposition

2019 ◽  
Vol 10 (1) ◽  
pp. 51-84 ◽  
Author(s):  
Elizabeth Allman ◽  
Hector Banos Cervantes ◽  
Serkan Hosten ◽  
Kaie Kubjas ◽  
Daniel Lemke ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Em Algorithm ◽  
Maximum Likelihood Estimator ◽  
Latent Class ◽  
Latent Class Model ◽  
Likelihood Estimation ◽  
Likelihood Estimator ◽  
Class Model ◽  
Small Models

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no 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. 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.

Sign in / Sign up

Export Citation Format

Share Document