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