Title: Latent Mixture Modeling for Clustered Data,
Abstract: This article proposes a mixture modeling approach to estimating cluster-wise
conditional distributions in clustered (grouped) data. We adapt the
mixture-of-experts model to the latent distributions, and propose a model in
which each cluster-wise density is represented as a mixture of latent experts
with cluster-wise mixing proportions distributed as Dirichlet distribution. The
model parameters are estimated by maximizing the marginal likelihood function
using a newly developed Monte Carlo Expectation-Maximization algorithm. We also
extend the model such that the distribution of cluster-wise mixing proportions
depends on some cluster-level covariates. The finite sample performance of the
proposed model is compared with some existing mixture modeling approaches as
well as linear mixed model through the simulation studies. The proposed model
is also illustrated with the posted land price data in Japan.