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We propose a tree-structured hierarchical architecture for estimating count variables that exhibit both excessive zeros and over-dispersion, which is commonly observed in practice. The underlying statistical model is based on the Mixture-of-experts (MoE) model, a generalization of finite mixture regression models. With two levels of experts, the proposed model can efficiently model both excessive zeros and the long right-tail, controlled by two gating networks at different levels in the hierarchy. We develop the general form of the maximum likelihood estimator for the proposed model based on the EM algorithm with two latent variables, which allows a natural interpretation and convenient optimization for the likelihood function. As a numerical application, we apply the proposed model to a well-known real dataset and found that it shows superior performance and allows better interpretations compared to other existing alternatives.

Hierarchical mixture-of-experts models for count variables with excessive zeros