On the Hierarchical Bernoulli Mixture Model Using Bayesian Hamiltonian Monte Carlo

The model developed considers the uniqueness of a data-driven binary response (indicated by 0 and 1) identified as having a Bernoulli distribution with finite mixture components. In social science applications, Bernoulli's constructs a hierarchical structure data. This study introduces the Hierarchical Bernoulli mixture model (Hibermimo), a new analytical model that combines the Bernoulli mixture with hierarchical structure data. The proposed approach uses a Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler (HMC/NUTS). The study has performed a compatible syntax program computation utilizing the HMC/NUTS to analyze the Bayesian Bernoulli mixture aggregate regression model (BBMARM) and Hibermimo. In the model estimation, Hibermimo yielded a result of ~90% compliance with the modeling of each district and a small Widely Applicable Information Criteria (WAIC) value.

Automated summary

The study introduces a new analytical model, the Hierarchical Bernoulli mixture model (Hibermimo), which combines the Bernoulli mixture with hierarchical structure data. By using the Hamiltonian Monte Carlo algorithm with a No-U-Turn Sampler, the model estimation shows that Hibermimo performs consistently well in modeling each district.