Likelihood-Based Inference for Joint Modeling of Correlated Count and Binary Outcomes with Extra Variability and Zeros // Inference approach for jointly modeling correlated count and binary outcomes. This formulation allows simultaneous modeling of zero inflation via the Bernoulli component while providing a more accurate assessment of the Hierarchical Zero-Inflated Poisson's parsimony (Lizandra C. Fabio, Jalmar M. F. Carrasco, Victor H. Lachos and Ming-Hui Chen, Likelihood-based inference for joint modeling of correlated count and binary outcomes with extra variability and zeros, 2026, under submission).