From Independence to Feedback

This book presents a staged, pedagogically driven framework for modeling dependence in longitudinal binary data, integrating modern AI-assisted computational workflows throughout the analysis. Rather than treating correlation, hierarchy, and endogeneity as technical afterthoughts, the book positions dependence as the central structural feature of longitudinal data. The text develops a six-stage modeling progression: 1. Pooled logistic regression (independence) 2. Clustered standard errors and generalized estimating equations (GEE) (correlation) 3. Two-stage feedback models (endogeneity) 4. Joint hierarchical models (correlation + feedback + hierarchy) 5. Bayesian joint hierarchical models (full uncertainty propagation) 6. Integrative synthesis and model comparison. A defining feature of the book is its simulation-first pedagogy. Each modeling stage is motivated through controlled simulation studies that allow readers to observe bias, RMSE, coverage failures, and inferential distortions before introducing more advanced methods. The framework is then applied to a real longitudinal health dataset from the Philippines IFPRI Child Health and Nutrition Survey, demonstrating how modeling decisions materially affect scientific conclusions The book’s primary contributions are: • A unified framework linking independence, correlation, feedback, hierarchy, and Bayesian inference; • Clear treatment of endogenous covariates and dynamic feedback in binary longitudinal data; • Practical guidance for hierarchical and Bayesian modeling, including multiple membership structures; • Responsible AI-assisted analysis through prompt-based code generation, reproducible workflows, and verification of AI-generated results.