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Advanced Statistical Modeling, Diagnostics and Simulations
This blog explores advanced statistical analyses built around principled model-based inference, focusing on how complex data structures are handled through modern regression frameworks. The analyses examine generalized linear models, linear and generalized mixed-effects models, and hierarchical formulations to account for non-Gaussian responses, dependence, and multilevel structure. Emphasis is placed on bias-reduced, penalized, and Bayesian estimation, simulation-based inference and bootstrap methods, likelihood- and resampling-based model comparison, and rigorous model diagnostics. Nonlinear effects are studied through spline-based modeling, with careful attention to residual behavior, uncertainty quantification, and the consequences of modeling assumptions for interpretation.