arXiv subjects

Jeffrey R. Wilson

Publications and source records attributed to Jeffrey R. Wilson.

3 recordsLinked to original sources

arXiv2026

Semi-partitioned Generalized Method of Moments for Longitudinal Data with Lagged and Feedback Covariates

We propose a semi-partitioned Generalized Method of Moments (GMM) framework for analyzing longitudinal data with time-dependent covariates, within a marginal modeling paradigm. This approach addresses limitations of both aggregated and fully partitioned GMM models. Aggregated methods obscure temporal dynamics by assuming constant effects, while fully partitioned approaches offer temporal specificity at the cost of increased model complexity and instability--particularly with moderate sample sizes or deep lag structures. Our method distinguishes immediate from lagged effects by estimating contemporaneous coefficients separately and grouping lagged moment conditions into structured sets, while retaining flexibility in the lag-specific effects. This yields a model that is both statistically efficient and interpretable, capturing essential temporal variation while mitigating variance inflation and convergence challenges associated with full partitioning. The framework accommodates feedback, supports both continuous and binary outcomes, and utilizes the Broyden--Fletcher--Goldfarb--Shanno (BFGS) algorithm for reliable optimization. Through simulations, we demonstrate that the semi-partitioned GMM achieves coverage and competitive efficiency relative to fully partitioned models when the grouped-lag structure approximates the underlying lag pattern. Applications to clinical datasets on knee osteoarthritis and adolescent obesity confirm that the method recovers consistent, interpretable effects and avoids instability associated with finely grained partitioning.

stat.ME↗

arXiv2026

Modeling Covariate Feedback, Reversal, and Latent Traits in Longitudinal Data: A Joint Hierarchical Framework

Time-varying covariates in longitudinal studies frequently evolve through reciprocal feedback, undergo role reversal, and reflect unobserved individual heterogeneity. Standard statistical frameworks often assume fixed covariate roles and exogenous predictors, limiting their utility in systems governed by dynamic behavioral or physiological processes. We develop a hierarchical joint modeling framework that unifies three key features of such systems: (i) bidirectional feedback between a binary and a continuous covariate, (ii) role reversal in which these covariates become jointly modeled outcomes at a prespecified decision phase, and (iii) a shared latent trait influencing both intermediate covariates and a final binary endpoint. The model proceeds in three phases: a feedback-driven longitudinal process, a reversal phase in which the two covariates are jointly modeled conditional on the latent trait, and an outcome model linking a binary, decision-relevant endpoint to observed and latent components. Estimation is carried out using maximum likelihood and Bayesian inference, with Hamiltonian Monte Carlo supporting robust posterior estimation for models with latent structure and mixed outcome types. Simulation studies show that the model yields well calibrated coverage, small bias, and improved predictive performance compared to standard generalized linear mixed models, marginal approaches, and models that ignore feedback or latent traits. In an analysis of nationally representative U.S. panel data, the model captures the co-evolution of physical activity and body mass index and their joint influence, moderated by a latent behavioral resilience factor, on income mobility. The framework offers a flexible, practically implementable tool for analyzing longitudinal decision systems in which feedback, covariate role transition, and unmeasured capacity are central to prediction and intervention.

stat.ME↗

arXiv2026

Latent Moment Models for Recurrent Binary Outcomes: A Bayesian and Quasi-Distributional Approach

Recurrent binary outcomes within individuals, such as hospital readmissions, often reflect latent risk processes that evolve over time. Conventional methods like generalized linear mixed models and generalized estimating equations estimate average risk but fail to capture temporal changes in variability, asymmetry, and tail behavior. We introduce two statistical frameworks that model each binary event as the outcome of a thresholded value drawn from a time-varying latent distribution defined by its location, scale, skewness, and kurtosis. Rather than treating these four quantities as nonparametric moment estimators, we model them as interpretable latent moments within a flexible latent distributional family. The first, BLaS-Recurrent, is a Bayesian model using the sinh-arcsinh distribution (a parametric family that provides explicit control over asymmetry and tail weight) to estimate latent moment trajectories; the second, QuaD-Recurrent, is a quasi-distributional approach that maps simulated moment vectors to event probabilities using a flexible nonparametric surface. Both models support time-dependent covariates, serial correlation, and multiple membership structures. Simulation studies show improved calibration, interpretability, and robustness over standard models. Applied to ICU readmission data from the MIMIC-IV database, both approaches uncover clinically meaningful patterns in latent risk, such as right-skewed escalation and widening dispersion, that are missed by traditional methods. These models provide interpretable, distribution-sensitive tools for longitudinal binary outcomes in healthcare while explicitly acknowledging that latent "moments" summarize but do not uniquely determine the underlying distribution.

stat.ME↗