Stochastic EM Estimation and Inference for Zero-Inflated Beta-Binomial Mixed Models for Longitudinal Count Data

2026-02-09

AI Summary

This study addresses the challenge of modeling overdispersed, zero-inflated count data with longitudinal structure by proposing a zero-inflated beta-binomial mixed-effects model. The approach uniquely integrates a zero-inflation mechanism with the beta-binomial distribution and incorporates subject-specific random effects to account for within-subject correlations over time. To handle the intractable likelihood, the authors employ a latent variable augmentation strategy combined with a stochastic approximation EM (SAEM) algorithm for efficient parameter estimation. Both theoretical analysis and simulation studies demonstrate that the proposed method substantially outperforms conventional zero-inflated models, particularly in small-sample settings. When applied to longitudinal microbiome data in conjunction with the ZIBR model, it enhances inferential robustness, underscoring its methodological novelty and practical utility.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Analyzing overdispersed, zero-inflated, longitudinal count data poses significant modeling and computational challenges, which standard count models (e.g., Poisson or negative binomial mixed effects models) fail to adequately address. We propose a Zero-Inflated Beta-Binomial Mixed Effects Regression (ZIBBMR) model that augments a beta-binomial count model with a zero-inflation component, fixed effects for covariates, and subject-specific random effects, accommodating excessive zeros, overdispersion, and within-subject correlation. Maximum likelihood estimation is performed via a Stochastic Approximation EM (SAEM) algorithm with latent variable augmentation, which circumvents the model's intractable likelihood and enables efficient computation. Simulation studies show that ZIBBMR achieves accuracy comparable to leading mixed-model approaches in the literature and surpasses simpler zero-inflated count formulations, particularly in small-sample scenarios. As a case study, we analyze longitudinal microbiome data, comparing ZIBBMR with an external Zero-Inflated Beta Regression (ZIBR) benchmark; the results indicate that applying both count- and proportion-based models in parallel can enhance inference robustness when both data types are available.

Problem

• zero-inflated
• overdispersed
• longitudinal count data
• mixed models
• beta-binomial

Innovation

• Zero-Inflated Beta-Binomial
• Mixed Effects Model
• Stochastic Approximation EM
• Longitudinal Count Data
• Overdispersion