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.

翻译：分析过度离散、零膨胀的纵向计数数据面临显著的建模与计算挑战，标准计数模型（如Poisson或负二项混合效应模型）难以充分应对。本文提出一种零膨胀Beta-Binomial混合效应回归（ZIBBMR）模型，该模型通过零膨胀组件、协变量的固定效应以及个体特异性随机效应扩展了beta-binomial计数模型，能够同时处理过量零值、过度离散及个体内相关性。我们采用基于潜变量增广的随机逼近EM（SAEM）算法进行最大似然估计，该方法规避了模型似然函数的难解性并实现了高效计算。模拟研究表明，ZIBBMR的准确性可与文献中主流的混合模型方法相媲美，且优于简单的零膨胀计数模型，尤其在小样本场景中表现更优。作为案例研究，我们分析了纵向微生物组数据，将ZIBBMR与外部零膨胀Beta回归（ZIBR）基准进行比较；结果表明，当同时具备计数与比例数据时，并行应用基于计数和基于比例的模型可提升推断的稳健性。