To analyze longitudinal zero-inflated count data, we extend existing models by introducing marginalized zero-inflated Poisson (MZIP) models with random effects, which explicitly capture the marginal effect of covariates and address limitations of previous methods. These models provide a clearer interpretation of the overall mean effect of covariates on zero-inflated count data. To further accommodate overdispersion, we develop marginalized zero-inflated negative binomial (MZINB) models. Both models incorporate subject-specific heterogeneity through a flexible random effects covariance structure. Simulation studies are conducted to evaluate the performance of the MZIP and MZINB models, comparing their inference under both homogeneous and heterogeneous random effects. Finally, we illustrate the applicability of the proposed models through an analysis of systemic lupus erythematosus data.

翻译：为分析纵向零膨胀计数数据，我们通过引入带有随机效应的边际化零膨胀泊松（MZIP）模型，扩展了现有模型，这些模型明确捕捉协变量的边际效应，并解决了先前方法的局限性。这些模型为协变量对零膨胀计数数据的总体均值效应提供了更清晰的解释。为进一步适应过度离散性，我们开发了边际化零膨胀负二项（MZINB）模型。两种模型均通过灵活的随机效应协方差结构纳入个体特异性异质性。我们进行了模拟研究以评估MZIP和MZINB模型的性能，比较它们在同质和异质随机效应下的推断结果。最后，通过分析系统性红斑狼疮数据，我们展示了所提模型的适用性。