基于Copula的多元零膨胀混合泊松模型框架
A Copula-Based Framework for Multivariate Zero-Inflated Mixed Poisson Models
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中文总结 AI 辅助
本文提出一种基于Copula的多元零膨胀混合泊松模型框架，分离结构零值与潜在强度的相依源，采用IFM或完全极大似然推断，经模拟及基准、医疗数据集验证，具良好性能与实用性。
中文摘要 AI 辅助
多元计数数据常包含过度离散、过多零值及复杂相依性。现有多元零膨胀计数模型通常采用单一相依结构联合建模结构零值与计数结果，这使得两类相依源难以单独解释，且常导致计算缓慢或似然函数难以处理。本文提出一种通用的多元零膨胀混合泊松模型框架，在统一的基于似然的公式中明确分离这两类相依源。所提出的分层模型结合了零膨胀混合泊松边际分布，以及针对结构零值和潜在强度分量的独立相依模型：结构零值间的相依性通过标准参数Copula建模，潜在混合变量间的相依性通过棋盘Copula建模。基于似然的推断采用边际推断函数（IFM）方法执行，当计算可行时，所提出的似然也支持完全最大似然估计。模拟研究表明，在不同相依结构和潜在混合分布下，该模型可实现准确的参数估计和良好的有限样本性能。将其应用于现有统计软件的基准数据集及医疗保健利用数据集，验证了该框架的灵活性、计算效率和实用价值。
英文摘要
Multivariate count data often contain overdispersion, excess zeros, and complex dependence. Existing multivariate zero-inflated count models usually use a single dependence structure to jointly model structural zeros and count outcomes. This makes the two sources of dependence difficult to interpret separately and often leads to slow computation or intractable likelihoods. This paper proposes a general framework for multivariate zero-inflated mixed Poisson models that explicitly separates these two sources of dependence within a unified likelihood-based formulation. The proposed hierarchical model combines zero-inflated mixed Poisson marginals with separate dependence models for the structural-zero and latent-intensity components. Dependence among structural zeros is modeled by standard parametric copulas, while dependence among latent mixing variables is modeled by checkerboard copulas. Likelihood-based inference is carried out using an inference-functions-for-margins procedure, and the proposed likelihood also supports full maximum likelihood estimation when computationally feasible. Simulation studies show accurate parameter estimation and good finite-sample performance under different dependence structures and latent mixing distributions. Applications to benchmark datasets from existing statistical software and a healthcare utilization dataset demonstrate the flexibility, computational efficiency, and practical usefulness of the proposed framework.
