Alam Entejar, Müller Peter, Rathouz Paul J
Department of Statistics and Data Sciences, The University of Texas at Austin, Austin, Texas, USA.
Department of Mathematics, The University of Texas at Austin, Austin, Texas, USA.
Stat Med. 2025 Feb 28;44(5):e10305. doi: 10.1002/sim.10305.
The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model. However, some inference summaries are not easily generated under existing maximum-likelihood-based inference (GLDRM). This includes uncertainty in estimation for model-derived functionals such as exceedance probabilities. The latter are critical in a clinical diagnostic or decision-making setting. In this article, by placing a Dirichlet prior on the baseline distribution, we propose a Bayesian model-based approach for inference to address these important gaps. We establish consistency and asymptotic normality results for the implied canonical parameter. Simulation studies and an illustration with data from an aging research study confirm that the proposed method performs comparably or better in comparison with GLDRM. The proposed Bayesian framework is most attractive for inference with small sample training data or in sparse-data scenarios.
与经典广义线性模型（GLM）相比，最近开发的半参数广义线性模型（SPGLM）通过将响应的基线或参考分布作为模型中的一个附加参数，提供了更大的灵活性。然而，在现有的基于最大似然的推断（GLDRM）下，一些推断总结不容易生成。这包括对模型衍生泛函（如超越概率）估计的不确定性。后者在临床诊断或决策环境中至关重要。在本文中，通过在基线分布上放置狄利克雷先验，我们提出了一种基于贝叶斯模型的推断方法来解决这些重要差距。我们为隐含的规范参数建立了一致性和渐近正态性结果。模拟研究以及来自一项衰老研究的数据示例证实，与GLDRM相比，所提出的方法表现相当或更好。所提出的贝叶斯框架对于使用小样本训练数据或在稀疏数据场景中的推断最具吸引力。
