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 (ML-SPGLM). 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 ML-SPGLM. The proposed Bayesian framework is most attractive for inference with small sample training data or in sparse-data scenarios.

翻译：近期发展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附加参数引入，相比经典GLM提供了更强的灵活性。然而，现有的基于最大似然估计的推断方法（ML-SPGLM）难以生成某些推论性汇总指标，例如超概率这类模型衍生函数的不确定性估计，而这些指标在临床诊断或决策制定中至关重要。本文通过为基线分布施加狄利克雷先验，提出了一种基于贝叶斯模型的推断方法，以弥补上述重要缺陷。我们证明了隐含典范参数的一致性和渐近正态性。模拟研究与基于老龄化研究数据的案例分析表明，所提方法的性能与ML-SPGLM相比具有可比性甚至更优。该贝叶斯框架尤其适用于小样本训练数据或稀疏数据场景下的推断。