Inference in Generalized Additive Mixed Models by Using Smoothing Splines
利用平滑样条进行广义可加混合模型推断AI 解读 ↓
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利用平滑样条进行广义可加混合模型推断
- 研究问题
- 对于过度离散且相关的聚类、层级或空间数据，如何同时刻画非线性协变量作用与随机效应，并统一推断各模型成分？
- 方法与思路
- 作者用平滑样条估计非参数函数，以边际拟似然联合估计平滑参数和方差成分，再用双重惩罚拟似然进行近似推断。
- 材料陈述的贡献
- 摘要称方法可借助工作广义线性混合模型实现统一推断，并提出稀疏数据偏差校正；传染病应用与模拟用于评价表现。
- 阅读关注点
- 阅读全文时应核对平滑项与随机效应的区分、积分近似误差、方差成分估计，以及稀疏数据偏差校正的条件。
- 阅读边界
- 仅据所给 Crossref 摘要，近似推断的误差、校正幅度及模拟结果未说明；软件可实现不等于所有数据设定下有效。
原文摘要
Summary Generalized additive mixed models are proposed for overdispersed and correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. This class of models allows flexible functional dependence of an outcome variable on covariates by using nonparametric regression, while accounting for correlation between observations by using random effects. We estimate nonparametric functions by using smoothing splines and jointly estimate smoothing parameters and variance components by using marginal quasi-likelihood. Because numerical integration is often required by maximizing the objective functions, double penalized quasi-likelihood is proposed to make approximate inference. Frequentist and Bayesian inferences are compared. A key feature of the method proposed is that it allows us to make systematic inference on all model components within a unified parametric mixed model framework and can be easily implemented by fitting a working generalized linear mixed model by using existing statistical software. A bias correction procedure is also proposed to improve the performance of double penalized quasi-likelihood for sparse data. We illustrate the method with an application to infectious disease data and we evaluate its performance through simulation.