Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models
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DOI：
10.1080/01621459.2012.737742
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发表时间：
2012-12-01
影响因子：
3.7
通讯作者：
Kneib, Thomas
中科院分区：
文献类型：
--
作者：
Scheipl, Fabian;Fahrmeir, Ludwig;Kneib, Thomas
结构化加性回归（星星）为复杂的高斯和非高斯回归模型提供了一个通用框架，其中预测因子包括非线性函数和表面、空间效应、变化系数、随机效应和其他回归项的任意组合。星星的巨大灵活性使得函数选择成为一项具有挑战性和重要性的任务，其目标是（1）选择相关协变量，（2）选择协变量对预测因子影响的适当和简约表示，以及（3）确定所需的相互作用。我们提出了一个尖峰和板前结构的功能选择，允许包括或排除单个系数以及代表特定模型项的系数块。一种新的乘法参数扩展需要获得良好的混合和收敛性能，马尔可夫链蒙特卡罗模拟方法，并诱导理想的收缩性能。在模拟研究和（真实的）基准分类数据，我们调查超参数设置的敏感性，并比较性能的竞争对手。我们的方法的灵活性和适用性证明了在加性分段指数模型与时变效应的右删失生存时间的重症监护患者脓毒症。在一个广泛的在线补充中讨论了地理加性和加性混合logit模型的应用。
Structured additive regression (STAR) provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects, and further regression terms. The large flexibility, of STAR makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor, and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a,Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In-simulation studies-and with (real)-benchmark classification data; we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive online supplement.