Smoothing spline ANOVA for multivariate Bernoulli observations, with application to ophthalmology data
Smoothing spline ANOVA for multivariate Bernoulli observations, with application to ophthalmology data
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DOI：
10.1198/016214501750332749
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发表时间：
2001-03-01
影响因子：
3.7
通讯作者：
Klein, B
中科院分区：
文献类型：
--
作者：
Gao, FY;Wahba, G;Klein, B
我们结合了方差（SS-ANOVA）模型的平滑样条分析和对数线性模型，以构建用于多元伯努利数据的部分灵活模型。估计预测变量上的联合分布条件。对数的比值比用于测量结果变量之间的关联。提出了基于宽松的块一步的数值方案Sor-Newton-Ralphson算法，以获取变异问题的近似解决方案。我们将广义近似交叉验证（GACV）和随机GACV扩展到选择：平滑参数到多元伯努利响应的情况。随机版本是快速且稳定的，可用于计算，并用于在每个块一步性迭代中自适应选择平滑参数。对于条件logit函数的柔性估计，获得了近似贝叶斯置信区间。进行了模拟研究，以使用比较的kullback-leibler距离作为码数来检查所提出的方法的性能。最后，该模型应用于Beaver Dam Eye研究的两眼观测数据，以检查色素异常和各种协变量的关联。
We combine a smoothing spline analysis of variance (SS-ANOVA) model and a log-linear model to build a partly flexible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block one-step successive over relaxation SOR-Newton-Ralphson algorithm is proposed to obtain an approximate solution for the variational problem. We extend the generalized approximate cross validation (GACV) and the randomized GACV for choosing: smoothing parameters to the case of multivariate Bernoulli responses. The randomized version is fast and stable to compute and is used to adaptively select smoothing parameters in each block one-step SOR iteration. Approximate Bayesian confidence intervals are obtained for the flexible estimates of the conditional logit functions. Simulation studies are conducted to check the performance of the proposed method, using the comparative Kullback-Leibler distance as a yardstick. Finally, the model is applied to two-eye observational data from the Beaver Dam Eye Study, to examine the association of pigmentary abnormalities and various covariates.