Engebretsen Solveig, Glad Ingrid K
SAMBA, Norwegian Computing Center, Oslo, Norway.
Department of Mathematics, University of Oslo, Oslo, Norway.
Stat Med. 2020 Nov 10;39(25):3549-3568. doi: 10.1002/sim.8680. Epub 2020 Aug 26.
In many statistical regression and prediction problems, it is reasonable to assume monotone relationships between certain predictor variables and the outcome. Genomic effects on phenotypes are, for instance, often assumed to be monotone. However, in some settings, it may be reasonable to assume a partially linear model, where some of the covariates can be assumed to have a linear effect. One example is a prediction model using both high-dimensional gene expression data, and low-dimensional clinical data, or when combining continuous and categorical covariates. We study methods for fitting the partially linear monotone model, where some covariates are assumed to have a linear effect on the response, and some are assumed to have a monotone (potentially nonlinear) effect. Most existing methods in the literature for fitting such models are subject to the limitation that they have to be provided the monotonicity directions a priori for the different monotone effects. We here present methods for fitting partially linear monotone models which perform both automatic variable selection, and monotonicity direction discovery. The proposed methods perform comparably to, or better than, existing methods, in terms of estimation, prediction, and variable selection performance, in simulation experiments in both classical and high-dimensional data settings.
在许多统计回归和预测问题中，假定某些预测变量与结果之间存在单调关系是合理的。例如，基因组对表型的影响通常被假定为单调的。然而，在某些情况下，假定部分线性模型可能是合理的，其中一些协变量可以被假定具有线性效应。一个例子是使用高维基因表达数据和低维临床数据的预测模型，或者在组合连续和分类协变量时。我们研究了拟合部分线性单调模型的方法，其中一些协变量被假定对响应具有线性效应，而一些被假定具有单调（可能是非线性）效应。文献中现有的用于拟合此类模型的大多数方法都受到这样的限制，即它们必须事先为不同的单调效应提供单调性方向。我们在此提出了用于拟合部分线性单调模型的方法，这些方法既执行自动变量选择，又进行单调性方向发现。在经典和高维数据设置的模拟实验中，就估计、预测和变量选择性能而言，所提出的方法与现有方法表现相当或更好。
