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.

中文翻译：

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具有自动变量选择和单调性方向发现的部分线性单调方法。

在许多统计回归和预测问题中，假设某些预测变量与结果之间存在单调关系是合理的。例如，通常认为基因组对表型的影响是单调的。但是，在某些情况下，假设部分协变量可能具有线性效应，则采用部分线性模型可能是合理的。一个示例是使用高维基因表达数据和低维临床数据，或者结合使用连续和分类协变量的预测模型。我们研究了拟合部分线性单调模型的方法，其中一些协变量被认为对响应具有线性影响，而一些协变量被认为具有单调（可能是非线性）影响。文献中用于拟合此类模型的大多数现有方法都受到限制，即必须为不同的单调效果先验地向它们提供单调性方向。在这里，我们介绍用于拟合部分线性单调模型的方法，该模型既执行自动变量选择，又执行单调性方向发现。在经典和高维数据设置中的模拟实验中，在估计，预测和变量选择性能方面，所提出的方法在性能上与现有方法相当或更好。