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Fitting monotone polynomials in mixed effects models

机译:在混合效应模型中拟合单调多项式

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摘要

We provide a method for fitting monotone polynomials to data with both fixed and random effects. In pursuit of such a method, a novel approach to least squares regression is proposed for models with functional constraints. The new method is able to fit models with constrained parameter spaces that are closed and convex, and is used in conjunction with an expectation-maximisation algorithm to fit monotone polynomials with mixed effects. The resulting mixed effects models have constrained mean curves and have the flexibility to include either unconstrained or constrained subject-specific curves. This new methodology is demonstrated on real-world repeated measures data with an application from sleep science. Code to fit the methods described in this paper is available online.
机译:我们提供了一种将单调多项式拟合到具有固定和随机效应的数据的方法。为了追求这种方法,针对具有功能约束的模型提出了一种最小二乘回归的新方法。该新方法能够拟合具有封闭和凸面约束参数空间的模型,并与期望最大化算法结合使用以拟合具有混合效应的单调多项式。生成的混合效果模型具有受约束的均值曲线,并且可以灵活地包含不受约束或受约束的特定对象曲线。睡眠科学的应用程序在现实世界中的重复测量数据上演示了这种新方法。在线可找到适合本文所述方法的代码。

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