R中形状约束广义加性模型的一些扩展
On some extensions of shape-constrained generalized additive modelling in R
AI总结：
本文扩展R中形状约束广义加性模型框架，支持平滑交互、线性泛函与残差自相关，并在scam包中实现。
摘要：
结合预测变量平滑函数来解释与响应变量关系的回归模型已获得广泛使用，并在各种应用中取得成功。通过纳入预测变量的平滑函数，这些模型能够捕捉响应与预测变量之间的复杂关系，同时仍允许对结果进行解释。在探索响应变量与预测变量之间关系的情况下，假设这些关系遵循某些形状约束并不罕见。此类约束的示例包括单调性和凸性。R的scam包已成为一个流行的包，用于对具有形状约束平滑项的指数族广义加性模型进行完整拟合。本文旨在扩展形状约束广义加性模型（SCAM）的现有框架，以容纳协变量的平滑交互、形状约束平滑项的线性泛函以及残差自相关的纳入。本文描述的方法已在scam包的最新版本中实现，该版本可在综合R档案网络（CRAN）上获取。
英文摘要：
Regression models that incorporate smooth functions of predictor variables to explain the relationships with a response variable have gained widespread usage and proved successful in various applications. By incorporating smooth functions of predictor variables, these models can capture complex relationships between the response and predictors while still allowing for interpretation of the results. In situations where the relationships between a response variable and predictors are explored, it is not uncommon to assume that these relationships adhere to certain shape constraints. Examples of such constraints include monotonicity and convexity. The scam package for R has become a popular package to carry out the full fitting of exponential family generalized additive modelling with shape restrictions on smooths. The paper aims to extend the existing framework of shape-constrained generalized additive models (SCAM) to accommodate smooth interactions of covariates, linear functionals of shape-constrained smooths and incorporation of residual autocorrelation. The methods described in this paper are implemented in the recent version of the package scam, available on the Comprehensive R Archive Network (CRAN).
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