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).

翻译：回归模型通过引入预测变量的平滑函数来解释与响应变量之间的关系，已得到广泛应用并在各类场景中取得成功。这些模型通过整合预测变量的平滑函数，既能捕捉响应变量与预测变量之间的复杂关系，又能保证结果的可解释性。在探索响应变量与预测变量间关系时，常假设这些关系符合特定形状约束，例如单调性和凸性。R语言的scam包已成为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的流行工具。本文旨在扩展现有的形状约束广义加性模型（SCAM）框架，以应对协变量平滑交互作用、形状约束平滑项的线性泛函以及残差自相关性的整合。本文所述方法已在最新版本的scam包中实现，该包可从综合R档案网络（CRAN）获取。