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：回归模型通过纳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被证明卓有成效。这类模型既能捕捉响应变量与预测变量间的复杂关联，又允许对结果进行解释。在探究响应变量与预测变量关系时，常需假定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包已成为对指数族广义加性模型实施完整拟合的主流工具，该模型对平滑项施加形状限制。本文旨在扩展现有形状约束广义加性模型（SCAM）框架，使其能够处理协变量的平滑交互作用、形状约束平滑项的线性泛函以及残差自相关性的纳入。本文所述方法已在最新版scam包中实现，该包可从综合R存档网络（CRAN）获取。