Moderation analyses are widely used in biomedical and psychosocial research to investigate differential treatment effects, with moderators frequently identified through testing the significance of the interaction between the predictor and the potential moderator under strong parametric assumptions. Without imposing any parametric forms on how the moderators may affect the relationship between predictors and responses, varying coefficient models address this fundamental problem of strong parametric assumptions with the current practice of moderation analysis and provide a much broader class of models for complex moderation relationships. Local polynomial, especially local linear (LL), methods are commonly used in estimating the varying coefficient models. Recently, a double-smoothing (DS) LL method has been proposed for nonparametric regression models, with nice properties compared to LL and local cubic (LC) methods. In this paper, we generalise DS to varying coefficient models, and show that it holds similar advantages over LL and LC methods.

中文翻译：

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变系数模型的双重平滑

调节分析广泛用于生物医学和社会心理研究，以研究不同的治疗效果，调节分析经常通过在强参数假设下测试预测因子和潜在调节因子之间相互作用的重要性来确定。在不对调节器如何影响预测变量和响应之间的关系施加任何参数形式的情况下，变系数模型通过当前调节分析的实践解决了强参数假设这一基本问题，并为复杂的调节关系提供了更广泛的模型类别。局部多项式，尤其是局部线性 (LL) 方法通常用于估计可变系数模型。最近，已经为非参数回归模型提出了一种双平滑 (DS) LL 方法，与 LL 和局部三次 (LC) 方法相比，它具有很好的特性。在本文中，我们将 DS 推广到变系数模型，并表明它与 LL 和 LC 方法相比具有类似的优势。