Many applications of generalised linear models (GLMs) can be improved by applying constraints that impose assumptions on the associations or improve consistency of the estimators. Yet, there are still barriers to the implementation and practical application of constrained GLMs. We present a general framework for fitting GLMs subject to linear constraints on the coefficients that offers original and interesting features. First, estimation is performed using constrained iteratively-reweighted least-squares (CIRLS), offering fast and stable algorithms with excellent convergence performance. Second, the development includes advanced inferential procedures based on truncated multivariate normal distribution and corrected degrees of freedom that account for the constrained nature of the estimation problem. Extensive simulation studies indicate good inferential and computational properties, even in the case of slightly overconstrained models. Third, the proposed methods are fully implemented in the 'cirls' library for the R software, embedding constrained estimation in standard regression routines with simple usage and syntax. Two real-data case studies provide examples of applications for constrained dose-response estimation and compositional data analysis. The CIRLS framework and software offer a unified approach for various constrained estimation problems across a wide range of research areas.

翻译：广义线性模型（GLM）的许多应用可以通过施加约束来改进，这些约束能够对关联性施加假设或提高估计量的一致性。然而，约束GLM的实施和实际应用仍存在障碍。我们提出了一个在系数上施加线性约束的GLM拟合通用框架，该框架具有原创性和有趣的特征。首先，估计采用约束迭代重加权最小二乘法（CIRLS）进行，提供了快速稳定的算法和优异的收敛性能。其次，该框架包含了基于截断多元正态分布和修正自由度的先进推断程序，这些程序考虑了估计问题的约束性质。广泛的模拟研究表明，即使在轻微过约束模型的情况下，该方法也具有良好的推断和计算特性。第三，所提出的方法已在R软件的'cirls'库中完全实现，将约束估计嵌入到标准的回归例程中，具有简单的使用方式和语法。两个真实数据案例研究为约束剂量-响应估计和成分数据分析的应用提供了示例。CIRLS框架和软件为跨广泛研究领域的各种约束估计问题提供了一个统一的方法。