A constrained iteratively-reweighted least-squares framework for generalised linear models

Abstract

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.