A0345
Title: Efficient and proper GLM modelling with power link functions
Authors: Vali Asimit - City University London (United Kingdom) [presenting]
Alexandru Badescu - University of Calgary (Canada)
Feng Zhou - City University of London (United Kingdom)
Abstract: Generalised linear modelling is a flexible predictive model for observational data that is widely used in practice. Such a predictive model requires a careful choice of the link function, and estimation is then achieved by maximum likelihood estimation, for which an optimisation algorithm is required. The computational efficiency is not well-understood, and we raised awareness of the importance of choosing the right link function so the goodness of fit tests and other model adequacy tests are meaningful. The main contributions are as follows: 1) formalise the concept of proper Generalised linear modelling so that a Generalised Linear Model is computationally more reliable, 2) raise awareness of the consequences of choosing an improper link function, 3) provide a novel and efficient numerical algorithm for self-concordant likelihood functions for Poisson and Gamma regression, and 4) provide a novel and efficient numerical algorithm for Inverse-Gaussian regression that violates our definition of properness though the numerical results are computationally stable. The latter two contributions are illustrated through a comprehensive comparison with all available off-the-shelf existing packages implemented in MATLAB, Python and R.
