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Title: On the estimation of the vector generalized linear model Authors:  Panagiotis Paoullis - Frederick University and Cyprus University of Technology (Cyprus) [presenting]
Ana Colubi - University of Giessen (Germany)
Erricos Kontoghiorghes - Cyprus University of Technology and Birkbeck University of London, UK (Cyprus)
Abstract: Vector Generalized Linear Models (VGLMs) is a class of regression models that are limited only by the assumption that the regression coefficients enter through a set of linear predictors. The VGLM class is very large and encompasses a wide range of multivariate response types and models, e.g. it includes univariate and multivariate distributions, categorical data analysis, time series, survival analysis, generalized estimating equations, correlated binary data and nonlinear least squares problems. Models such as Generalised Linear Model, zero-inflated Poisson regression, zero-altered Poisson regression, positive-Poisson regression, and negative binomial regression are all special cases of VGLMs. The algorithm that is employed to find the Maximum Likelihood Estimate (MLE) of VGLM is based on iteratively reweighted least squares (IRLS) and Fisher scoring. Three methods for computing the IRLS of VGLM are presented. The first method transforms the VGLM in each iteration to an ordinary linear model and uses the QR decomposition to find the estimate. The other two employ the generalized QR decomposition to estimate the MLE of VGLM, formulated as iterative generalized linear least-squares problems. Strategies to exploit the special characteristics and properties of the problem are discussed.