Vector generalized linear model

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In statistics, the class of vector generalized linear models (VGLMs) was proposed to enlarge the scope of models catered for by generalized linear models (GLMs). In particular, VGLMs allow for response variables outside the classical exponential family and for more than one parameter. Each parameter (not necessarily a mean) can be transformed by a link function. The VGLM framework is also large enough to naturally accommodate multiple responses; these are several independent responses each coming from a particular statistical distribution with possibly different parameter values.

Vector generalized linear models are described in detail in Yee (2015).^[1] The central algorithm adopted is the iteratively reweighted least squares method, for maximum likelihood estimation of usually all the model parameters. In particular, Fisher scoring is implemented by such, which, for most models, uses the first and expected second derivatives of the log-likelihood function.