Vector generalized linear model

In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the class of vector generalized linear models (VGLMs) was proposed to 
enlarge the scope of models catered for by <a href="/facts/Generalized_linear_models/Sf1htm5W">generalized linear models</a> (GLMs).
In particular, VGLMs allow for response variables outside the classical <a href="/facts/Exponential_family/1LkkqEIf">exponential family</a>
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).
The central algorithm adopted is the <a href="/facts/Iteratively_reweighted_least_squares/cqU60Scd">iteratively reweighted least squares</a> <a href="/facts/Iterative_method/uKMAJhEh">method</a>,
for <a href="/facts/Maximum_likelihood/0Yq2dpQD">maximum likelihood</a> 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.

Vector generalized linear model open-in-new

Vector generalized linear model