Dear All
Prof John Nelder is going to give a seminar talk at Mathematics Department,
The University of Manchester this Weds afternoon (2nd April 2003).
Details are given as below.
All are welcome.
With All the Best
Jianxin Pan
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Dr Jianxin Pan
Department of Mathematics
The University of Manchester
Oxford Road, Manchester
M13 9PL
Tel: 0161-27-55864
Fax: 0161-27-55819
Email: [log in to unmask]
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Wednesday, 2 April 2003 at 2.30pm in Room1.08, Maths, University of
Manchester
Title: Double Hierarchical Generalized Linear Models: Extended likelihood
inference applied to a new class of models
By Professor John Nelder, FRS, Imperial College, London
A B S T R A C T
Random-effect models require an extension of Fisher likelihood. Extended
likelihood (Pawitan) or, equivalently, h-likelihood (Lee & Nelder), provide
a basis for likelihood inference applicable to random-effect models. The
model class, called hierarchical generalized linear models (HGLMs), is
derived from generalized linear models (GLMs). It supports (1) joint
modelling of mean and dispersion; (2) GLM errors for the response; (3)
random effects in the linear predictor for the mean, with distributions
following any conjugate distribution of a GLM distribution; (4) structured
dispersion components depending on covariates. Fitting of fixed and random
effects, given dispersion components, reduces to fitting an augmented GLM,
while fitting dispersion components, given fixed and random effects, uses an
adjusted profile h-likelihood and reduces to a second interlinked GLM,
which generalizes REML to all the GLM distributions. A single algorithm
can fit all members of the class and does not require either prior
distributions or the multiple quadrature needed for methods using marginal likelihood.
Model checking also generalizes from GLMs and allows the visual checking of
all aspects of the model. The model class can be extended to cover
correlated data expressed by random terms in the model, thus allowing fitting of
spatial and temporal models with GLM errors. Correlations can be expressed by
transformations of white noise, by structured covariance matrices, or by structured
precision matrices. Finally the class can be extended to double HGLMs, which allow random
effects in the dispersion model as well as in the mean. This leads, among
other things, to a potentially large expansion of classes of models used in
finance, the properties of which have still to be investigated.
Youngjo Lee, Seoul National University, Korea. J. A.Nelder, Imperial
College London.
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