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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, November 12, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl J. A. Nelder}
\centerline{\sl Imperial College, London}
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\centerline{\bf Extended likelihood inference applied to a new class of models}
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               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.

Joint work with Youngjo Lee, Seoul National Univ., Korea.

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