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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Lecture on modelling: Mixed effects non-linear and generalized linear models

## Lecture on modelling: Mixed effects non-linear and generalized linear modelsAdd to your list(s) Download to your calendar using vCal - Bates, D (Wisconsin-Madison)
- Tuesday 09 August 2011, 09:30-10:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Design and Analysis of Experiments Mixed-effects models are defined by the distributions of two vector-valued random variables, an n-dimensional response vector, Y and an unobserved q-dimensional random-effects vector, B. The mean of the conditional distribution, Y|B=b, depends on a linear predictor expression of the form X+Zb where is a p-dimensional fixed-effects parameter vector and the fixed and known model matrices, X and Z, are of the appropriate dimension. For linear mixed-effects models the conditional mean is the linear predictor; for generalized linear mixed-effects models the conditional mean is the value of an inverse link function applied to the linear predictor and for a nonlinear mixed-effects model the conditional mean is the result of applying a nonlinear model function for which the parameter vector is derived from the linear predictor. We describe the formulation of these mixed-effects models and provide computationally effective expressions for the profiled deviance function through which the maximum likelihood parameter estimates can be determined. In the case of the linear mixed-effects model the profiled deviance expression is exact. For generalized linear or nonlinear mixed-effects models the profiled deviance is approximated, either through a Laplace approximation or, at the expense of somewhat greater computational effort, through adaptive Gauss-Hermite quadrature. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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