Lecture on modelling: Mixed effects non-linear and generalized linear models
1 hour 2 mins 5 secs,
56.85 MB,
MP3
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| Description: |
Bates, D (Wisconsin-Madison)
Tuesday 09 August 2011, 09:30-10:30 |
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| Created: | 2011-08-10 13:20 | ||||
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| Collection: | Design and Analysis of Experiments | ||||
| Publisher: | Isaac Newton Institute | ||||
| Copyright: | Bates, D | ||||
| Language: | eng (English) | ||||
| Distribution: |
World
(downloadable)
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| Credits: |
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| Explicit content: | No | ||||
| Aspect Ratio: | 16:9 | ||||
| Screencast: | No | ||||
| Bumper: | UCS Default | ||||
| Trailer: | UCS Default | ||||
| Abstract: | 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 Xß+Zb where ß 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. |
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