Direct Likelihood Approximations for Generalized Linear Mixed Models

Name: Direct Likelihood Approximations for Generalized Linear Mixed Models
Brand: VDM Verlag
SKU: 9783639286939
Price: 274.05 RON
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An Adaptive Approach

Autor: Basheer Ahmad

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Editura: VDM Verlag

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It is a standard approach to consider the maximum likelihood estimation procedure for the estimation...

Informații despre carte

Autor

Basheer Ahmad

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2010

Pagini

120

EAN

9783639286939

ISBN

3639286936

Enbook ID

06835835

Editura

VDM Verlag

Greutate

186

Dimensiuni

152 x 229 x 7

Descriere completă

It is a standard approach to consider the maximum likelihood estimation procedure for the estimation of parameters in statistical modelling. The sample likelihood function has a closed form representation only if the two densities in the integrand are conjugate to each other. In case of any non- conjugate pair, no closed form representation exists. In such situations, we need to approximate the integral by making use of some numerical techniques. A first or second order Laplace approximation or the (adaptive) Gauss-Hermite quadrature method can be applied in order to get an approximative objective function. The resulting approximation of the likelihood function still needs to be numerically maximized with respect to all unknown parameters. For such a numerical maximization, all required derivatives are provided in the scope of this work. We explore the use of the (adaptive) Gauss-Hermite quadrature for Generalized Linear Mixed Models, when the conditional density of the response given the random effects is a member of the linear exponential family and the random effects are Gaussian.

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Direct Likelihood Approximations for Generalized Linear Mixed Models

An Adaptive Approach

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Descriere completă

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