Direct Likelihood Approximations for Generalized Linear Mixed Models: An Adaptive Approach - Softcover

Ahmad, Basheer

Softcover

ISBN 10: 3639286936 ISBN 13: 9783639286939

Publisher: VDM Verlag Dr. Müller, 2010

Synopsis

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.

About this title

About the Author

He is a Professor of Statistics/Mathematics at Iqra University Karachi, Pakistan. He obtained his PhD from Graz University of Technology, Austria. His main area of research is Generalized Linear Mixed Models (GLMMs). He has developed direct likelihood approximation methods in GLMMs.

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2010
• Language: English
• ISBN 10: 3639286936
• ISBN 13: 9783639286939
• Binding: Paperback
• Number of pages: 120