Fisher information under Gaussian quadrature models

Marques da Silva Júnior, Antonio Hermes; Einbeck, Jochen; Craig, Peter S.

Abstract

This paper develops formulae to compute the Fisher information matrix for the regression parameters of generalized linear models with Gaussian random effects. The Fisher information matrix relies on the estimation of the response variance under the model assumptions. We propose two approaches to estimate the response variance: the first is based on an analytic formula (or a Taylor expansion for cases where we cannot obtain the closed form), and the second is an empirical approximation using the model estimates via the expectation–maximization process. Further, simulations under several response distributions and a real data application involving a factorial experiment are presented and discussed. In terms of standard errors and coverage probabilities for model parameters, the proposed methods turn out to behave more reliably than does the ‘disparity rule’ or direct extraction of results from the generalized linear model fitted in the last expectation–maximization iteration.

Citation

Marques da Silva Júnior, A. H., Einbeck, J., & Craig, P. S. (2018). Fisher information under Gaussian quadrature models. Statistica Neerlandica, 72(2), 74-89. https://doi.org/10.1111/stan.12116

• Journal Article Type: Article
• Acceptance Date: Aug 16, 2017
• Online Publication Date: Sep 10, 2017
• Publication Date: May 1, 2018
• Deposit Date: Sep 11, 2017
• Publicly Available Date: Sep 10, 2018
• Journal: Statistica Neerlandica
• Print ISSN: 0039-0402
• Electronic ISSN: 1467-9574
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 72
• Issue: 2
• Pages: 74-89
• DOI: https://doi.org/10.1111/stan.12116
• Public URL: https://durham-repository.worktribe.com/output/1376811