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Fisher information under Gaussian quadrature models

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

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Antonio Hermes Marques da Silva Júnior


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.


Marques da Silva Júnior, A. H., Einbeck, J., & Craig, P. S. (2018). Fisher information under Gaussian quadrature models. Statistica Neerlandica, 72(2), 74-89.

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


Accepted Journal Article (294 Kb)

Copyright Statement
This is the accepted version of the following article: Marques da Silva Júnior, Antonio Hermes, Einbeck, Jochen & Craig, Peter S. (2018). Fisher information under Gaussian quadrature models. Statistica Neerlandica, 72(2): 74-89, which has been published in final form at This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

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