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Fisher information under Gaussian quadrature models.

Marques da Silva Júnior, Antonio Hermes and Einbeck, Jochen and Craig, Peter S. (2018) 'Fisher information under Gaussian quadrature models.', Statistica Neerlandica., 72 (2). pp. 74-89.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher 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.
Date accepted:16 August 2017
Date deposited:12 September 2017
Date of first online publication:10 September 2017
Date first made open access:10 September 2018

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