Fisher information under Gaussian quadrature models. (10th September 2017)

• Record Type: Journal Article
• Authors: Marques da Silva Júnior, Antonio Hermes; Einbeck, Jochen; Craig, Peter S.
• Is Part Of: Statistica Neerlandica. Volume 72:Number 2(2018)
• Page Start: 74
• Page End: 89
• Publication Date: 2017-09-10
• Subjects: Gaussian random effects -- generalized linear models -- overdispersion -- standard errors; Statistics -- Periodicals; 519.5; 314.92
• DOI: 10.1111/stan.12116
• Languages: English
• ISSNs: 0039-0402

Abstract

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.