Antonio Hermes Marques da Silva Júnior
Fisher information under Gaussian quadrature models
Marques da Silva Júnior, Antonio Hermes; Einbeck, Jochen; Craig, Peter S.
Professor Jochen Einbeck firstname.lastname@example.org
Professor Peter Craig email@example.com
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. 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|
|Peer Reviewed||Peer Reviewed|
Accepted Journal Article
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 https://doi.org/10.1111/stan.12116. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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