, Volume 81, Issue 8, pp 985–1004 | Cite as

Assessing the robustness of estimators when fitting Poisson inverse Gaussian models

  • Kimberly S. WeemsEmail author
  • Paul J. Smith


The generalized linear mixed model (GLMM) extends classical regression analysis to non-normal, correlated response data. Because inference for GLMMs can be computationally difficult, simplifying distributional assumptions are often made. We focus on the robustness of estimators when a main component of the model, the random effects distribution, is misspecified. Results for the maximum likelihood estimators of the Poisson inverse Gaussian model are presented.


Poisson mixed models Inverse Gaussian distribution Influence function Directional derivative Maximum likelihood estimation 



The authors thank the Editor, reviewers, Dr. Dennis Boos (North Carolina State University) and Dr. Kimberly F. Sellers (Georgetown University) for helpful comments and suggestions that significantly improved this paper.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsNorth Carolina Central UniversityDurhamUSA
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA

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