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The Augmented Hat‐Matrix of Hierarchical Generalised Linear Models and Its Use in Leverage Diagnostics

Gianfranco Lovison et al.

International Statistical Review2026https://doi.org/10.1111/insr.70030article
AJG 3ABDC A
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0.50

Abstract

Summary Defining a ‘hat‐matrix’ for a model is essential in many model diagnostic procedures, as it acts as an orthogonal projector from the observation space to the model space. In this paper, we introduce a unique Hat‐matrix for the class of hierarchical generalised linear models (HGLMs), which includes, as a special case, the subclass of generalised linear mixed models (GLMMs). We provide a practical discussion on interpreting the hat matrix values in HGLMs across various settings, aimed at assisting practitioners in model diagnostics. Additionally, we propose two new empirical thresholds to identify high‐leverage observations and clusters. We demonstrate the advantages of using these empirical thresholds over the traditional approach with a simulation study. Lastly, we present an application to real data to illustrate the effectiveness of our proposed methodology in real‐world scenarios.

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https://doi.org/https://doi.org/10.1111/insr.70030

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@article{gianfranco2026,
  title        = {{The Augmented Hat‐Matrix of Hierarchical Generalised Linear Models and Its Use in Leverage Diagnostics}},
  author       = {Gianfranco Lovison et al.},
  journal      = {International Statistical Review},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1111/insr.70030},
}

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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