The Augmented Hat‐Matrix of Hierarchical Generalised Linear Models and Its Use in Leverage Diagnostics
Year: 2026
Type: article
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.
Source: International Statistical Review
DOI: 10.1111/insr.70030
Institution: University of Palermo
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,880
OpenAlex ID: W7130419932
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