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May 1, 2023Biometrical JournalOpen Access

An adjusted coefficient of determination (R2) for generalized linear mixed models in one go

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Authors

HPHans‐Peter PiephoUniversity of Hohenheim

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Implication

Statistical study demonstrates an adjusted coefficient of determination for generalized linear mixed models, indicating accurate goodness of fit without needing a separate null model.

Key Points

  • To introduce a single-step adjusted coefficient of determination for generalized linear mixed models that directly accounts for correlation among observed responses.
  • Derived a goodness-of-fit formulation incorporating random and correlated residual effects without requiring the fitting of a baseline null model.
  • Integrated an analytical bias correction to estimate variance explained by fixed effects and tested the estimator using three illustrative examples and numerical simulations.
  • Enabled direct calculation of the coefficient of determination solely from the candidate model fit in a single procedure.
  • Demonstrated through simulation that the proposed adjusted R-squared estimator achieves goodness-of-fit estimation with minimal bias.

Cite This Study

Hans‐Peter Piepho (2023) studied this question.

synapsesocial.com/papers/6a1eba4b5dae381e029a84e8https://doi.org/10.1002/bimj.202200290
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Also Consider

Synapse has enriched 2 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1A coefficient of determination ( R 2 ) for generalized linear mixed models2019 · 150 citations
  2. 2Bias correction in generalised linear mixed models with a single component of dispersion1995 · 498 citations