A coefficient of determination (R² ) for generalized linear mixed models

Area of Science:

• Statistics
• Bioinformatics
• Data Analysis

Background:

• Linear models are widely used for biological data analysis.
• Established goodness-of-fit measures (e.g., R-squared) lack consensus for generalized linear and mixed models.
• Accounting for heteroscedasticity and covariance in these models remains an open challenge.

Purpose of the Study:

• To propose a universally applicable goodness-of-fit measure for generalized linear and mixed models.
• To address the complexities of heteroscedasticity and covariance in model evaluation.
• To provide a unified approach for diverse variance-covariance structures.

Main Methods:

• Development of a new goodness-of-fit approach.
• Application to generalized linear models and generalized linear mixed models.
• Demonstration with arbitrary variance-covariance structures, including spatial and repeated measures data.

Main Results:

• The proposed method offers a unified approach to assess model fit.
• It effectively accounts for complex error structures, including heteroscedasticity and covariance.
• The approach is validated using three distinct biological datasets.

Conclusions:

• The new goodness-of-fit measure provides a robust and versatile tool for evaluating complex statistical models in biology.
• This work advances the assessment of model performance in the presence of intricate data dependencies.
• The proposed method facilitates more reliable analysis of biological data with non-standard error structures.