Deletion diagnostics for the generalised linear mixed model with independent random effects.

Area of Science:

• Statistics
• Environmental Science
• Biostatistics

Background:

• Generalized linear mixed models (GLMMs) are crucial for analyzing environmental data.
• Influential observations can significantly distort exposure-response curves, especially at high exposure levels.
• Existing deletion diagnostics often rely on simplifying assumptions that may not hold true.

Purpose of the Study:

• To develop novel deletion diagnostics for GLMMs that account for the interdependence of mean and variance parameters.
• To provide a method for calculating standardized DFBETAs for both mean and variance parameters.
• To improve the reliability of GLMMs in the presence of influential observations.

Main Methods:

• Developed an approximate formula for deleted estimates and Cook's distance in GLMMs.
• The method does not assume variance parameter estimates are unaffected by data deletion.
• Investigated the probabilistic behavior of residuals and proposed a simulation-based standardization procedure.

Main Results:

• The proposed diagnostics allow for the calculation of standardized DFBETAs for both mean and variance parameters.
• Identified influential individuals in an occupational cohort exposed to silica using the new method.
• Demonstrated that neglecting variance component diagnostics can lead to inaccurate fitted curves and unstable confidence intervals.

Conclusions:

• The new GLMM diagnostics offer a more robust approach to identifying influential observations.
• Accurate identification of influential points is essential for reliable environmental data modeling.
• Failure to assess variance components can compromise the integrity of statistical analyses and conclusions.