Model Averaging Methods for Weight Trimming in Generalized Linear Regression Models.

Area of Science:

• Statistics
• Survey Methodology

Background:

• Unequal probability sampling can bias estimates, especially in regression models with misspecification or nonignorable sampling.
• Inverse probability weights are common but can be highly variable in disproportional designs, leading to bias when trimmed.
• Current weight trimming methods are often ad hoc and do not optimize bias-variance trade-offs.

Purpose of the Study:

• To develop data-driven weight trimming estimators using Bayesian model averaging.
• To extend previous linear regression results to generalized linear regression models.
• To create robust estimators that balance bias correction and variance reduction.

Main Methods:

• Utilizing Bayesian model averaging to construct estimators.
• Extending existing methods for linear regression to generalized linear models.
• Developing models that adapt to the importance of bias correction versus variance reduction.

Main Results:

• The proposed Bayesian model averaging approach provides data-driven weight trimming.
• The developed estimators approximate fully-weighted estimates when bias is critical.
• The estimators approximate unweighted estimates when variance reduction is prioritized.

Conclusions:

• Bayesian model averaging offers a principled approach to weight trimming in complex sample surveys.
• The new methods provide robust estimators for generalized linear regression models with unequal probability sampling.
• These data-driven estimators effectively manage the bias-variance trade-off in survey data analysis.