The use of sampling weights in Bayesian hierarchical models for small area estimation

Area of Science:

• Statistics
• Biostatistics
• Spatial Analysis

Background:

• Hierarchical modeling is common for small area estimation.
• Standard models often neglect complex survey design weights.
• Ignoring design weights can lead to inaccurate estimations.

Purpose of the Study:

• To develop computationally efficient Bayesian spatial smoothing models that incorporate design weights.
• To evaluate the impact of ignoring design weights and the benefits of spatial smoothing.
• To reduce bias and variance in small area estimation.

Main Methods:

• Bayesian spatial smoothing models.
• Integrated Nested Laplace Approximation (INLA) for efficient computation.
• Extensive simulation study including non-response and non-random selection.

Main Results:

• Proposed methods significantly reduce mean squared error compared to standard approaches.
• Inclusion of design weights reduces bias.
• Hierarchical smoothing achieves variance reduction.
• Models are efficient and easily implemented in R.

Conclusions:

• The developed Bayesian spatial smoothing models effectively integrate design weights for improved small area estimation.
• These methods offer substantial improvements in accuracy and efficiency.
• The approach is practical for real-world data analysis, as demonstrated with the BRFSS data.