Hierarchical Gaussian Processes for Survey Weighting: Local Equivalent Weights in Structured Populations
Abstract
Regression-based survey weighting connects model-based population estimation with design-based inference through equivalent weights. For nonlinear models, equivalent weights can be defined locally through the sensitivity of a poststratified population estimator. However, conventional regression models may inadequately capture nonlinear relationships and complex interactions across sparse poststratification cells. We develop a survey-weighting framework based on hierarchical Gaussian process (HGP) regression, combining structured group-level effects with kernel-based smoothing to share information across related cells. We derive Gaussian posterior prediction formulas that exploit the structured covariance representation to reduce computational costs. We also establish a uniform convergence result for the posterior predictive mean under stated regularity conditions and construct local equivalent weights by matching the first-order sensitivity of a plug-in poststratified estimand to that of a weighted average of fitted response means, with both derivatives taken with respect to the latent mean-scale vector. Simulations show that HGP achieves lower population-weighted prediction error under nonparametric structure, whereas logistic regression performs well under correct parametric specification. Additional analyses examine sample size, frame coverage, subgroup prediction, and population-mean agreement. An application to the Future of Families and Child Wellbeing Study illustrates the method. Overall, this work extends local equivalent-weight construction to nonparametric modeling and provides a computational framework and conditional theoretical results for survey weighting in structured, sparse populations.
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BibTeX
@misc{lee2026hierarchical,
title = {{Hierarchical Gaussian Processes for Survey Weighting: Local Equivalent Weights in Structured Populations}},
author = {Seonghun Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20321},
eprint = {2610.20321},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20321},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hierarchical Gaussian Processes for Survey Weighting: Local Equivalent Weights in Structured Populations
AU - Seonghun Lee
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.20321
UR - https://arxiv.org/abs/2610.20321
AB - Regression-based survey weighting connects model-based population estimation with design-based inference through equivalent weights. For nonlinear models, equivalent weights can be defined locally through the sensitivity of a poststratified population estimator. However, conventional regression models may inadequately capture nonlinear relationships and complex interactions across sparse poststratification cells. We develop a survey-weighting framework based on hierarchical Gaussian process (HGP) regression, combining structured group-level effects with kernel-based smoothing to share information across related cells. We derive Gaussian posterior prediction formulas that exploit the structured covariance representation to reduce computational costs. We also establish a uniform convergence result for the posterior predictive mean under stated regularity conditions and construct local equivalent weights by matching the first-order sensitivity of a plug-in poststratified estimand to that of a weighted average of fitted response means, with both derivatives taken with respect to the latent mean-scale vector. Simulations show that HGP achieves lower population-weighted prediction error under nonparametric structure, whereas logistic regression performs well under correct parametric specification. Additional analyses examine sample size, frame coverage, subgroup prediction, and population-mean agreement. An application to the Future of Families and Child Wellbeing Study illustrates the method. Overall, this work extends local equivalent-weight construction to nonparametric modeling and provides a computational framework and conditional theoretical results for survey weighting in structured, sparse populations.
ER -