Inference at the data's edge: Gaussian processes for modeling and inference under model-dependency, poor overlap, and extrapolation

• URL: http://arxiv.org/abs/2407.10442v1
• Date: Mon, 15 Jul 2024 05:09:50 GMT
• Title: Inference at the data's edge: Gaussian processes for modeling and inference under model-dependency, poor overlap, and extrapolation
• Authors: Soonhong Cho, Doeun Kim, Chad Hazlett,
• Abstract summary: The Gaussian Process (GP) is a flexible non-linear regression approach. It provides a principled approach to handling our uncertainty over predicted (counterfactual) values. This is especially valuable under conditions of extrapolation or weak overlap.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Gaussian Process (GP) is a highly flexible non-linear regression approach that provides a principled approach to handling our uncertainty over predicted (counterfactual) values. It does so by computing a posterior distribution over predicted point as a function of a chosen model space and the observed data, in contrast to conventional approaches that effectively compute uncertainty estimates conditionally on placing full faith in a fitted model. This is especially valuable under conditions of extrapolation or weak overlap, where model dependency poses a severe threat. We first offer an accessible explanation of GPs, and provide an implementation suitable to social science inference problems. In doing so we reduce the number of user-chosen hyperparameters from three to zero. We then illustrate the settings in which GPs can be most valuable: those where conventional approaches have poor properties due to model-dependency/extrapolation in data-sparse regions. Specifically, we apply it to (i) comparisons in which treated and control groups have poor covariate overlap; (ii) interrupted time-series designs, where models are fitted prior to an event by extrapolated after it; and (iii) regression discontinuity, which depends on model estimates taken at or just beyond the edge of their supporting data.

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