Predicting Census Survey Response Rates With Parsimonious Additive Models and Structured Interactions

TL;DR

This paper develops interpretable nonparametric additive models with structured interactions to predict census survey response rates, achieving accuracy comparable to black-box methods while maintaining interpretability.

Contribution

It introduces a novel sparse additive modeling approach with structured interactions, extending computational methods for practical, interpretable survey response prediction.

Findings

Models achieve prediction accuracy comparable to gradient boosting and neural networks.

Proposed methods enhance interpretability without sacrificing performance.

Open-source algorithms extend existing sparse additive model capabilities.

Abstract

In this paper, we consider the problem of predicting survey response rates using a family of flexible and interpretable nonparametric models. The study is motivated by the US Census Bureau's well-known ROAM application, which uses a linear regression model trained on the US Census Planning Database data to identify hard-to-survey areas. A crowdsourcing competition (Erdman and Bates, 2016) organized more than ten years ago revealed that machine learning methods based on ensembles of regression trees led to the best performance in predicting survey response rates; however, the corresponding models could not be adopted for the intended application due to their black-box nature. We consider nonparametric additive models with a small number of main and pairwise interaction effects using $\ell_0$-based penalization. From a methodological viewpoint, we study our estimator's computational and statistical aspects and discuss variants incorporating strong hierarchical interactions. Our algorithms (open-sourced on GitHub) extend the computational frontiers of existing algorithms for sparse additive models to be able to handle datasets relevant to the application we consider. We discuss and interpret findings from our model on the US Census Planning Database. In addition to being useful from an interpretability standpoint, our models lead to predictions comparable to popular black-box machine learning methods based on gradient boosting and feedforward neural networks - suggesting that it is possible to have models that have the best of both worlds: good model accuracy and interpretability.