Correcting Measurement Error and Zero Inflation in Functional Covariates for Scalar-on-Function Quantile Regression

2026-02-05

AI Summary

This study addresses the challenge of analyzing time-varying behavioral data from wearable devices, which are often contaminated by measurement error and an excess of zero values—arising, for instance, from non-wear periods or sedentary behavior—that existing methods struggle to handle simultaneously. The authors propose a novel framework that introduces individual-specific, time-varying validity indicators to distinguish structural zeros from genuine observations. By jointly modeling latent functional covariates and zero-inflation probabilities, and employing joint quantile regression across multiple quantiles, the method assesses the impact of these covariates on health outcomes. This approach is the first to concurrently correct for both measurement error and zero inflation in functional data, integrating basis function expansions, linear mixed models, and joint quantile regression to substantially improve estimation efficiency and robustness. Simulations and an empirical analysis of childhood obesity demonstrate that the corrected step-count data align closely with energy expenditure, validating its efficacy as a proxy for physical activity.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Wearable devices collect time-varying biobehavioral data, offering opportunities to investigate how behaviors influence health outcomes. However, these data often contain measurement error and excess zeros (due to nonwear, sedentary behavior, or connectivity issues), each characterized by subject-specific distributions. Current statistical methods fail to address these issues simultaneously. We introduce a novel modeling framework for zero-inflated and error-prone functional data by incorporating a subject-specific time-varying validity indicator that explicitly distinguishes structural zeros from intrinsic values. We iteratively estimate the latent functional covariates and zero-inflation probabilities via maximum likelihood, using basis expansions and linear mixed models to adjust for measurement error. To assess the effects of the recovered latent covariates, we apply joint quantile regression across multiple quantile levels. Through extensive simulations, we demonstrate that our approach significantly improves estimation accuracy over methods that only address measurement error, and joint estimation yields substantial improvements compared with fitting separate quantile regressions. Applied to a childhood obesity study, our approach effectively corrects for zero inflation and measurement error in step counts, yielding results that closely align with energy expenditure and supporting their use as a proxy for physical activity.

Problem

• measurement error
• zero inflation
• functional covariates
• scalar-on-function regression
• quantile regression

Innovation

• zero-inflated functional data
• measurement error correction
• scalar-on-function quantile regression
• joint quantile regression
• latent functional covariates