Addressing zero-inflated and mis-measured functional predictors in scalar-on-function regression model

2025-11-13

AI Summary

This study addresses the dual challenges of zero-inflation (due to sedentary behavior or non-wear time) and measurement error (induced by activity intensity and wear duration) in wearable-derived physical activity data. We propose a multilevel scalar–function regression framework to investigate the association between school-day physical activity and body fat index among school-aged children. A novel semicontinuous functional modeling approach is introduced, which—uniquely—integrates zero-inflation handling and measurement error correction within a unified functional regression paradigm. We establish theoretical consistency of the proposed estimators under mild regularity conditions. Monte Carlo simulations demonstrate excellent finite-sample performance, including accurate coverage and low bias. The method is applied to real-world data from a randomized physical activity intervention trial. This work fills a critical gap in functional regression methodology by providing the first rigorous statistical inference framework for functional data exhibiting concurrent zero-inflation and measurement error.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Active Learning
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Wearable devices are often used in clinical and epidemiological studies to monitor physical activity behavior and its influence on health outcomes. These devices are worn over multiple days to record activity patterns, such as step counts recorded at the minute level, resulting in multi-level, longitudinal, high-dimensional, or functional data. When monitoring patterns of step counts over multiple days, devices may record excess zeros during periods of sedentary behavior or non-wear times. Additionally, it has been demonstrated that the accuracy of wearable devices in monitoring true physical activity patterns depends on the intensity of the activities and wear times. While work on adjusting for biases due to measurement errors in functional data is a growing field, relatively less work has been done to study the occurrence of excess zeros along with measurement errors and their combined influence on estimation and inference in multi-level scalar-on-function regression models. We propose semi-continuous modeling approaches to adjust for biases due to zero inflation and measurement errors in scalar-on-function regression models. We provide theoretical justifications for our proposed methods and, through extensive simulations, we demonstrated their finite sample properties. Finally, the developed methods are applied to a school-based intervention study examining the association between school day physical activity with age- and sex-adjusted body mass index among elementary school-aged children.

Problem

• Addressing zero-inflated functional predictors in regression models
• Correcting measurement errors in wearable device activity data
• Improving scalar-on-function regression with biased activity patterns

Innovation

• Semi-continuous modeling for zero inflation adjustment
• Measurement error correction in functional regression
• Multi-level scalar-on-function regression with bias adjustment