Corrected score approach to estimating logistic functional regression models with measurement error

Music City Center 

Although measurement error (ME) in functional covariates has been addressed in generalized functional linear regression models, attempts to simultaneously account for measurement error in both functional and scalar covariates are limited. We propose a Monte Carlo corrected score (MCCS) method that uses complex variable simulation-extrapolation for functional logistic regression to fill this gap. The MCCS method effectively handles serially correlated ME without relying on distributional assumptions about the true or observed measures, in contrast to approaches that assume discrete MEs. MCCS is used when the exact forms of the corrected score do not exist. We conducted simulation studies under Gaussian and non-Gaussian ME distributions to evaluate its performance. Our simulations showed that the biases of MCCS estimations were consistently smaller than those of average and naive estimations. Furthermore, the MCCS estimation is robust to increased ME scales and non-Gaussian ME distributions. The method is applied to examine how device-based physical activity and self-reported fiber intake relate to type 2 diabetes risk among U.S. adults.

Measurement Error

Functional Data

Corrected Score

Physical Activity 

Section on Statistical Computing