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Generalized Functional Linear Regression Models With Functional and Scalar Covariates Prone to Measurement Error.

Yuanyuan Luan1, Roger S Zoh1, Sneha Jadhav2

  • 1Department of Epidemiology and Biostatistics, School of Public Health, Indiana University, Bloomington, Indiana, USA.

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Summary
This summary is machine-generated.

New methods address measurement error in functional and scalar covariates for generalized linear regression. Joint functional simulation extrapolation (FSIMEX) and mixed effects model-based (MEM) approaches reduce bias, outperforming naive estimators.

Keywords:
NHANESdietary intakefunctional datameasurement errorphysical activitywearable accelerometer

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Generalized linear regression models often struggle with measurement error in covariates.
  • Existing methods primarily address scalar covariates, leaving a gap for mixed functional and scalar covariate scenarios.

Purpose of the Study:

  • To develop and evaluate novel methods for adjusting measurement error in generalized functional linear regression with mixed covariate types.
  • To compare the performance of joint functional simulation extrapolation (FSIMEX) and mixed effects model-based (MEM) approaches against existing methods and an Oracle estimator.

Main Methods:

  • Development of joint FSIMEX and MEM estimators for generalized functional linear regression with classical measurement errors in functional and scalar covariates.
  • Extensive simulations were conducted to compare the proposed methods with Oracle, PACE, Naive_ave, and Naive_one estimators.
  • Application of the methods to NHANES data to assess the relationship between physical activity, caloric intake, and type 2 diabetes status.

Main Results:

  • Joint FSIMEX and MEM estimators demonstrated low bias, closely approximating the Oracle estimator.
  • SIMEX and MEM methods significantly outperformed Naive_one estimators lacking measurement error adjustment.
  • Naive_ave and PACE estimators showed limitations in handling heteroscedasticity and scalar predictors, respectively.

Conclusions:

  • Failing to account for measurement error in functional and scalar covariates leads to biased estimations in generalized functional linear regression.
  • The developed joint FSIMEX and MEM methods provide effective bias adjustment for mixed covariate types.
  • Accurate covariate measurement error adjustment is crucial for reliable statistical inference, as demonstrated in the NHANES diabetes analysis.