While extensive work has been done to correct for biases due to measurement error in scalar-valued covariates prone to errors in generalized linear regression models, limited work has been done to address biases associated with functional covariates prone to errors or the combination of scalar and functional covariates prone to errors in these models. We propose Simulation Extrapolation (SIMEX) and Regression Calibration approaches to correct measurement errors associated with a mixture of functional and scalar covariates prone to classical measurement errors in generalized functional linear regression. The simulation extrapolation method is developed to handle the functional and scalar covariates prone to errors. We also develop methods based on regression calibration extended to our current measurement error settings. Extensive simulation studies are conducted to assess the finite sample performance of our developed methods. The methods are applied to the 2011-2014 cycles of the National Health and Examination Survey data to assess the relationship between physical activity and total caloric intake with type 2 diabetes among community-dwelling adults living in the United States. We treat the device-based measures of physical activity as error-prone functional covariates prone to complex arbitrary heteroscedastic errors, while the total caloric intake is considered a scalar-valued covariate prone to error. We also examine the characteristics of observed measurement errors in device-based physical activity by important demographic subgroups including age, sex, and race.

翻译：在广义线性回归模型中，针对存在测量误差的标量协变量进行偏差校正已有大量研究，但针对函数型协变量误差或两种类型协变量同时存在测量误差的偏差校正研究仍十分有限。我们提出模拟外推法和回归校准法，以校正广义函数线性回归中同时存在经典测量误差的函数型与标量协变量的混合误差。针对含误差的函数型与标量协变量，开发了模拟外推法；同时将回归校准方法拓展至当前测量误差场景。通过大量模拟实验评估所提方法的有限样本性能。基于2011-2014年美国国家健康与营养调查数据，将方法应用于评估美国社区居民的身体活动与总热量摄入对2型糖尿病的影响。我们将设备测量的身体活动视为存在复杂异方差测量误差的函数型协变量，总热量摄入视为存在测量误差的标量协变量。同时，按年龄、性别、种族等重要人口统计学分组，分析设备测量身体活动中可观测测量误差的特征。