  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.
