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While extensive work has been done to correct for biases due to measurementerror in scalar-valued covariates prone to errors in generalized linearregression models, limited work has been done to address biases associated withfunctional covariates prone to errors or the combination of scalar andfunctional covariates prone to errors in these models. We propose SimulationExtrapolation (SIMEX) and Regression Calibration approaches to correctmeasurement errors associated with a mixture of functional and scalarcovariates prone to classical measurement errors in generalized functionallinear regression. The simulation extrapolation method is developed to handlethe functional and scalar covariates prone to errors. We also develop methodsbased on regression calibration extended to our current measurement errorsettings. Extensive simulation studies are conducted to assess the finitesample performance of our developed methods. The methods are applied to the2011-2014 cycles of the National Health and Examination Survey data to assessthe relationship between physical activity and total caloric intake with type 2diabetes among community-dwelling adults living in the United States. We treatthe device-based measures of physical activity as error-prone functionalcovariates prone to complex arbitrary heteroscedastic errors, while the totalcaloric intake is considered a scalar-valued covariate prone to error. We alsoexamine the characteristics of observed measurement errors in device-basedphysical activity by important demographic subgroups including age, sex, andrace.

Generalized functional linear regression models with a mixture of complex function-valued and scalar-valued covariates prone to measurement error