Page 368 - Contributed Paper Session (CPS) - Volume 4

CPS2292 Roger S. Zoh, PhD et al.
Instrumental Variable Approach to Estimating
the Scalar-on-Function Regression Model with
Measurement Error with Application to Energy
Expenditure Assessment in Childhood Obesity
1
2
1
Carmen D. Tekwe , Roger S. Zoh *, Lan Xue
1 Department of Epidemiology and Biostatistics, Indiana University, Bloomington, IN, USA
2 Department of Statistics, Oregon State University, Corvallis, OR, USA

Abstract
Wearable device technology allows continuous monitoring of biological
markers and thereby enables study of time-dependent relationships. For
example, in this paper, we are interested in the impact of daily energy
expenditure over a period of time on subsequent progression toward obesity
among children. Data from these devices appear as either sparsely or densely
observed functional data and methods of functional regression are often used
for their statistical analyses. We study the scalar-on function regression model
with imprecisely measured values of the predictor function. In this setting, we
have a scalar-valued response and a function-valued covariate that are both
collected at a single time period. We propose a generalized method of
moments-based approach for estimation while an instrumental variable
belonging in the same time space as the imprecisely measured covariate is
used for model identification. Additionally, no distributional assumptions
regarding the measurement errors are assumed, while complex covariance
structures are allowed for the measurement errors in the implementation of
our proposed methods. We demonstrate that our proposed estimator is L2
consistent and enjoys the optimal rate of convergence for univariate
nonparametric functions. In a simulation study, we illustrate that ignoring
measurement error leads to biased estimations of the functional coefficient.
The simulation studies also confirm our ability to consistently estimate the
function-valued coefficient when compared to approaches that ignore
potential measurement errors. Our proposed methods are applied to our
motivating example to assess the impact of baseline levels of energy
expenditure on BMI among elementary school-aged children.

Keywords
Childhood obesity; Energy expenditure; Functional data; Measurement error;
Instrumental variable

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