TITLE:
Empirical Likelihood Based Longitudinal Data Analysis
AUTHORS:
Tharshanna Nadarajah, Asokan Mulayath Variyath, J Concepción Loredo-Osti
KEYWORDS:
Longitudinal Data, Generalized Estimating Equations, Empirical Likelihood, Adjusted Empirical Likelihood, Extended Empirical Likelihood
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.4,
July
13,
2020
ABSTRACT: In longitudinal data
analysis, our primary interest is in the estimation of regression parameters
for the marginal expectations of the longitudinal responses, and the
longitudinal correlation parameters are of secondary interest. The joint
likelihood function for longitudinal data is challenging, particularly due to
correlated responses. Marginal models, such as generalized estimating equations
(GEEs), have received much attention based on the assumption of the first two
moments of the data and a working correlation structure. The confidence regions
and hypothesis tests are constructed based on the asymptotic normality. This
approach is sensitive to the misspecification of the variance function and the
working correlation structure which may yield inefficient and inconsistent
estimates leading to wrong conclusions. To overcome this problem, we propose an
empirical likelihood (EL) procedure based on a set of estimating equations for
the parameter of interest and discuss its characteristics
and asymptotic properties. We also provide an algorithm based on EL
principles for the estimation of the regression parameters and the construction
of its confidence region. We have applied the proposed method in two case
examples.