Empirical likelihood based longitudinal studies
2016
In longitudinal data analysis, our primary interest is in the regression parameters for
the marginal expectations of the longitudinal responses; the longitudinal correlation
parameters are of secondary interest. The joint likelihood function for longitudinal
data is challenging, particularly for correlated discrete outcome data. Marginal modeling
approaches such as generalized estimating equations (GEEs) have received much
attention in the context of longitudinal regression. These methods are based on the
estimates of the first two moments of the data and the working correlation structure.
The confidence regions and hypothesis tests are based on the asymptotic normality.
The methods are sensitive to misspecification of the variance function and the
working correlation structure. Because of such misspecifications, the estimates can
be inefficient and inconsistent, and inference may give incorrect results. 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 a confidence region
for the parameter of interest. We extend our approach to variable selection for highdimensional
longitudinal data with many covariates. In this situation it is necessary
to identify a submodel that adequately represents the data. Including redundant
variables may impact the model’s accuracy and efficiency for inference. We propose a
penalized empirical likelihood (PEL) variable selection based on GEEs; the variable
selection and the estimation of the coefficients are carried out simultaneously. We
discuss its characteristics and asymptotic properties, and present an algorithm for optimizing
PEL. Simulation studies show that when the model assumptions are correct,
our method performs as well as existing methods, and when the model is misspecified,
it has clear advantages. We have applied the method to two case examples.
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