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Empirical Likelihood Based Longitudinal Data Analysis

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Document pages: 29 pages

Abstract: In longitudinal dataanalysis, our primary interest is in the estimation of regression parametersfor the marginal expectations of the longitudinal responses, and thelongitudinal correlation parameters are of secondary interest. The jointlikelihood function for longitudinal data is challenging, particularly due tocorrelated responses. Marginal models, such as generalized estimating equations(GEEs), have received much attention based on the assumption of the first twomoments of the data and a working correlation structure. The confidence regionsand hypothesis tests are constructed based on the asymptotic normality. Thisapproach is sensitive to the misspecification of the variance function and theworking correlation structure which may yield inefficient and inconsistentestimates leading to wrong conclusions. To overcome this problem, we propose anempirical likelihood (EL) procedure based on a set of estimating equations forthe parameter of interest and discuss its characteristicsand asymptotic properties. We also provide an algorithm based on ELprinciples for the estimation of the regression parameters and the constructionof its confidence region. We have applied the proposed method in two caseexamples.

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