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Inferences in semi-parametric fixed and mixed models for longitudinal discrete data
Longitudinal data analysis for discrete such as count and binary data has been an
important research topic over the last three decades. With regard to inferences for
this type of data, the marginal model approach using ‘working’ correlation based
GEE (generalized estimating equation), and an auto-correlation class based GQL
(generalized quasi-likelihood) approach have been used, among others. This later
GQL approach was suggested because of certain efficiency drawbacks of the GEE
approach. Many studies were also done using the GQL approach for longitudinal
mixed models. In this thesis, we study the longitudinal count and binary data in a
wider semi-parametric longitudinal fixed and mixed model setup. For inferences, the
SQL (semi-parametric quasi-likelihood), SGQL (semi-parametric generalized quasilikelihood)
and SML (semi-parametric maximum likelihood) have been used wherever
appropriate. The asymptotic properties such as consistency of the estimators produced
by these approaches have been studied in detail. We also study the finite
sample properties of the new approaches and compare them where applicable with
existing SGEE (semi-parametric generalized estimating equation) approaches. The
proposed models and the estimation methodologies are also illustrated with some real
life data