Inferences in semi-parametric fixed and mixed models for longitudinal discrete data

Zheng, Nan (2017) Inferences in semi-parametric fixed and mixed models for longitudinal discrete data. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

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.

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