Parameters estimation for longitudinal data models in presence of missing data / Mohamed Youssef Ezz Eldine Sabry ; Supervised Ahmed Mahmoud Gad , Rasha Mohamed Bahgat Elkholy

Thesis (Ph.D.) - Cairo University - Faculty of Economics and Political Science - Department of Statistics

Longitudinal data models have several applications in medicine, epidemiology, agri-culture and education. Longitudinal data models analysis is usually characterized by its complexity due to inter-correlation within each subject as a result of re- peated measurements on the subject. Incorporating this inter-correlation leads to extend the generalized linear model (GLM) to the generalized linear mixed model (GLMM) via including the random e{uFB00}ects component. When the random e{uFB00}ects distribution has more complex features than the symmetric, unimodal and normal density e.g., it has a multi-modal, skewed density, heavy tailed, or not belonging to exponential family, the complexity problem will increase, as well as introduce critical features of subject heterogeneity. Thus, statistical techniques based on relaxing normality parametric assumption for the random e{uFB00}ects distribution are of interest. This thesis aims to obtain the maximum likelihood estimates for the parameters of the linear mixed model (LMM); a special case of GLMM when link function is the identity, assuming the presence of missing data, when the normal- ity assumption for the random e{uFB00}ects is relaxed and a multivariate t distribution is used instead. Actually, a multivariate t is a typical example for the case of heavy tailed distributions, as well as not belonging to exponential family class, this increases complexity from di{uFB00}erent perspectives. Firstly, violating normality, leads to a conditional distribution with unknown analytical form

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