The public defence of the PhD thesis Graphical models and structural equation modeling by Fatma Abdelkhalek is scheduled on the 13th Dec 2021 starting at 14.00 in the room H607 and via MS Teams. The supervisor of the thesis is Marianna Bolla. The abstract ot the thesis is the following:
This thesis investigates some multivariate statistical methods: graphical models (GM), structural equation modeling (SEM), and vector autoregression (VAR) models. It shows the distinctive characteristics of GM and SEM and that they share some characteristics, especially in the Gaussian case. In this case, the two approaches can be connected with time series analysis through the causal VAR model. Further, the SEM equations are considered as a linear dynamical system to which the celebrated R. Kalman’s filtering technique is applicable. Throughout the thesis we mainly work with exponential family distributions. In this framework, a multi-cluster contingency table model is introduced, and the convergence of the algorithm, based on an EM iteration, is proved. For each underlying technique, some novel results are obtained. In addition, various applications are conducted using Egyptian demographic and sociological reallife data.