Graphical models and structural equation modeling - PhD public defence

2021. 12. 13. 14:00
H607 and MS Teams
Fatma Abdelkhalek (BME MI)

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. K´alm´an’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.