Rudas T. Lectures on Advanced Topics in Categorical Data Analysis

Springer, 2024. — 385 p.This book continues the mission of the previous text by the author, Lectures on Categorical Data Analysis, by expanding on the introductory concepts from that volume and providing a mathematically rigorous presentation of advanced topics and current research in statistical techniques which can be applied in the social, political, behavioral, and life sciences. It presents an intuitive and unified discussion of an array of themes in categorical data analysis, and the emphasis on structure over stochastics renders many of the methods applicable in machine learning environments and for the analysis of big data.
The book focuses on graphical models, their application in causal analysis, the analytical properties of parameterizations of multivariate discrete distributions, marginal models, and coordinate-free relational models. To guide the readers in future research, the volume provides references to original papers and also offers detailed proofs of most of the significant results. Like the previous volume, it features exercises and research questions, making it appropriate for graduate students, as well as for active researchers.Preface
Acknowledgments
Introduction
Undirected Graphical Models
Directed Graphical Models
Causal Analysis Using DAGs: Theory
Causality and Intuition
Causal Analysis Using DAGs: Applications and Limitations
Marginal Log-Linear Parameterization
Smoothness of Parameterizations of Discrete Distributions
Smoothness of Marginal Log-Linear Parameterizations
Marginal Log-Linear Models
Coordinate-Free Relational Models
Index