Regression Graph Models for Categorical Data: Parameterization and Inference

This book consolidates knowledge on regression chain graph models, often referred to as regression graph models, with a particular emphasis on their parameterizations and inference for the analysis of categorical data. It presents regression graphs, their interpretation in terms of sequences of multivariate regressions, interpretable parameterizations for categorical data, and inference and model selection within the frequentist and Bayesian approaches. The aim is to reveal the benefits of this family of graphical models for statistical data analysis and to encourage applications of these models as well as further research in the field. Data and R code used in the book are available online. The text is primarily intended for graduate and PhD students in statistics and data science who are familiar with the basics of graphical Markov models and of categorical data analysis, and for motivated researchers in specific applied fields.

Monia Lupparelli is an Associate Professor at the Department of Statistics, Computer Science and Applications, University of Florence, Italy. Besides graphical Markov models and categorical data analysis, her main research interests include causal inference with emphasis on statistical methods for causal discovery, statistical models for the analysis of dynamic network data, and latent Markov models for longitudinal data analysis with application in several fields.

Giovanni Maria Marchetti is a Full Professor at the Department of Statistics, Computer Science and Applications, University of Florence, Italy. His research interests include the theory and applications of multivariate analysis, generalized linear models for circular data and graphical Markov models. His more recent publications concern the representations of independencies in chain and mixed graphs and the properties of the symmetric Ising distributions.

Claudia Tarantola is a Full Professor at the Department of Economics, Management and Quantitative Methods, University of Milan, Italy. Besides graphical models and categorical data analysis, her research interests include Bayesian methods, Markov Chain Monte Carlo techniques, statistical models for financial risk, data science, and quantitative methods for diversity and inclusion.