1st Edition

# Modern Applied Regressions Bayesian and Frequentist Analysis of Categorical and Limited Response Variables with R and Stan

286 Pages 29 Color & 40 B/W Illustrations
by Chapman & Hall

286 Pages 29 Color & 40 B/W Illustrations
by Chapman & Hall

Also available as eBook on:

Modern Applied Regressions creates an intricate and colorful mural with mosaics of categorical and limited response variable (CLRV) models using both Bayesian and Frequentist approaches. Written for graduate students, junior researchers, and quantitative analysts in behavioral, health, and social sciences, this text provides details for doing Bayesian and frequentist data analysis of CLRV models. Each chapter can be read and studied separately with R coding snippets and template interpretation for easy replication. Along with the doing part, the text provides basic and accessible statistical theories behind these models and uses a narrative style to recount their origins and evolution.

This book first scaffolds both Bayesian and frequentist paradigms for regression analysis, and then moves onto different types of categorical and limited response variable models, including binary, ordered, multinomial, count, and survival regression. Each of the middle four chapters discusses a major type of CLRV regression that subsumes an array of important variants and extensions. The discussion of all major types usually begins with the history and evolution of the prototypical model, followed by the formulation of basic statistical properties and an elaboration on the doing part of the model and its extension. The doing part typically includes R codes, results, and their interpretation. The last chapter discusses advanced modeling and predictive techniques—multilevel modeling, causal inference and propensity score analysis, and machine learning—that are largely built with the toolkits designed for the CLRV models previously covered.

The online resources for this book, including R and Stan codes and supplementary notes, can be accessed at https://sites.google.com/site/socjunxu/home/statistics/modern-applied-regressions.

1. Introduction
2. Binary Regression
3. Polytomous Regression
4. Count Regression
5. Survival Regression
6. Extensions

### Biography

Dr. Jun Xu is professor of sociology and data science at Ball State University. His quantitative research interests include Bayesian statistics, categorical data analysis, causal inference, machine learning, and statistical programming. His methodological works have appeared in journals such as Sociological Methods and Research, Social Science Research, and The Stata Journal. He is an author of Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives (with Dr. Andrew S. Fullerton by Chapman & Hall). In the past two decades or so, he has authored or co-authored several statistical application commands and packages, including gencrm, grcompare and the popular SPost9.0 package in Stata, and stdcoef in R.

"I think that the text is a very brave attempt at bringing together (most of) the major topics in the analysis of CLRVs (we will return to this), from both Frequentist and Bayesian approaches, along with a very hands-on and empirical approach, and all bound together with the ubiquitous use of the R software. [...] Not only is this a very brave attempt, the author succeeds in it exceptionally well. It is a very easy read: I read the full text coverto-cover in just a few days. [...] Overall this is an excellent text that I could happily throw to any starting Ph.D. student/junior researcher who had little-to-no experience in CLRV models."
-Mark N. Harris, in Journal of the American Statistical Association, July 2023

"Overall, the materials are presented in an easy to comprehend manner, not only the main results and reviews of the basics, but also their important variants and extensions. In addition to the basic theories, the comments or narratives of their origins and developments certainly help enhance the readability, accessibility and interpretability of the materials, especially the advanced parts. The illustrative examples, extensive R codes and outputs, data analyses and their explanations in the doing part are extremely useful. The presentation of both Bayesian and frequentist approaches in a parallel manner provides additional value to the reader. Each chapter can be read or studied independently, and there is a website devoted to the relevant R code with supplementary notes. I enjoyed reading the book. It is a very welcome addition to the literature, and is especially handy for those who study or work with regression modelling and data analytics."
-Shuangzhe Liu, in International Statistical Review, June 2023

"This book fills an important gap in the field of categorical data analysis by combining a rigorous theoretical treatment of the subject matter with hands-on techniques to get the reader started in state-of-the-art statistical modeling. The topics covered in this book cannot easily be separated from parallel developments in computing, including modern software components that exploit advances in computing machinery. This is an excellent reference book, benefitting applied researchers wishing to understand and use advanced methodologies and explore the relevance of Bayesian approaches as well as machine learning. It also serves well as an advanced graduate textbook for graduate courses in categorical data analysis with a focus on R and modern Bayesian implementations available in Stan."
- Dan Powers, University of Texas at Austin

"There are many outstanding books that show how to use Stata for Categorical Data Analysis. I am pleased that R users finally have a book that competes with the best of them; and given his outstanding record, I am not surprised that Jun Xu is the person who has written that book. For those with a basic background in statistical methods, Modern Applied Regressions provides a solid explanation of advanced methods like logistic regression, ordinal and multinomial models, count models, and survival analysis, using both Bayesian and Frequentist approaches. If there were no statistical code in it, the book would still be excellent because of the straightforward ways it explains methods. Certainly, there are a lot of equations, but those are coupled with intuitive explanations and examples. But, the use of R and Stan is what makes the book a real standout for me. For those who learn best by doing (and I count myself among them) the numerous examples of statistical code and output are invaluable. I’ll enthusiastically recommend this book to anyone who is interested in its topics."
- Richard Williams, University of Notre Dame

"This Chapman & Hall book by Jun Xu is a thorough introduction to a range of generalized linear or categorical response variable (termed limited response variable in the book) models that will benefit data analysts focused on applications. As an author who has written on such models including two books, I find this new book a treasure for the following reasons. First, the book provides both the Bayesian and the frequentist treatments of generalized linear or categorical response variable models in the main chapters, each of which deals with one type of such models. Second, the author uses graphics and R and rstan/rstanarm code profusely and effectively to enhance learning by way of real-world application examples. Third, the book, while giving the reader a good exposure to a range of models, is particularly strong in the presentation of polytomous regression such as models of ordered and of unordered response since the author has done a good deal of research on models with ordered response. Fourth, the text gives importance to essential statistical tests, especially the likelihood ratio, score, and Wald tests as well as tests of the parallel lines/proportional odds assumption and of the proportional hazard assumption. Finally, the books will be particularly useful for instructors of graduate-level applied statistics on generalized linear models who primarily teach in the frequentist tradition but will want to provide a Bayesian alternative."
- Tim Liao, SUNY Stony Brook & University of Illinois