Modern Applied Regressions

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.

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.

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