Estimate and Interpret Results from Ordered Regression Models
Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives presents regression models for ordinal outcomes, which are variables that have ordered categories but unknown spacing between the categories. The book provides comprehensive coverage of the three major classes of ordered regression models (cumulative, stage, and adjacent) as well as variations based on the application of the parallel regression assumption.
The authors first introduce the three "parallel" ordered regression models before covering unconstrained partial, constrained partial, and nonparallel models. They then review existing tests for the parallel regression assumption, propose new variations of several tests, and discuss important practical concerns related to tests of the parallel regression assumption. The book also describes extensions of ordered regression models, including heterogeneous choice models, multilevel ordered models, and the Bayesian approach to ordered regression models. Some chapters include brief examples using Stata and R.
This book offers a conceptual framework for understanding ordered regression models based on the probability of interest and the application of the parallel regression assumption. It demonstrates the usefulness of numerous modeling alternatives, showing you how to select the most appropriate model given the type of ordinal outcome and restrictiveness of the parallel assumption for each variable.
More detailed examples are available on a supplementary website. The site also contains JAGS, R, and Stata codes to estimate the models along with syntax to reproduce the results.
Table of Contents
Introduction. Parallel Models. Partial Models. Nonparallel Models. Testing the Parallel Regression Assumption. Extensions. References. Index.
Andrew S. Fullerton is an associate professor of sociology at Oklahoma State University. His primary research interests include work and occupations, social stratification, and quantitative methods. His work has been published in journals such as Social Forces, Social Problems, Sociological Methods & Research, Public Opinion Quarterly, and Social Science Research.
Jun Xu is an associate professor of sociology at Ball State University. His primary research interests include Asia and Asian Americans, social epidemiology, and statistical modeling and programing. His work has been published in journals such as Social Forces, Social Science & Medicine, Sociological Methods & Research, Social Science Research, and The Stata Journal.
"The book is intended to be a starter for somebody not familiar with the subject. It was written primarily for social scientists (published in the CRC Statistics in the Social and Behavioral Sciences Series) and as such, it can be read easily without any statistical pre-requisites beyond very basic Statistics and some working knowledge of logistic regression. Nevertheless, the book is certainly useful far beyond the social sciences themselves – in particular for epidemiologists, medical researchers and also statisticians of students of Statistics/Biostatistics who want to learn basic facts about ordered regression and perhaps motivate further study of this interesting field. The style of exposition is quite informal and intuitive."
~International Society for Clinical Biostatistics