Ordered Regression Models : Parallel, Partial, and Non-Parallel Alternatives book cover
1st Edition

Ordered Regression Models
Parallel, Partial, and Non-Parallel Alternatives

ISBN 9781466569737
Published April 5, 2016 by Chapman and Hall/CRC
172 Pages - 18 B/W Illustrations

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Book Description

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.

Web Resource
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

Ordinal Variables versus Ordinal Models
Brief History of Binary and Ordered Regression Models
Three Approaches to Ordered Regression Models
The Parallel Regression Assumption
A Typology of Ordered Regression Models
Link Functions
Asymmetrical Relationships in Partial and Nonparallel Models
Hypothesis Testing and Model Fit in Ordered Regression Models
Datasets Used in the Empirical Examples
Example: Education and Welfare Attitudes
Organization of the Book

Parallel Models
Parallel Cumulative Model
Parallel Continuation Ratio Model
Parallel Adjacent Category Model

Partial Models
Unconstrained versus Constrained Partial Models
Partial Cumulative Models
Partial Continuation Ratio Models
Partial Adjacent Category Models
Dimensionality in Partial Models

Nonparallel Models
The Nonparallel Cumulative Model
The Nonparallel Continuation Ratio Model
The Nonparallel Adjacent Category Model
Practical Issues in the Estimation of Nonparallel Models

Testing the Parallel Regression Assumption
Wald and LR Tests
The Score Test
The Brant Test
Additional Wald and LR Tests
Limitations of Formal Tests of the Parallel Assumption
Model Comparisons Using the AIC and the BIC
Comparing Coefficients across Cutpoint Equations
Comparing AMEs and Predicted Probabilities across Models

Heterogeneous Choice Models
Empirical Examples of Heterogeneous Choice Models
Group Comparisons Using Heterogeneous Choice Models
Introduction to Multilevel Ordered Response Regression
Bayesian Analysis of Ordered Response Regression
Empirical Examples of Bayesian Ordered Regression Models



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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