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Ordered regression models: parallel, partial, and non-parallel alternatives

By: Fullerton, Andrew S.
Contributor(s): Xu, Jun.
Series: Chapman &​ Hall/​CRC statistics in the social and behavioral sciences. Publisher: Boca Raton CRC Press 2016Description: xi, 171 p.ISBN: 9781466569737.Subject(s): Regression analysisDDC classification: 519.5​36 Summary: 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. (https://www.crcpress.com/Ordered-Regression-Models-Parallel-Partial-and-Non-Parallel-Alternatives/Fullerton-Xu/p/book/9781466569737)
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Table of Contents:

1. Introduction
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

2. Parallel Models
Parallel Cumulative Model
Parallel Continuation Ratio Model
Parallel Adjacent Category Model
Estimation
Conclusions
Appendix

3. Partial Models
Unconstrained versus Constrained Partial Models
Partial Cumulative Models
Partial Continuation Ratio Models
Partial Adjacent Category Models
Dimensionality in Partial Models
Conclusions
Appendix

4. Nonparallel Models
The Nonparallel Cumulative Model
The Nonparallel Continuation Ratio Model
The Nonparallel Adjacent Category Model
Practical Issues in the Estimation of Nonparallel Models
Conclusions
Appendix

5. 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
Conclusions
Appendix

6. Extensions
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
Conclusion

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.

(https://www.crcpress.com/Ordered-Regression-Models-Parallel-Partial-and-Non-Parallel-Alternatives/Fullerton-Xu/p/book/9781466569737)

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