# 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: 519.536 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)Item type | Current location | Item location | Collection | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|---|---|

Books | Vikram Sarabhai Library | Slot 1426 (0 Floor, East Wing) | Non-fiction | 519.536 F8O7 (Browse shelf) | Available | 192273 |

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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