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

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 ResourceMore 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.

IntroductionOrdinal Variables versus Ordinal ModelsBrief History of Binary and Ordered Regression ModelsThree Approaches to Ordered Regression ModelsThe Parallel Regression AssumptionA Typology of Ordered Regression ModelsLink FunctionsAsymmetrical Relationships in Partial and Nonparallel ModelsHypothesis Testing and Model Fit in Ordered Regression ModelsDatasets Used in the Empirical ExamplesExample: Education and Welfare AttitudesOrganization of the Book Parallel ModelsParallel Cumulative ModelParallel Continuation Ratio ModelParallel Adjacent Category ModelEstimationConclusionsAppendix Partial ModelsUnconstrained versus Constrained Partial ModelsPartial Cumulative ModelsPartial Continuation Ratio ModelsPartial Adjacent Category ModelsDimensionality in Partial ModelsConclusionsAppendix Nonparallel ModelsThe Nonparallel Cumulative ModelThe Nonparallel Continuation Ratio ModelThe Nonparallel Adjacent Category ModelPractical Issues in the Estimation of Nonparallel ModelsConclusionsAppendix Testing the Parallel Regression AssumptionWald and LR TestsThe Score TestThe Brant TestAdditional Wald and LR TestsLimitations of Formal Tests of the Parallel AssumptionModel Comparisons Using the AIC and the BICComparing Coefficients across Cutpoint EquationsComparing AMEs and Predicted Probabilities across ModelsConclusionsAppendix ExtensionsHeterogeneous Choice ModelsEmpirical Examples of Heterogeneous Choice ModelsGroup Comparisons Using Heterogeneous Choice ModelsIntroduction to Multilevel Ordered Response RegressionBayesian Analysis of Ordered Response RegressionEmpirical Examples of Bayesian Ordered Regression ModelsConclusion 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.