Workshop: Ordered Regression Models

Ordinal outcomes are very common in the social and behavioral sciences.The most popular regression method for ordinal outcomes is the cumulative odds model, which requires the restrictive proportional odds assumption.  In this short course, we consider a wide range of regression models for ordinal outcomes that relax the proportional odds assumption to varying degrees and allow one to consider several different probabilities of interest.We also consider formal and informal tests of the proportional odds assumption and the role they play in ordinal model selection.  This course focuses on examples of these models and tests in Stata using regular and user-written commands.Stata experience is not required, but it does help.  It is also possible to estimate these models using other software packages and programs, such as the VGAM package in R (see the chapter appendices in Fullerton and Xu 2016).

Indicative literature:

Brant, Rollin. 1990. “Assessing Proportionality in the Proportional Odds Model for Ordinal Logistic Regression.” Biometrics 46: 1171-1178.

Buis, Maarten L. 2007. "SEQLOGIT: Stata module to fit a sequential logit model" http://ideas.repec.org/c/boc/bocode/s456843.html.

Fullerton, Andrew S. 2009. “A Conceptual Framework for Ordered Logistic Regression Models.” Sociological Methods & Research 38: 306-347.Fullerton, Andrew S. and Jun Xu. 2012. “The Proportional Odds with Partial Proportionality

Constraints Model for Ordinal Response Variables.” Social Science Research 41: 182-198.

Fullerton, Andrew S. and Jun Xu. 2016. Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives. Boca Raton, FL: Chapman & Hall/CRC Press.

Williams, Richard. 2006. “Generalized Ordered Logit/Partial Proportional Odds Models for Ordinal Dependent Variables.” Stata Journal 6: 58–82.

Yee, Thomas W. 2010. “The VGAM Package for Categorical Data Analysis.” Journal of Statistical Software 32: 1-34.