Cumulative Link Models for Ordinal Regression with the R Package ordinal

This paper introduces the R-package ordinal for the analysis of ordinal data using cumulative link models. The model framework implemented in ordinal includes partial proportional odds, structured thresholds, scale effects and flexible link functions. The package also support cumulative link models with random effects which are covered in a future paper. A speedy and reliable regularized Newton estimation scheme using analytical derivatives provides maximum likelihood estimation of the model class. The paper describes the implementation in the package as well as how to use the functionality in the package for analysis of ordinal data including topics on model identifiability and customized modelling. The package implements methods for profile likelihood confidence intervals, predictions of various kinds as well as methods for checking the convergence of the fitted models.