Description
Ordinal data exists in many fields of study. Many types of data also have a hierarchical or cluster structure. Extending the methods for dichotomous outcomes to ordinal outcomes has been actively pursued. Developments have been mainly in terms of logistic and probit regression models. In particular, because the pro-portional odds assumption, which is based on the logistic regression formulation, is a common choice for analysis of ordinal data. Many of the mixed models for ordinal data are generalizations of this model and include the proportional odds assumption (or its equivalent under the probit or complementary log-log link function).
For non-proportional odds, different extensions of the proportional odds model are presented. In a somewhat different extension of the proportional odds model, the scale of the regressor effects are allowed to vary, in other words, the underlying variance of the logistic distribution can vary as a function of covariates. By bringing together extensions of the proportional odds model, for longitudinal ordinal data, a mixed ordinal location-scale model was presented which include a log-linear structure for both the within-subject and between-subject variances, allowing covariates to influence both sources of variation, and also include a subject-level random effect in the within-subject variance specification.
No multivariate model for simultaneously analysis of multiple ordinal outcomes has been introduced for clustered data in location-scale models framework so far. In this study, we extended the location-scale approach for multivariate clustered ordinal data to simultaneously model two ordinal outcomes.