# Rank-Ordered Logit Model With Ties

The *rank-ordered logit model with ties*^{[1]} is a generalization of the Sequential Logit Model which is, in turn, a generalization of the Multinomial Logit Model.

Key aspects of the model are:

- Its interpretation is identical to that of the Multinomial Logit Model. That is, the parameters have the same interpretation and predictions are made in the same way (e.g., a Choice Simulator can be constructed from the rank-ordered logit model with ties).
- The Outcome Variable is assumed to be a ranking, where ties are permitted (i.e., a partial ranking).

## Computation of the log-likelihood

The model assumes that all possible rankings consistent with the an observed ranking containing ties are equally likely. For example, if a respondent that has given the following ranking: C > A = B > D > E (i.e., where A and B are tied), then there are two possible rankings consistent with this data: C > A > B > D > E and C > B > A > D > E.

The likelihood is then computed as the average of all of the possible likelihoods, where the likelihood for a possible ranking is computed using same approach as employed with the Sequential Logit Model.

## Software

SAS has a procedure called PHREG that can estimate this model.^{[2]}

Q has a generalized version of this model that estimates latent class and random parameter logit models.