Rank-Ordered Logit Model With Ties

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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.

References

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  1. ↑ Allison, P. D. and N. A. Christakis (1994). "Logit Models for Sets of Ranked Items." Sociological Methodology 24: 199-228.
  2. ↑ SAS (2008). The PHREG Procedure. SAS/STAT® 9.2 User’s Guide. Cary, NC, SAS Institute Inc.
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