A note on the use of rank-ordered logit models for ordered response categories

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Ranking models typically analyze unordered alternatives, limiting their application to ordered response categories.
• Existing models for top choices are less efficient than ranking models.
• There's a need for efficient ranking models applicable to ordered response categories.

Purpose of the Study:

• To adapt rank ordered logit models for analyzing ordered response categories.
• To propose a method for eliciting rank orders consistent with category ordering.
• To demonstrate the utility of this approach through simulations and examples.

Main Methods:

• Developed a variant of the rank ordered logit model.
• Truncated the distribution of rankings to admissible rankings consistent with category order.
• Utilized stereotype regression and rating scale item response models for demonstration.

Main Results:

• The proposed model yields lower standard errors compared to single top-choice models.
• Restricting rankings to admissible sets simplifies respondent decision-making.
• The adapted model effectively models rankings in ordered response categories.

Conclusions:

• The adapted rank ordered logit model provides a more efficient estimation for ordered response categories.
• This approach enhances the applicability of ranking models in fields with ordered data.
• The method reduces respondent burden while improving statistical efficiency.