Rank-ordered logit and incomplete/tied rankings

[Oleg Iva]

Dear StataList users,

I am dealing with a survey data, where individual respondents ranked 20 alternatives by assigning scores 1, 2, 3, 4, or 5, with 1 being the most preferable and 5 being the least preferable. Since the number of alternatives is greater than the number of ranks (1-5), we have an incomplete or partial ordering, in which subsets of alternatives S1, S2, ... , S5 partition the full set of alternatives: S1 contains the most preferred ones, S2 contains the set of next most preferred, and so on. And within these subsets, the alternatives are not ranked, so we can think of them as being "tied" for the rank.

The rank-ordered logistic regression routine as implemented in Stata can deal with ties and seemed initially as a good place to start. However, in the manual for rologit (http://www.stata.com/manuals13/rrologit.pdf), section on Incomplete Rankings and Ties, it is stated that "[an] example of incompleteness that cannot be analyzed with rologit is data in which respondents select the three alternatives they like best but are not requested to express their preferences among the three selected alternatives."

Does this mean that rologit can deal with ties at lower ranks but at the highest rank there has to be a unique alternative? In terms of the above notation, the subset S1 has to contain a single element?

If this is the case, then, I guess, rologit cannot be used without modifications, since about 80% of respondents have indicated more than one alternative in the most preferred subset S1. Would you have any suggestions for modifications of either the routine or dataset that enable me to proceed?

Thank you for your time,
oleg

[Kariyushi Rao]

I am equally confused by the Stata manual's apparent contradictions on page 8 of rologit. The following three statements appear in the manual. Statement #2 and Statement #3 each contradict Statement #1. The combination of Statements #2 and #3 strongly contradict Statement #1. Could someone please explain how all three of these statements could be true at the same time?

Statement #1: "Another example of incompleteness that cannot be analyzed with rologit is data in which respondents select the three alternatives they like best but are not requested to express their preferences among the three selected alternatives."

Statement #2: "rologit also permits ties in rankings."

Statement #3: "By treating choice data as incomplete ranking data with only the most preferred alternative marked, rologit may be used to estimate the model parameters for clustered choice data."

I am applying rologit to a multiarmed bandit context where experimental participants select 3 arms on each trial out of a list of 20 arms. I am treating "selection" as Rank = 1, and "non-selection" as Rank = 0. I thus have a three-way tie for Rank 1, and a 17-way tie for Rank 2 on each trial for each participant. Could someone verify whether this context is covered by Statements #2 and #3 above, or if it falls under Statement #1?