David Shor writes:

I’m dealing with a situation where I have two datasets, one that assigns each participant a discrete score out of five for a set of particular traits (Dog behavior characteristics by breed), and another from an independent source that ranks each breed by each characteristic. It’s also possible to obtain the results of a survey, where experts were asked to rank 7 randomly picked breeds by characteristics.

I’m interested in obtaining estimates for each trait, and intuitively, it seems clear that the second and third dataset provide a lot of information. But it’s unclear how to incorporate them to infer latent variables, since only sample ranks are observed. This seems like it is a common problem, do you have any suggestions?

My quick answer is that you can treat ranks as numbers (a point we make somewhere in Bayesian Data Analysis, I believe) and just fit an item-response model from there.

Val Johnson wrote an article on this in Jasa a few years ago, “Bayesian analysis of rank data with application to primate intelligence experiments.” He also did similar work calibrating college grades.