http://www.ces.iisc.ernet.in/biodiversity/pubs/ces_pubs/pubs_2010/theme2_24.pdf

Check out this 2010 review. 

You could organise all dominance interactions in a sociometric matrix which takes into account the identity of each opponent and all the interactions and minimises inconsistencies. You can then test for linearity using Kendall’s coefficient of linearity and calculate a rank order most consistent with the linear hierarchy by minimizing the number of inconsistencies and then minimizing the total strength of inconsistencies.

See papers by de Vries et al:

de Vries, H.1995. An improved test of linearity in dominance hierarchies containing unknown or tied relationships. Animal Behaviour, 50,1375e1389.

de Vries, H. 1998. Finding a dominance order most consistent with a linear hier- archy: a new procedure and review. Animal Behaviour, 55,827e843.

de Vries, H., Netto, W. J. & Hanegraaf, P. L. H. 1993. MatMan: a program for the analysis of sociometric matrices and behavioural transition matrices. Behaviour, 125,157e175.

I have used this method successfully in a 2013 paper on dominance in rooks, see attached.

Article Dominance, pair bonds and boldness determine social-foraging...

Thanks Alan and Jolle

Matt

A general approach is based on the Bradley Terry model.

Here is a description http://projecteuclid.org/download/pdf_1/euclid.aos/1079120141

The reference is Hunter, David R. "MM algorithms for generalized Bradley-Terry models." Annals of Statistics (2004): 384-406.  There has been a great deal of work on this type of model (think betting on cricket, you have to do something to make the game interesting). There is an R package to run quite general Bradley Terry models http://cran.r-project.org/web/packages/BradleyTerry2/vignettes/BradleyTerry.pdf

Good luck

Hi Matt, 

The two papers below analysed social hierarchies in wild dogs. The first looks at dyadic interactions with winners/losers between all individuals in the pack, and the second (coalition formation paper) goes more in-depth with group-level interactions and coalitions formed between members of the pack. 

Hope it helps!

Article Social Dynamics and the Cortisol Response to Immobilization ...

Article Patterns of coalition formation and spatial association in a...

Hi Matt,

You might be interested in this recent preprint in bioRxiv: A practical guide for inferring reliable dominance hierarchies and estimating their uncertainty. http://biorxiv.org/content/early/2017/02/23/111146

All the best,

Alfredo.

http://biorxiv.org/content/early/2017/02/23/111146

Thanks Alfredo

Thanks Michael, we ended up using David's index and the paper is now accepted in Journal of Mammalogy