# Inter-rater reliability with many non-overlapping raters

I have a data set of 11,000+ distinct items, each of which was classified on a nominal scale by at least 3 different raters on Amazon's Mechanical Turk.

88 different raters provided judgments for the task, and no one rater completed more about 800 judgments. Most provided significantly fewer than that.

My question is this:

I would like to calculate some measure of inter-rater reliability for the ratings, something better than a simply looking at consensus. I believe, however, that Fleiss Kappa, which is the measure I know best, would require a consistent group of raters for the entire set of items, and so I cannot use Fleiss Kappa to check IRR with my data. Is this correct? Is there another method I could use?

Any advice would be much appreciated!

-
Welcome to the site! Similar questions were asked before with these tags -- have you checked whether a working solution can be found among these? –  StasK Aug 24 '11 at 22:49
Thanks! I sure did check. I only found one directly relevant question, but it has received no answers. –  Judd Antin Aug 24 '11 at 23:19

If you just need to convince yourself (rather than report a number for another party), you could fit a cross-classified hierarchical/mixed model, with items and raters being two random effects. Then the intraclass correlation for the raters is [variance of the raters' random effect]/[variance of the raters' random effect + variance of the items' random effect + (variance of the logistic distribution = $\pi^2/3$)]. A specific implementation depends on the computational platform you are using; the default on CV is R, so you'd be using nlme with it, but you may have something different like SPSS or Stata.