Rating the raters in a mixed model: An approach to deciphering the rater reliability

Rating the raters has attracted extensive attention in recent years. Ratings are quite complex in that the subjective assessment and a number of criteria are involved in a rating system. Whenever the human judgment is a part of ratings, the inconsistency of ratings is the source of variance in scores, and it is therefore quite natural for people to verify the trustworthiness of ratings. Accordingly, estimation of the rater reliability will be of great interest and an appealing issue. To facilitate the evaluation of the rater reliability in a rating system, we propose a mixed model where the scores of the ratees offered by a rater are described with the fixed effects determined by the ability of the ratees and the random effects produced by the disagreement of the raters. In such a mixed model, for the rater random effects, we derive its posterior distribution for the prediction of random effects. To quantitatively make a decision in revealing the unreliable raters, the predictive influence function (PIF) serves as a criterion which compares the posterior distributions of random effects between the full data and rater-deleted data sets. The benchmark for this criterion is also discussed. This proposed methodology of deciphering the rater reliability is investigated in the multiple simulated and two real data sets.