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This study investigated fifth grade teachers’ predictions of the performance of their students on multiple-choice science assessment items. A two-way cross-classified model reflected the dependence among predictions by the same teacher, or about the same item. This paper demonstrates an innovative use of Bayesian estimation to examine the variability of the model parameter estimates, and to estimate posterior distributions for the intraclass correlations (ICCs). Results from two different commonly used methods for setting priors were compared. Posterior distributions for the ICCs show that there is great uncertainty about the ICC estimates, reflecting the uncertainty of estimation of the variance components.