Modified Profile Likelihood Approach for Certain Intraclass Correlation Coefficient

In this paper we consider the problem of constructing confidence intervals and lower bounds for the intraclass correlation coefficient in an interrater reliability study where the raters are randomly selected from a population of raters.The likelihood function of the interrater reliability is derived and simplified, and the profile likelihood based approach is readily available for computing the confidence intervals of the interrater reliability. Unfortunately, the confidence intervals computed by using the profile likelihood function are in general too narrow to have the desired coverage probabilities. From the point view of practice, a conservative approach, if is at least as precise as any existing method, is preferred since it gives the correct results with a probability higher than claimed. Under this rationale, we propose the so-called modified profile likelihoodapproach in this paper. Simulation study shows that, the proposed method in general has better performance than currently used methods. INDEX WORDS: Interrater reliability, Profile likelihood, Confidence intervals, Generalized P-values, Modified large-sample approach MODIFIED PROFILE LIKELIHOOD APPROACH FOR CERTAIN INTRACLASS CORRELATION COEFFICIENTS