Modified profile likelihood approach for certain intraclass correlation coefficients

• Published in: Computational statistics Vol. 28; no. 5; pp. 2241 - 2265
• Main Authors: Xiao, Yuanhui, Liu, Huayu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2013; Springer Nature B.V
• Subjects: Approximation; Computation; Computational mathematics; Computer simulation; Confidence; Confidence intervals; Correlation coefficients; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematical analysis; Mathematical models; Mathematics and Statistics; Methods; Original Paper; Probability; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Random variables; Simulation; Statistics; Studies; Variance analysis; Confidence intervals; Modified large-sample approach; Interrater reliability; Profile likelihood; Generalized pivots
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-013-0405-x

In this paper we consider the problem of constructing confidence intervals and confidence 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 practical point of view, a conservative approach, if 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 likelihood approach in this paper. Simulation study shows that, the proposed method in general has better performance than currently used methods.