Inferences On The Intraclass Correlation Coefficients In Several Statistical Models

The accuracy and reliability of the results among multiple investigators or methods is vrey important in many areas,which are the basis for later study. And the accuracy and reliability can be measured by agreement evaluation. At present, the main statistical method used is the intraclass correlation coefficient (ICC) method in agreement evaluation between the quantitative results among multiple investigators or methods. This paper will study the application of the generalized approach (generalized p-value and generalized confidence interval) and the modified large-sample approach's statistical inferences on ICC,which are uesed to measure the reliability of the results among multiple investigators or methods, in the balanced,unblanced three-fold nested classification models, and furthermore this generalized approach on ICC has been successfully extended to the general balanced random effects model.In chapterâ…¡,we study the issues of ICC's testing and interval estimation in the balanced three-fold nested classification model. Present two approaches:the generalized approach (GA) and modified large-sample approach (MLA).Finally,an example is given to compare the perfor-mance of the two methods, and the results indicate that MLA is superior in the expected length of the confidence interval, but GA can be easily generalized to give p values, and can effectively control the effective probability of committing type I error.In chapterâ…¢,ICC's testing and interval estimation are considered in unbalanced three-fold nested classification model.First,using the USS and the harmonic average,the generalized p-values and generalized confidence intervals determined by the GA are given, then we study and demonstrate a number of statistical properties of the generalized confidence interval. Secondly, we propose the MLA which has made more reasonable improvement comparing with the balanced situation. Finally we carry out some simulations of these tests and confidence intervals,the results display that these tests have a type I error not exceeding the nominal significance level,and these coverage probabilities of confidence intervals are closer to the nominal confidence level. In chapterâ…£,we discuss the problem of ICC's testing and interval estimation in the general balanced random effects model. Based on the spectral decomposition theory,we suggest the test-ing method and the generalized confidence interval determined by GA, then applying this general results to two specific models,we obtain conclusions consistent with the former literatures,fully illustrate the reliability of the general results in this paper.