A General Approach for Modeling and Inference

• Published in: Measuring Agreement Vol. 34; pp. 71 - 93
• Main Authors: Nagaraja, Haikady N, Choudhary, Pankaj K
• Format: Book Chapter
• Language: English
• Published: United States John Wiley & Sons, Incorporated 2017; John Wiley & Sons, Inc
• Subjects: CLINICAL & INTERNAL MEDICINE; homoscedasticity; inference; MATHEMATICS; method comparison data; mixed‐effects models; model diagnostics; model fitting; SCIENCE: GENERAL ISSUES
• ISBN: 1118078586; 9781118078587
• DOI: 10.1002/9781118553282.ch3

This chapter deals with linear mixed‐effects models, prediction, model ?tting, and model diagnostics, examining the large‐sample methodology for statistical inference based on ML estimators. The chapter chiefly focuses on the construction of confidence intervals and bounds using both the standard large‐sample theory and bootstrap. The errors and residuals do not have identical distributions, and the same holds for the random effects and their predicted values. The presence in the plot of a trend or a non‐constant vertical scatter casts doubt on the respective assumptions of zero mean and homoscedasticity. The mixed‐effects model offers a general framework for handling method comparison. It allows modeling of the mean functions through both common and method‐specific fixed effects. It also allows for dependence in a subject's multiple measurements from the same method through both common and method‐specific random effects of the subject. The principle of model parsimony calls for not having more parameters in the model than what is really necessary. A key goal in the analysis of method comparison data is evaluation of similarity and agreement of the methods.