Modeling Association plus Agreement among Multi-Raters for Ordered Categories

In square contingency tables, analysis of agreement between the row and column classifications is of interest. In such tables, the kappa-like statistics are used as a measure of reliability. In addition to the kappa coefficients, several authors discussed agreement in terms of log-linear models. Log-linear agreement models are suggested for use to summarize the degree of agreement between nominal variables. To analyze the agreement between ordinal categories, the association models with agreement parameter can be used. In the recent studies, researchers pay more attention to the assessment of agreement among more than two raters’ decisions, especially in areas of medical and behavioral sciences. This article focuses on the approaches to study of uniform and non-uniform association with inter-rater agreement for multi-raters with ordered categories. In this article, we proposed different modifications of association plus agreement models and illustrate use of the approaches over two numerical examples.