Log-linear non-uniform association models for agreement between two ratings on an ordinal scale

In agreement studies, when objects are rated independently by two raters (or twice by the same rater), an association between their ratings on two categories arises, reflecting the distinguishability of these two categories for these raters. When ratings are performed on an ordinal scale, this association between ratings on two categories increases when the distance between these categories increases on the ordinal scale. Goodman's log-linear models derived for the analysis of agreement between two raters on an ordinal scale assume that distinguishabilities between adjacent categories are either constant, or a priori fixed. Log-non-linear models that allow variations of the distinguishabilities between adjacent categories along the scale, may lead to difficulties in parameter estimation. This paper describes a new class of log-linear non-uniform association models. These models extend the log-linear uniform association model by allowing variations of distinguishability between adjacent categories (along the scale). These new models are used to analyse ordinal agreement between dermatologists when assessing the severity of different cutaneous signs of ageing on women faces.