A simple method for estimating a regression model for κ between a pair of raters

Agreement studies commonly occur in medical research, for example, in the review of X‐rays by radiologists, blood tests by a panel of pathologists and the evaluation of psychopathology by a panel of raters. In these studies, often two observers rate the same subject for some characteristic with a discrete number of levels. The κ‐coefficient is a popular measure of agreement between the two raters. The κ‐coefficient may depend on covariates, i.e. characteristics of the raters and/or the subjects being rated. Our research was motivated by two agreement problems. The first is a study of agreement between a pastor and a co‐ordinator of Christian education on whether they feel that the congregation puts enough emphasis on encouraging members to work for social justice (yes versus no). We wish to model the κ‐coefficient as a function of covariates such as political orientation (liberal versus conservative) of the pastor and co‐ordinator. The second example is a spousal education study, in which we wish to model the κ‐coefficient as a function of covariates such as the highest degree of the father of the wife and the father of the husband. We propose a simple method to estimate the regression model for the κ‐coefficient, which consists of two logistic (or multinomial logistic) regressions and one linear regression for binary data. The estimates can be easily obtained in any generalized linear model software program.