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A simple method for estimating a regression model for $$\kappa$$ between a pair of raters. (English) Zbl 1002.62523
Summary: 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 $$\kappa$$-coefficient is a popular measure of agreement between the two raters. The $$\kappa$$-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 $$\kappa$$-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 $$\kappa$$-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 $$\kappa$$-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.

##### MSC:
 62P10 Applications of statistics to biology and medical sciences; meta analysis 62J99 Linear inference, regression
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