QUASI-SYMMETRICAL LATENT CLASS MODELS, WITH APPLICATION TO RATER AGREEMENT

Suppose we observe responses on several categorical variables having t he same scale. We consider latent class models for the joint classific ation that satisfy quasi-symmetry. The models apply when subject-speci fic response distributions are such that (i) for a given subject, resp onses on different variables are independent, and (ii) odds ratios com paring marginal distributions of the variables are identical for each subject. These assumptions are often reasonable in modeling multirater agreement, when a sample of subjects is rated independently by differ ent observers. In this application, the model parameters describe two components of agreement-strength of association between classification s by pairs of observers and degree of heterogeneity among the observer s' marginal distributions. We illustrate the models by analyzing a dat a set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma, yielding seven categorical classific ations with the same binary scale. A good-fitting model has a latent c lassification that differentiates between subjects on whom there is ag reement and subjects on whom there is disagreement.