Quasi-symmetric latent class models, with application to rater agreement

Suppose we observe responses on several categorical variables having the same scale. We consider latent class models for the joint classification that satisfy quasi-symmetry. The models apply when subject-specific response distributions are such that (i) for a given subject, responses on different variables are independent, and (ii) odds ratios comparing 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 different observers. In this application, the model parameters describe two components of agreement--strength of association between classifications by pairs of observers and degree of heterogeneity among the observers' marginal distributions. We illustrate the models by analyzing a data set in which seven pathologists classified 118 subjects in terms of presence or absence of carcinoma, yielding seven categorical classifications with the same binary scale. A good-fitting model has a latent classification that differentiates between subjects on whom there is agreement and subjects on whom there is disagreement.