Measurement errors in caries diagnosis: some further latent class models

Latent class models have been proposed for assessing relative errors in discrete measurements arising, for example, in caries diagnosis. Those models, however, that turned out to fit empirical data (N = 3,869 teeth, 5 dentists) to a sufficient degree, needed the inclusion of interaction terms for pairs of raters at the latent levels in order to describe the observed interrelations of the judgments. Now it is shown that instead of giving up the concept of local stochastic independence, increasing the number of classes while possibly restricting their parameters in the end has the same effect: Both the unrestricted three-class model, which can be interpreted to be the generalization of the Carlos-Senning assumptions, and a restricted four-class model, which resembles the latent distance model well known from psychometrics, give good and excellent fit, respectively, to the caries data. For the case of the four-class model, a second solution exists that exhibits exactly the same fit, giving rise to warnings against the possibility of multiple solutions to the likelihood equations.