When do latent class models overstate accuracy for diagnostic and other classifiers in the absence of a gold standard?

Latent class models are increasingly used to assess the accuracy of medical diagnostic tests and other classifications when no gold standard is available and the true state is unknown. When the latent class is treated as the true class, the latent class models provide measures of components of accuracy including specificity and sensitivity and their complements, type I and type II error rates. The error rates according to the latent class model differ from the true error rates, however, and empirical comparisons with a gold standard suggest the true error rates often are larger. We investigate conditions under which the true type I and type II error rates are larger than those provided by the latent class models. Results from Uebersax (1988, Psychological Bulletin 104, 405-416) are extended to accommodate random effects and covariates affecting the responses. The results are important for interpreting the results of latent class analyses. An error decomposition is presented that incorporates an error component from invalidity of the latent class model.