Latent class representation of the Grade of Membership model

Latent class and the Grade of Membership (GoM) models are two examples of latent structure models. Latent class models are discrete mixture models. The GoM model has been originally developed as an extension of latent class models to a continuous mixture. This note describes a constrained latent class model which is equivalent to the GoM model, and provides a detailed proof of this equivalence. Implications for model fitting and interpretation are discussed. Some key words: Class membership, Contingency tables, Latent structure, Mixture models, Stochastic subject.