A note on the binomial model with simplex constraints

Liu (2000) considered maximum likelihood estimation and Bayesian estimation in a binomial model with simplex constraints using the expectationmaximization (EM) and data augmentation (DA) algorithms. By introducing latent variables {Z_ij}and {Y_ij} (to be defined later), he formulated the constrained parameter problem into a missing data problem. However, the derived DA algorithm does not work because he actually assumed that the {Y_ij} are known. Furthermore, although the final results from the derived EM algorithm are correct, his findings are based on the assumption that the {Y_ij} are observable. This note provides a correct DA algorithm. In addition, we obtained the same E-step and M-step under the assumption that the {Y_ij} are unobservable. A real example is used for illustration. Copyright © 2011 Elsevier B.V. All rights reserved.